Testing the predictability of commodity prices in stock

Salisu A. A., Isaah K. and Raheem I. D. (2018): Testing the predictability of commodity prices in stock returns: A new perspective - Centre for Econometric and Allied Research, University of Ibadan Working Papers Series, CWPS 0061

WORKING PAPER SERIES: WPS/0061

Testing the predictability of commodity prices in stock returns: A new perspective

Afees A. Salisu, Kazeem Isah and Ibrahim D. Raheem

Cite as: Salisu A. A., Isaah K. and Raheem I. D. (2018): Testing the predictability of commodity prices in stock returns: A new perspective Centre for Econometric and Allied Research, University of Ibadan Working Papers Series, CWPS 0061

1


Testing the predictability of commodity prices in stock returns: A new perspective Afees A. Salisu1,2,3,*, Kazeem O. Isah3 and Ibrahim D. Raheem4

1Department

for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam 2Faculty

of Business Administration, Ton Duc Thang University, Ho Chi Minh City, Vietnam 3Centre

for Econometric & Allied Research, University of Ibadan, Nigeria. 4School

of Economics, University of Kent, Canterbury, UK

*Correspondence:

Email: [email protected]; [email protected]; [email protected] Mobile: (+234) 8034711769

2


Testing the predictability of commodity prices in stock returns: A new perspective

Abstract In this paper, we offer an alternative approach for testing the predictive power of commodity prices in stock returns using monthly data of about six decades. In the process, we account for prominent features of predictive models such as asymmetry, conditional heteroscedasticity, endogeneity, persistence, and structural breaks that may bias the forecast outcomes. Using the G7 stock exchanges, three findings are discernible from the various analyses. First, commodity prices are good predictors of stock returns both for in-sample and out-of-sample forecasts. Second, the proposed commodity-based model for stock returns that accounts for the highlighted features outperforms both the traditional predictive model as well historical average models that ignore same. Thirdly, these conclusions are robust to different components of commodity prices, multiple data samples and alternative forecast horizons. Keywords: Stock prices, Commodity prices, G7 countries, Asymmetry, Persistence, Endogeneity; Conditional heteroscedasticity; Structural breaks.

3


Testing the predictability of commodity prices in stock returns: A new perspective 1.

Introduction

There is a growing consensus in the literature as regards the co-movement between commodity prices and stock returns (see Campbell, 1987, Campbell and Shiller, 1988; Fama and French, 1988; Hodrick, 1992; Rapach et al., 2005; Ang and Bekaert, 2007; Hjalmarsson, 2010; Kellard et al., 2010; Cochrane, 2011). The shortfall of these studies, however is their inability to exploit such co-movements to produce better insample and out-sample forecast results for stock returns. Meanwhile, findings from Goyal and Welch (2003) suggest that it may be inappropriate to use the in-sample results to generalize for out-of-sample forecasts. Thus, what is new in the literature is whether the established co-movements between the two variables can be exploited to produce better in-sample and out-of-sample forecasts for stock returns. The only exceptions, to the best of our knowledge, are the studies by Black et al. (2014) and Jordan et al. (2016) covering the US and Canada respectively. However, we offer a broader perspective to the issue of predictability between commodity prices and stock returns in the following ways. First, there are some salient features of commodity prices which may affect their forecast performance in the predictive model of stock returns. The work of Narayan and Liu (2011) finds that some commodity prices tend to exhibit persistence in the presence of shocks, which may have implications on their precision in forecasting stock returns (see also Westerlund and Narayan, 2012, 2015). In addition, a number of studies have evaluated the dynamics of commodity prices and they find evidence of possible reverse causality between the two variables (see for example, Reboredo and Ugolini, 2017), which may introduce endogeneity bias in the predictive model of stock returns where commodity prices are seen as predictors. Also, since the current study intends to use high frequency series, there may be need to account for conditional heteroscedastcitity in the estimation process. All these potential features of our predictive model, may have implications on the forecast results (see also Lewellen, 2004; Westerlund and Narayan, 2012, 2015). Therefore, we follow the 4


approach of Westerlund and Narayan (2012, 2015) which allows us to capture all these effects simultaneously in the estimation process. For the purpose of model validation and robustness, the forecast performance of the proposed predictive model that accounts for all the mentioned effects is compared with the traditional variant that ignores same. Secondly, recent evidence on the nexus between commodity prices and stock returns suggests that high market volatility due to crises/disaster can affect the correlations between the two variables (Öztek and Öcal, 2017). Thus, we test whether structural break(s) have a role to play in the predictability of commodity prices for both the insample and out-of-sample forecasts of stock returns. Thirdly, the reaction of commodity prices to shocks tends to be asymmetric (see for example, Marvasti and Lamberte, 2016), thus, we follow the approach of Salisu and Isah (2018) which extend the Westerlund and Narayan (2012, 2015) in order to account for any probable asymmetric response of stock returns to changes in commodity prices. For the purpose of empirical analyses, we utilize all the available data for the G7 countries and the analyses are conducted singly for individual countries. For robustness purpose, we consider the following: multiple data samples, alternative forecast measures, multiple forecast horizons and a number of variants of commodity sector indices including agricultural, energy, metals and non-energy commodity index. All the analyses are rendered for both the in-sample and out-ofsample forecasts and meaningful policy implications of findings are well documented in the paper. In addition to this introductory section of the paper, the rest of the paper is structured as follows: Section 2 provides the theoretical model, econometric methods and the forecast performance measures for evaluating the predictability of stock returns. Data discussion and preliminary analyses are contained in Section 3 of the paper. Section 4 presents and discusses the results while Section 5 concludes the paper.

5


2.

The model and procedure for estimation and forecasting

The relationship between commodity prices and stock returns can be pitched under three main theories: the Capital Asset Pricing Model (CAPM), the Arbitrage Pricing Theory (APT), and the Discounted Cash Flow or Present Value Model (PVM). The edge of APT over other theories lies in its ability to account for various macroeconomic and financial risks in the valuation of stocks. However, the intention here is to isolate commodity prices while also accounting for any potential bias that may result from doing so. Thus, a bivariate single predictive regression model for stock returns is as given below:

rt     zt 1   r ,t

(1)

where rt denotes the stock returns and is computed as log  pt pt 1  ; pt is the stock price index; and zt is the log of commodity price index. Different commodity price indexes namely, energy, agriculture, industrial metals, precious metals and nonenergy, are used and each is singly captured in equation (1). The underlying null hypothesis of no predictability is that   0 and it is evaluated using the Ordinary Least Squares (OLS) method. Thus, the predictive model for commodity-stock returns as in equation (1) can be described as the baseline model and named Model 1 since it follows the traditional approach of formulating a predictive model for analysing economic relationships (see for example, Narayan and Gupta, 2015; Phan et al., 2015 and Devpura et al., 2018). However, studies such as Narayan and Sharma (2014), Narayan and Gupta (2015), Phan et al. (2015) and Devpura et al. (2018) have suggested the need to account for conditional heteroscedasticity, endogeneity and persistence effects when forecasting stock returns. In doing so, they employ the Westerlund and Narayan (2012, 2015)1 [henceforth; WN] estimator which accounts for same in the estimation process. Thus, equation (1) is re-specified in line with the WN predictive model as follows: rt     zt 1    zt   zt 1    r ,t

(2)

The first attempt was made by Lewellen (2004) whose work motivates the need to account for endogeneity and persistence effects in the predictability of stock returns. Thereafter, WN (2012, 2014) extend the Lewellen approach to account for conditional heteroscedasticity. 1

6


where rt and zt remain as earlier defined, while  is the first order autocorrelation coefficient where the inclusion of the second term for instance  zt   zt 1  is meant to capture any potential persistent effect in the predictive model (see Lewellen, 2004); and the endogeneity effect is subsumed in  .2 Thus, estimating equation (2) using the OLS method is expected to correct for possible endogeneity bias, and therefore, yields a bias-adjusted OLS estimator for  (Lewellen, 2004). This is described as





ˆadj  ˆ  ˆ ˆ   . However, to account for conditional heteroscedasticity effect in a predictive model, WN (2012, 2015) suggest pre-weighting the series in equation (2) with 1 ˆ and estimate the resulting equation with OLS. This augmented OLS approach is what WN (2012, 2015) term as Feasible Quasi Generalized Least Squares estimator and named Model 2 in the context of this study. Thus, Model 2 as specified in equation (2) can be described as the extended version of Model 1. The evaluation of the forecast performance is carried out using 50% and 75% coverage of the total sample periods for robustness purpose3. Also, a recursive window approach which accounts for the time-varying behaviour in the stock commodity prices relationship is employed (see also Phan et al., 2015). The forecast evaluation is implemented for both the in-sample and out-of-sample periods. For forecast evaluation, both the single and pairwise forecast measures are used. The Mean Square Error (MSE)4 is for the former and the Campbell-Thompson (C-T)





ˆ ˆ statistic is for the latter. The C-T statistic is computed as 1  MSE 2 MSE1 , where ˆ MSE 1

and

ˆ MSE 2 are the mean square errors (MSE) of Model 1 and Model 2,

respectively. A positive value of the statistic suggests that Model 2 outperforms Model 1 and vice-versa if otherwise. In addition, the Clark and West (2007) [C-W hereafter] test is employed to determine the statistical significance of the C-T

The underlying motivation and computational details for persistence and endogeneity effects in equation (2) are documented in Lewellen (2004) and Westerlund and Narayan (2012, 2015). 3 We are guided by the literature as regards the selection of the sample size (for example, see Narayan and Gupta, 2015). Nonetheless, there is no formal rule for creating sub-samples for forecast analyses. This explains the choice of multiple data samples for robustness. 4 We also consider other variants of the single forecast measures namely, root mean square error (RMSE) and mean average error (MAE). Please see the appendix for more details. 2

7


statistic.5 The underlying procedure for the C-W test involves calculating the following: 2 2 2 fˆt  k   rt  k  rˆ1t ,t  k     rt  k  rˆ2 t ,t  k    rˆ1t ,t  k  rˆ2 t ,t  k    

r

where k is the forecast period;

t k

(3)

 rˆ1t ,t  k  is the squared error for the restricted 2

model (i.e. Model 1);  rt  k  rˆ2 t ,t  k  is the squared error for the unrestricted model (i.e. 2

Model 2); while  rˆ1t ,t  k  rˆ2t ,t  k  is the adjusted squared error introduced by C-W to 2

correct for any noise associated with the larger model’s forecast. Thus, the sample average of fˆt  k can be expressed as: MSE1   MSE2  adj. and each term is computed as: MSE1  P 1   rt  k  rˆ1t ,t  k  ; 2

MSE2  P 1   rt  k  rˆ2t ,t  k  ; and 2

adj.=P 1   rˆ1t ,t  k  rˆ2t ,t  k 

2

where P is the number of predictions used in competing these averages. To test for equality of forecast performance between Model 1 and Model 2, the fˆt  k is regressed on a constant and the resulting t-statistic for a zero coefficient is used to draw inference. Since the Null hypothesis tests for equality of MSEs; the alternative hypothesis implies otherwise. The null hypothesis is rejected if the test statistic is greater than +1.282 (for a one sided 0.10 test) or +1.645 (for a one-sided 0.05 test).

3.

Data and Preliminary Analysis

3.1

Data Description and Sources

Data used for the empirical analysis of this study are monthly frequency series ranging from the month January 1960 to the month of October 2017, thus totaling 696 observations for the full-sample period. Not only is the number of observations sufficient for forecasting analysis, it also enables us to capture some effects which

An alternative test is the Diebold and Mariano (1995) test. However, the test is only suitable for nonnested models while the Clark and West (2007) test is appropriate for nested models which is the case in this study. 5

8


constitute the traditional characteristics of long time series such as persistence and conditional heteroscedasticity. However, while the monthly share prices index for each of the G7 countries under consideration were sourced mainly from the International Financial Statistic (IFS) database, the various global commodity indexes under consideration are obtained from the World bank/Global Economic Monitor

Commodities

via

(http://data.worldbank.org/data-catalog/global-

economic-monitor). Presented in Table 1 below is a detailed description of the variants of commodity sector indices including Agricultural (AGR), Energy (ENE), Industrial Metals (IDM), Precious Metals (PRM) and Non-energy (NENE) commodity indexes.

9


Table 1: Description and Classification of Global Tradable Commodities Individual Series Index Series Natural Gas Brent Spot Price WTI Spot Price

Oil

ENERGY (ENE)

Dubai Spot Price Coal Aluminum Copper Zinc Nickel Tin Iron Ore Lead Gold Cocoa Coffee Tea Coconut oil Groundnut oil Palm oil Soybeans Soybean oil Soybean meal Maize Rice Wheat Barley Banana Beef Chicken Meat Oranges Tropical Hard Log Sawn-wood Cotton Rubber Tobaccos Natural Phosphate Rock Phosphate Potassium and Nitrogenous Products Commodities contain in AGR and IDM indices

INDUSTRIAL METALS (IDM)

PRECIOUS METALS (PRM) Beverage

Fat and Oil Food Grains

AGRICULTURAL (AGR)

Other Foods

Timber Other Agricultural Material

Raw

Agricultural Raw Materials

NON-ENERGY (NENE)

10


3.2 Preliminary Analysis Results The descriptive statistics reported in Table 2A include the means, standard deviations, skewness and kurtosis for all the variables under consideration. Starting with the mean statistic, Italy and Germany with mean values of 0.0035 and 0.0036 are the countries with the least average stock returns over the period under consideration. Relatively, UK and US with 0.0052 and 0.0051 mean values are the countries with the highest monthly average stock returns, while Canada, France and Japan have rather taken a mid-position given their mean values of 0.0048 and 0.0046, respectively. However, the standard deviation values appear generally low for all the G7 countries, notwithstanding, the US stock returns has the least standard deviation value followed by the Canadian stock returns, while Italy and France record the highest standard deviation values. This by implication suggests that stock returns in the US and Canada are the least volatile relative to the volatility of stock returns in Italy, France and other G7 countries. In the case of the commodity price indexes, the oil and energy sectors appear the most volatile, while agricultural and the non-energy sectors are the least volatile. With respect to the statistical distribution of the series, the skewness appears to be mostly negative for all the series with the exception of the UK stock returns. For the kurtosis statistic, the result is predominantly leptokurtic for the stock returns and platykurtic for all the commodities variables. Also reported in Table 2A are the stochastic properties of each of the variables of interest. The stationarity test results seem to reveal the stock returns series as stationary irrespective of the country under investigation, while the predictor series across the different commodity prices indexes as non-stationary. The stochastic behaviour of both the predicted and predictor series aligns with equations (1) and (2) and are therefore correctly specified. In other words, the variables are specified in a form that exhibits their level of stationarity. In the B part of Table 2, we also test for evidence

of

autocorrelation

(using

the

Ljung-Box

test)

and

conditional

heteroscedasticity (using the ARCH-LM test) in both series. The results of these tests seem to indicate significant presence of autocorrelation and heteroscedasticity effects 11


in the series regardless of the choice of lags. The presence of persistence and endogeneity effects is also evaluated, whose result is presented in Table 3. These effects can enhance the forecast performance of stock returns if found to be significant (see Lewellen, 2004; Narayan and Gupta, 2015; Phan et al., 2015; and Devpura et al., 2018). Our finding shows evidence of high degree of persistence in the predictors and this is not unexpected for predictor series that are integrated of order one (see Table 3A). However, the result is mixed for endogeneity test.

k 2

Q  Stat k 5

ADF Test Level -20.2566a*** -23.6317*** -17.4200*** -17.8409*** -16.9948*** -17.8495*** -22.5461*** -2.2618a -1.3647a -1.8884 -3.1329b -1.3376b -2.3361

First Difference -16.4331b*** -21.4529a*** -21.5988b*** -19.0843a*** -17.9292b*** -16.3120a*** ARCH LM Test

Q 2  Stat

k  10

k 2

k 5

I(d) I(0) I(0) I(0) I(0) I(0) I(0) I(0) I(1) I(1) I(1) I(1) I(1) I(1)

k  10

k 2

k 5

k  10

CAN 45.392*** 47.524** 52.700*** 16.036*** 20.512*** 26.207*** 7.376*** 3.467*** 2.091** FRC 12.508*** 20.733*** 35.461*** 29.175*** 42.096*** 56.849*** 14.082*** 7.479*** 5.212*** GRM 72.118*** 75.363*** 80.802*** 14.986*** 18.236*** 33.529*** 7.065*** 3.299*** 2.837*** ITL 42.451*** 52.392*** 60.860*** 41.051*** 59.941*** 81.639*** 18.254*** 8.541*** 5.969*** JPN 66.905*** 73.974*** 79.151*** 11.972*** 20.648*** 37.469*** 6.022*** 3.639*** 2.944*** UK 55.679*** 60.543*** 70.957*** 31.976*** 43.353*** 65.015*** 14.650*** 7.226*** 4.385*** US 50.678*** 57.910*** 70.626*** 26.340*** 39.101*** 59.001*** 13.836*** 7.185*** 4.660*** AGR 1374.7*** 3380.4*** 6565.6*** 1370.1*** 3337.6*** 6364.7*** 66625.*** 26461.*** 13164.*** ENE 1377.7*** 3403.3*** 6672.1*** 1375.8*** 3381.2*** 6566.2*** 71475.*** 28771.*** 14032.*** OIL 1376.2*** 3394.9*** 6643.8*** 1374.4*** 3371.3*** 6531.8*** 57324.*** 23235.*** 11375.*** IDM 1367.8*** 3344.2*** 6424.5*** 1341.7*** 3181.8*** 5787.1*** 20829.*** 8226.*** 4064.*** PRM 1377.5*** 3405.1*** 6678.2*** 1377.9*** 3402.9*** 6659.0*** 12913.*** 51022.*** 24934.*** NENE 1375.1*** 3383.0*** 6569.7*** 1366.8*** 3312.5*** 6258.1*** 59328.*** 23512.*** 11840.*** Note: CAN, FRC, GRM, ITL, JPN, UK and U.S.A. are the acronyms for the G7 countries, namely; Canada, France, Germany, Italy, Japan, United Kingdom and United States of America in that order. The reported values for the Ljung-Box test are the Q- and Q2 statistics and ARCH-LM test are the F-statistics. Three different lag lengths (k) of 2, 5 and 10 are considered for robustness purpose. The null hypothesis for the autocorrelation test is that there is no serial correlation, while the null for the ARCH-LM test is that there is no conditional heteroscedasticity. *** indicates significance at 1%.

Commodities Prices Index

Stock Price Returns

Commodities Prices Index

Stock Price Returns

Table 2: Preliminary statistics Table 2: Descriptive statistics and ADF test Descriptive Statistics Variable Standard Mean Deviation Skewness Kurtosis CAN 0.0048 0.0388 -1.0338 7.5566 FRC 0.0046 0.0529 -0.5584 6.3400 GRM 0.0036 0.0440 -0.9775 7.1085 ITL 0.0035 0.0575 -0.0828 4.3527 JPN 0.0046 0.0445 -0.4840 4.5357 UK 0.0052 0.0436 0.0977 11.8575 US 0.0051 0.0361 -1.1164 8.0043 AGR 3.9345 0.4874 -0.4327 2.3368 ENE 2.9720 1.3661 -0.6237 2.1702 OIL 2.6609 1.4023 -0.5868 2.1547 IDM 3.5602 0.6141 0.1352 2.3036 PRM 5.5247 1.1853 -0.4633 2.1662 NENE 3.8249 0.5207 -0.2655 2.3151 Table 2B: Serial Correlation and Conditional Heteroscedasticity Tests

12


Table 3: Testing for Endogeneity and Persistence of the Predictors Predictor Table 3A: Persistence test results Canada France Germany Italy Japan UK USA AGR 0.9973*** 0.9973*** 0.9973*** 0.9973*** 0.9973*** 0.9973*** 0.9973*** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) ENE 0.9973*** 0.9973*** 0.9973*** 0.9973*** 0.9973*** 0.9973*** 0.9973*** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) OIL 0.9970*** 0.9970*** 0.9970*** 0.9970*** 0.9970*** 0.9970*** 0.9970*** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) IDM 0.9968*** 0.9968*** 0.9968*** 0.9968*** 0.9968*** 0.9968*** 0.9968*** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) PRM 0.9986*** 0.9986*** 0.9986*** 0.9986*** 0.9986*** 0.9986*** 0.9986*** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) NENE 0.9976*** 0.9976*** 0.9976*** 0.9976*** 0.9976*** 0.9976*** 0.9976*** (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) Table 3B: Endogeneity test results AGR 0.0280 -0.1588** -0.1108* 0.0139 -0.0202 -0.2512*** -0.1038** (0.6167) (0.0375) (0.0815) (0.8667) (0.7518) (0.0001) (0.0465) ENE 0.0255 -0.0647** -0.0438** -0.0640** -0.0018 -0.0360 -0.0123 (0.2045) (0.0185) (0.0551) (0.0321) (0.9358) (0.1114) (0.5096) OIL 0.0171 -0.0561** -0.0386** -0.0643** -0.0029 -0.0329* -0.0134 (0.3164) (0.0163) (0.0468) (0.0113) (0.8821) (0.0874) (0.4015) IDM 0.0804** 0.1137** 0.0183 0.0540 0.0701* 0.0145 0.0288 (0.0145) (0.0115) (0.6243) (0.2699) (0.0627) (0.6944) (0.3473) PRM 0.0569* -0.0494 -0.0371 0.0241 0.0026 -0.0222 -0.0131 (0.0822) (0.2695) (0.3181) (0.6189) (0.9432) (0.5452) (0.6661) NENE 0.0795 -0.0406 -0.0739 0.0380 0.0305 -0.2065*** -0.0658 (0.1564) (0.5966) (0.2457) (0.6483) (0.6349) (0.0010) (0.2077) Note: The persistence test is conducted by regressing each of the predictors on its first lag: z t     z t 1   t using the OLS estimator. The first order autocorrelation coefficient   captures the persistence effect and the null is that there is no presence of the effect. The closer the value of  to one, the higher the degree of persistence. For the endogeneity test, it follows a three-step procedure: First, we run a predictive regression model with the OLS estimator: rt     z t  1   r , t , where rt denotes the stock returns and zt 1 is the predictor variable such as AGR, ENE, OIL, IDM, PRM and NENE. In the second step, we follow WN (2015) and model the predictor variable as follows:

z t   (1   )   z t  1   z , t and in the final step, the relationship between the two error terms (  r ,t and

captured using the following regression:

 z ,t )

is

 r ,t   z ,t  t . If the coefficient  is statistically different from zero at any

of the conventional chosen levels of significance; then, the predictor variable is endogenous; otherwise is strictly exogenous.

The preliminary analysis is also extended to include visual inspection of historical trends in the commodity prices and the stock prices of G7 economies. The essence here is to trace any evidence of co-movement between the G7 stock prices and each of the sectoral commodity prices under consideration. To achieve this, we plot the stock prices of the individual G7 countries against each of the predictors. The evidence of possible co-movements between the two series seems evident for all the G7 countries considered (see Figures 1-6). Such correlations have also been reported

13


in the literature and are found to have increased over time particularly since the 2000s (see e.g, Tang and Xiong, 2012; Creti et. al., 2013).

4.

Results and Discussions

4.1

Results of the predictability test

This section examines the significance of commodity prices in the predictive model of stock returns using 50% and 75% of the available data sample and the results are presented in Tables 4 and 5 respectively. For the two data samples, there is substantial evidence of significant response of stock returns to changes in commodity prices for virtually all the G7 countries with the exception of Germany and relatively Italy. From the statistical point of view, Model 1 offers more significant estimates than Model 2 under the 50% data sample while the reverse holds for 75% data sample. In terms of the direction of relationship, all the coefficients are positively signed implying that commodities such as those highlighted in the results tables can be a good hedge against stock market plunge. A number of related studies have also reported similar evidence in the literature. For instance, Junttila et al. (2018) find that gold market provides a better hedge than the oil market against the stock market risks (see also Junttila & Raatikainen, 2017 and some papers cited therein). Like the case of Germany, the results of Ntantamis and Zhou (2015) suggest that there is little evidence that the bull and bear market phases identified for the individual stocks are related to those for the commodity prices. In a similar vein, Wen and Nguyen (2017) show that even tough commodity futures are not helpful in improving the risk-adjusted returns of energy stocks, but they can significantly reduce the volatilities and expected-shortfalls of the diversified portfolios. Notwithstanding these mixed findings, investors in well diversified economies like those of the G7 countries considered in this study may find some hedging effectiveness between the two markets.

14


Table 4: Predictability test results using 50% of the total sample Table 4A: Model 1 Canada France Germany Italy Predictor AGR ENE OIL IDM PRM NENE

0.0013** (0.0005) 0.0020** (0.0008) 0.0021** (0.0009) 0.0015** (0.0006) 0.0010** (0.0004) 0.0014** (0.0005)

0.0014* (0.0008) 0.0026** (0.0013) 0.0028* (0.0014) 0.0017* (0.0010) 0.0012* (0.0006) 0.0015* (0.0009)

0.0008 (0.0005) 0.0016* (0.0008) 0.0019** (0.0009) 0.0008 (0.0006) 0.0006 (0.0004) 0.0008 (0.0006)

0.0015* (0.0008) 0.0033** (0.0013) 0.0039*** (0.0014) 0.0017* (0.0010) 0.0013** (0.0006) 0.0015* (0.0009)

Japan

UK

USA

0.0026*** (0.0005) 0.0037*** (0.0008) 0.0038*** (0.0009) 0.0031*** (0.0006) 0.0020*** (0.0004) 0.0028*** (0.0006)

0.0018** (0.0007) 0.0030*** (0.0011) 0.0033*** (0.0012) 0.0020** (0.0008) 0.0014** (0.0005) 0.0018** (0.0007)

0.0011** (0.0005) 0.0019** (0.0008) 0.0021** (0.0009) 0.0013** (0.0006) 0.0009** (0.0004) 0.0012** (0.0005)

Table 4B: Model 2 0.0021*** 0.0009*** 0.0007 0.0006 0.0021*** 0.0025*** 0.0014*** (0.0005) (1.71E-05) (0.0005) (0.0009) (0.0005) (0.0006) (0.0005) 0.0029*** 0.0021*** 0.0019** 0.0027** 0.0027*** 0.0033*** 0.0020*** ENE (0.0008) (0.0005) (0.0009) (0.0013) (0.0007) (0.0009) (0.0007) 0.0031*** 0.0026 0.0022** 0.0034** 0.0029*** 0.0042*** 0.0022*** OIL (0.0009) (0.0017) (0.0010) (0.0014) (0.0007) (0.0010) (0.0007) 0.0019*** 0.0007*** 0.0009 0.0004 0.0024*** 0.0026*** 0.0014** IDM (0.0003) (0.0001) 0.0006 (0.0010) (0.0005) (0.0007) (0.0005) 0.0016*** 0.0006*** 0.0005 0.0005 0.0016*** 0.0019*** 0.0010*** PRM (0.0004) (0.0002) 0.0004 (0.0006) (0.0003) (0.0004) (0.0003) 0.0021*** 0.0008*** 0.0007 0.0004 0.0022*** 0.0026*** 0.0014*** NENE (0.0005) (9.41E-06) 0.0005 (0.0009) (0.0005) (0.0006) (0.0005) Note that values in parentheses ( ) denote standard errors. The in-sample predictability is obtained by AGR

estimating the equation rt     zt 1    zt   zt 1    r ,t , where



is a measure of predictability.

***, ** and * represent rejection of null hypothesis of no predictability at 1%, 5% and 10%, respectively.

15


Table 5: Predictability test results using 75% of the total sample Table 5A: Model 1 Canada France Germany Italy Predictor AGR ENE OIL IDM PRM NENE

0.0012*** (0.0004) 0.0015** (0.0006) 0.0016** (0.0007) 0.0013*** (0.0005) 0.0009*** (0.0003) 0.0012*** (0.0004)

0.0012** (0.0006) 0.0018** (0.0008) 0.0019** (0.0009) 0.0014** (0.0007) 0.0009** (0.0004) 0.0013** (0.0006)

0.0007 (0.0005) 0.0010 (0.0006) 0.0011 (0.0007) 0.0007 (0.0005) 0.0005 (0.0003) 0.0007 (0.0005)

0.0012* (0.0006) 0.0021** (0.0009) 0.0024** (0.0010) 0.0014* (0.0007) 0.0010** (0.0005) 0.0013* (0.0007)

Japan

UK

USA

0.0011** (0.0004) 0.0009 (0.0006) 0.0009 (0.0007) 0.0012** (0.0005) 0.0007** (0.0003) 0.0011** (0.0005)

0.0015*** (0.0005) 0.0021*** (0.003) 0.0023*** (0.0008) 0.0017*** (0.0006) 0.0011*** (0.0003) 0.0016*** (0.0005)

0.0013*** (0.0004) 0.0019*** (0.0005) 0.0020*** (0.0006) 0.0015*** (0.0004) 0.0010*** (0.0002) 0.0014*** (0.0004)

Table 5B: Model 2 0.0018*** 0.0010 0.0011** 0.0007 0.0014*** 0.0021*** 0.0016*** (0.0004) (0.0006) (0.0004) (0.0007) (0.0004) (0.0004) (0.0003) 0.0024*** 0.0015* 0.0018*** 0.0016* 0.0016** 0.0028*** 0.0025*** ENE (0.0006) (0.0009) (0.0006) (0.0009) (0.0006) (0.0006) (0.0005) 0.0026*** 0.0017* 0.0020*** 0.0019* 0.0017** 0.0031*** 0.0023*** OIL (0.0007) (0.0010) (0.0007) (0.0010) (0.0006) (0.0007) (0.0004) 0.0019*** 0.0011 0.0012** 0.0007 0.0015*** 0.0024*** 0.0018*** IDM (0.0005) (0.0007) (0.0005) (0.0008) (0.0005) (0.0005) (0.0004) 0.0013*** 0.0008* 0.0009*** 0.0006 0.0010*** 0.0015*** 0.0012*** PRM (0.0003) (0.0004) (0.0003) (0.0005) (0.0003) (0.0003) (0.0002) 0.0019*** 0.0010 0.0011** 0.0006 0.0014*** 0.0022*** 0.0017*** NENE (0.0004) (0.0006) (0.0004) (0.0007) (0.0004) (0.0004) (0.0003) Note that values in parentheses ( ) denote standard errors. The in-sample predictability is obtained by AGR

estimating the equation rt     zt 1    zt   zt 1    r ,t , where



is a measure of predictability.

***, ** and * represent rejection of null hypothesis of no predictability at 1%, 5% and 10%, respectively.

4.2

Forecast performance evaluation results

Having shown that information contained in the commodity prices can be exploited to forecast the G7 stock returns, this section further conducts some exercises to validate this proposition. Both the in-sample and out-of-sample forecast results are evaluated. Table 6 reports the mean squared error (MSE) for Model 1 and it shows considerably small values for all the predictors across all the countries being examined. These results are consistent regardless of forecast horizon and data sample. Similar trends are observed for Model 2 (see Table 7). Alternative single forecast measures involving the root mean square error (RMSE) and mean absolute error (MAE) are also computed for the two models and the conclusion remains the same.6 It is however important to note that the forecast accuracy varies from one 6

Please check the supplementary file for the additional results obtained from using RMSE and MAE.

16


commodity to another and likewise the countries under examination. Similarly, since we are dealing with two nested models; one model is more likely to outperform the other, notwithstanding the fact that their MSE values are quite small. Thus, in the section that immediately follows, we compare the forecast performance of the two models in order to justify our preference for Model 2 (the unrestricted model) over

G7

Model 1 (the restricted model).

UK

Japan

Italy

Germany

France

C a n a d a

Table 6: Forecast performance results of Model 1 using MSE 50% of the data sample 75% of the data sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8

h=12

AGR ENE OIL IDM PRM NENE

0.001479 0.001482 0.001483 0.001480 0.001478 0.001480

0.001471 0.001473 0.001475 0.001472 0.001470 0.001472

0.001459 0.001460 0.001462 0.001459 0.001456 0.001459

0.001446 0.001447 0.001449 0.001446 0.001444 0.001446

0.001585 0.001588 0.001589 0.001586 0.001584 0.001585

0.001579 0.001582 0.001583 0.001580 0.001578 0.001579

0.001569 0.001572 0.001574 0.001570 0.001569 0.001570

0.001562 0.001565 0.001566 0.001563 0.001562 0.001563

AGR ENE OIL IDM PRM NENE AGR ENE OIL IDM PRM NENE AGR ENE OIL IDM PRM NENE AGR ENE OIL IDM PRM NENE AGR ENE OIL

0.003507 0.003495 0.003497 0.003506 0.003501 0.003507 0.001620 0.001613 0.001612 0.001621 0.001619 0.001621 0.003664 0.003627 0.003622 0.003664 0.003652 0.003664 0.001520 0.001535 0.001545 0.001518 0.001514 0.001520 0.002505 0.002493 0.002495

0.003503 0.003489 0.003491 0.003501 0.003495 0.003502 0.001606 0.001598 0.001597 0.001607 0.001604 0.001606 0.003630 0.003593 0.003588 0.003629 0.003618 0.003630 0.001514 0.001528 0.001539 0.001512 0.001508 0.001514 0.002505 0.002491 0.002493

0.003471 0.003457 0.003459 0.003469 0.003464 0.003471 0.001602 0.001592 0.001591 0.001602 0.001599 0.001602 0.003601 0.003562 0.003557 0.003600 0.003588 0.003601 0.001500 0.001514 0.001525 0.001498 0.001494 0.001500 0.002483 0.002469 0.002471

0.003475 0.003462 0.003464 0.003473 0.003468 0.003475 0.001597 0.001588 0.001587 0.001598 0.001595 0.001597 0.003586 0.003549 0.003544 0.003585 0.003574 0.003586 0.001487 0.001501 0.001511 0.001485 0.001481 0.001487 0.002479 0.002466 0.002468

0.003143 0.003142 0.003143 0.003143 0.003141 0.003143 0.001862 0.001861 0.0018661 0.001863 0.001862 0.001862 0.003550 0.003538 0.003537 0.003551 0.003545 0.003550 0.001821 0.001832 0.001833 0.001822 0.001822 0.001821 0.002127 0.002126 0.002127

0.003127 0.003125 0.003126 0.003127 0.003124 0.003127 0.001865 0.001863 0.001863 0.001866 0.001864 0.001865 0.003528 0.003516 0.003515 0.003529 0.003523 0.003529 0.001827 0.001838 0.001841 0.001829 0.001829 0.001828 0.002114 0.002113 0.002115

0.003106 0.003104 0.003105 0.003106 0.003103 0.003106 0.001859 0.001857 0.001857 0.001860 0.001858 0.001859 0.003504 0.003491 0.003490 0.003505 0.003499 0.003504 0.001830 0.001841 0.001843 0.001831 0.001831 0.001830 0.002098 0.002097 0.002099

0.003085 0.003083 0.003084 0.003085 0.003082 0.003085 0.001852 0.001850 0.001850 0.001853 0.001851 0.001852 0.003479 0.003466 0.003465 0.003480 0.003474 0.003480 0.001837 0.001848 0.001851 0.001838 0.001838 0.001837 0.002083 0.002082 0.002084

17

G7

USA


UK

Japan

Italy

Germany

France

C a n a d a

IDM 0.002507 0.002506 0.002484 0.002480 0.002128 0.002116 PRM 0.002500 0.002499 0.002476 0.002473 0.002125 0.002112 NENE 0.002506 0.002483 0.002483 0.002479 0.002127 0.002115 AGR 0.001356 0.001354 0.001345 0.001336 0.001240 0.001241 ENE 0.001361 0.001349 0.001340 0.001331 0.01239 0.001239 OIL 0.001362 0.001350 0.001341 0.001332 0.01240 0.001240 IDM 0.001366 0.001354 0.001346 0.001337 0.001240 0.001241 PRM 0.001362 0.001351 0.001342 0.001333 0.001238 0.001239 NENE 0.001365 0.001354 0.001345 0.001336 0.001240 0.001241 Note: The smaller the MSE value, the better the forecast accuracy of a predictor or model

Table 7: Forecast performance results of Model 2 using MSE 50% of the total sample Out-of-sample Predictor In-sample h=4 h=8 h=12 AGR 0.001485 0.001477 0.001463 0.001451 ENE 0.001473 0.001464 0.001450 0.001438 OIL 0.001475 0.001465 0.001452 0.001440 IDM 0.00141 0.001396 0.001388 0.001374 PRM 0.001445 0.001437 0.001423 0.001412 NENE 0.001462 0.001455 0.001443 0.001430 AGR 0.003495 0.003492 0.003462 0.003466 ENE 0.003495 0.003488 0.003456 0.003461 OIL 0.003497 0.003490 0.003458 0.003463 IDM 0.003504 0.003500 0.003471 0.003475 PRM 0.003495 0.003493 0.003463 0.003466 NENE 0.003496 0.003492 0.003463 0.003467 AGR 0.001609 0.001595 0.001590 0.001585 ENE 0.001614 0.001600 0.001594 0.001589 OIL 0.001612 0.001598 0.001591 0.001587 IDM 0.001615 0.001601 0.001601 0.001595 PRM 0.001619 0.001604 0.001600 0.001596 NENE 0.001617 0.001603 0.001598 0.001594 AGR 0.003666 0.003632 0.003605 0.003591 ENE 0.003624 0.003590 0.003560 0.003547 OIL 0.003618 0.003585 0.003554 0.003541 IDM 0.003601 0.003567 0.003556 0.003538 PRM 0.003555 0.003522 0.003496 0.003486 NENE 0.003650 0.003616 0.003594 0.003580 AGR 0.001524 0.001518 0.001505 0.001492 ENE 0.001537 0.001531 0.001517 0.001504 OIL 0.001514 0.001527 0.001541 0.001547 IDM 0.001479 0.001492 0.001507 0.001513 PRM 0.001519 0.001513 0.001499 0.001486 NENE 0.001523 0.001517 0.001503 0.001490 AGR 0.002494 0.002492 0.002469 0.002466 ENE 0.002498 0.002495 0.002472 0.002470 OIL 0.002499 0.002496 0.002473 0.002471 IDM 0.002468 0.002472 0.002451 0.002449 PRM 0.002504 0.002501 0.002478 0.002476

0.002100 0.002096 0.002099 0.001236 0.001234 0.001235 0.001236 0.001233 0.001236

0.002085 0.002081 0.002084 0.001231 0.001229 0.001230 0.001232 0.001229 0.001231

75% of the total sample Out-of-sample In-sample h=4 h=8 0.001586 0.001579 0.001569 0.001586 0.001579 0.001569 0.001588 0.001581 0.001570 0.001547 0.001540 0.001529 0.001556 0.001549 0.001538 0.001573 0.001567 0.001556 0.003137 0.003121 0.003100 0.003142 0.003125 0.003104 0.003142 0.003126 0.003105 0.003138 0.003121 0.003100 0.003141 0.003125 0.003104 0.003137 0.003120 0.003099 0.001856 0.001857 0.001851 0.001865 0.001865 0.001858 0.001866 0.001867 0.001859 0.001862 0.001863 0.001856 0.001863 0.001864 0.001858 0.001862 0.001864 0.001585 0.003551 0.003530 0.003506 0.003540 0.003518 0.003494 0.003538 0.003516 0.003492 0.003520 0.003498 0.003473 0.003523 0.003501 0.003476 0.003541 0.003520 0.003496 0.001823 0.001828 0.001830 0.001832 0.001836 0.001839 0.001837 0.001842 0.001844 0.001818 0001823 0.001826 0.001822 0.001827 0.001829 0.001823 0.001828 0.001830 0.002110 0.002097 0.002082 0.002129 0.002116 0.002100 0.002128 0.002115 0.002099 0.002124 0.002111 0.002095 0.002120 0.002108 0.002092

18

h=12 0.001561 0.001561 0.001563 0.001520 0.001531 0.001548 0.003079 0.003084 0.003084 0.003079 0.003084 0.003078 0.001844 0.001850 0.001852 0.001848 0.001850 0.001851 0.003481 0.003464 0.003467 0.003449 0.003452 0.003472 0.001837 0.001844 0.001850 0.001831 0.001835 0.001836 0.002066 0.002085 0.002084 0.002080 0.002077

USA


NENE 0.002528 0.002526 0.002503 0.002501 0.002127 0.002114 AGR 0.001362 0.001350 0.001342 0.001332 0.001239 0.001240 ENE 0.001359 0.001347 0.001338 0.001329 0.001246 0.001246 OIL 0.001360 0.001349 0.001339 0.001330 0.001245 0.001246 IDM 0.001345 0.001334 0.001328 0.001318 0.001232 0.001232 PRM 0.001358 0.001346 0.001337 0.001329 0.001248 0.001249 NENE 0.001367 0.001356 0.001347 0.001338 0.001242 0.001243 Note: The smaller the MSE value, the better the forecast accuracy of a predictor or model

0.002099 0.001235 0.001241 0.001240 0.001226 0.001244 0.001237

0.002083 0.001230 0.001236 0.001235 0.001220 0.001239 0.001232

4.2.1 Traditional model vs Proposed model (Model 1 vs Model 2) For the forecast comparison, the C-T test is used and the way it is constructed as previously highlighted in the methodology section. A positive C-T test statistic implies that the unrestricted model (Model 2) outperforms Model 1 and the reverse is the case if it is negative. As shown in Table 8, the C-T test statistics are mainly positive in the case of Canada and USA. This, by implication, suggests that accounting for persistence, endogeneity and heteroscedasticity as reflected in Model 2 matter for enhancing the accuracy of in-sample and out-of-sample forecasts of stock returns of both countries. In a similar development, the C-T test statistics appear predominantly positive for the case of France and Italy, particularly when the sample usage is 50% of the total sample period. However, the C-T test statistics are rather mixed for some of the G7 countries when the sample period is extended to 75%. On the overall, it can be reasonably deduced that the commodity prices predictability of G7 stock returns is likely to be more accurate when persistence, endogeneity and heteroscedasticity effects of the predictor series are captured in a predictive model. To ascertain the significance of the C-T test, the Clark and West (2007) [C-W] test is employed. The rationale here is to determine whether the difference between the forecast results of the two alternative models (Model 1 and Model 2), as obtained from the C-T test is statistically signiﬁcant. A non-rejection of the null of the C-W test implies identical forecast accuracy between the two models while a rejection favours Model 2 for a positive C-T statistic and Model 1 for a negative C-T statistic. Presented in Table 9 are the calculated t-statistics for the C-W test. Recall that the C-T test results are mainly positive for quite a reasonable number of the G7 economies. 19


However, the C-W test results appear mixed as a number of the positive C-T statistics are not significant. For instance, the null for the C-W test seems consistently rejected for virtually all the commodity indexes and irrespective of the forecast horizons and sample periods, but mainly in the case of the Canadian economy. There are however pockets of t-statistics that are statistically significant for other countries. Notwithstanding, in this instance where some of the C-W test results indicate statistically identical MSE values between the two models, then, the model

G7

with the lower MSE values, which is Model 2, is preferred.

UK

Japan

Italy

Germany

France

C an ad a

Table 8: C-T Test Forecast Performance Evaluation Results (Model 1 vs Model 2) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 AGR -0.0040 -0.0036 -0.0032 -0.0039 -0.0008 -0.0002 0.0003 ENE 0.0054 0.0065 0.0066 0.0061 0.0011 0.0020 0.0025 OIL 0.0056 0.0068 0.0069 0.0064 0.0007 0.0016 0.0020 IDM 0.0532 0.0518 0.0484 0.0495 0.0242 0.0254 0.0262 PRM 0.0224 0.0222 0.0226 0.0219 0.0177 0.0188 0.0196 NENE 0.0118 0.0116 0.0110 0.0108 0.0072 0.0079 0.0087 AGR 0.0034 0.0030 0.0026 0.0027 0.0020 0.0018 0.0019 ENE 0.0001 0.0005 0.0003 0.0003 3.40E-05 -0.0001 -0.0001 OIL -0.0001 0.0002 0.0001 0.0001 0.0003 0.0001 0.0001 IDM 0.0006 0.0002 -0.0004 -0.0004 0.0017 0.0017 0.0017 PRM 0.0017 0.0007 0.0002 0.0004 -0.0002 -0.0003 -0.0003 NENE 0.0029 0.0027 0.0021 0.0021 0.0021 0.0020 0.0021 AGR 0.0070 0.0071 0.0071 0.0074 0.0034 0.0041 0.0042 ENE -0.0010 -0.0010 -0.0007 -0.0006 -0.0017 -0.0008 -0.0002 OIL -0.0003 -0.0002 6.26E-05 5.59E-05 -0.0028 -0.0017 -0.0011 IDM 0.0037 0.0038 0.0009 0.0018 0.0006 0.0015 0.0022 PRM 6.33E-06 -8.98E-08 -0.0002 -0.0004 -0.0006 2.51E-05 0.0003 NENE 0.0020 0.0019 0.0022 0.0022 0.0001 0.0007 0.0009 AGR -0.0005 -0.0005 -0.0012 -0.0013 -0.0002 -0.0004 -0.0004 ENE 0.0006 0.0008 0.0005 0.0005 -0.0004 -0.0006 -0.0007 OIL 0.0008 0.0010 0.0008 0.0008 -0.0003 -0.0004 -0.0005 IDM 0.0171 0.0171 0.0120 0.0130 0.0088 0.0089 0.0090 PRM 0.0263 0.0264 0.0256 0.0244 0.0062 0.0063 0.0063 NENE 0.0038 0.0038 0.0017 0.0015 0.0025 0.0024 0.0024 AGR -0.0024 -0.0028 -0.0029 -0.0032 -0.0009 -0.0004 -0.0003 ENE -0.0017 -0.0019 -0.0019 -0.0024 -4.19E-05 0.0011 0.0009 OIL -0.0013 -0.0014 -0.0015 -0.0019 -0.0020 -0.0005 -0.0006 IDM 0.0035 0.0034 0.0039 0.0038 0.0020 0.0029 0.0027 PRM -0.0029 -0.0035 -0.0035 -0.0038 8.20E-05 0.0007 0.0008 NENE -0.0017 -0.0021 -0.0020 -0.0025 -0.0006 -0.0001 -1.38E-05 AGR 0.0043 0.0051 0.0054 0.0051 0.0078 0.0080 0.0080 ENE -0.0018 -0.0013 -0.0011 -0.0016 -0.0012 -0.0011 -0.0011 OIL -0.0016 -0.0010 -0.0007 -0.0010 -0.0003 -0.0002 -0.0001 IDM 0.0156 0.0135 0.0130 0.0127 0.0021 0.0024 0.0026

20

h=12 0.0008 0.0028 0.0024 0.0275 0.0199 0.0095 0.0019 -0.0002 6.49E-05 0.0018 -0.0004 0.0022 0.0043 -0.0001 -0.0010 0.0026 0.0004 0.0009 -0.0005 -0.0007 -0.0005 0.0090 0.0062 0.0023 9.57E-05 0.0022 0.0006 0.0035 0.0014 0.0007 0.0080 -0.0011 -0.0002 0.0024

G7

USA


US A

UK

Japan

Italy

Germany

France

C an ad a

PRM -0.0017 -0.0009 -0.0007 -0.0010 0.0022 0.0022 0.0022 0.0021 NENE -0.0089 -0.0084 -0.0082 -0.0085 -0.0001 2.66E-05 0.0001 9.27E-05 AGR 0.0020 0.0023 0.0027 0.0028 0.0002 0.0006 0.0009 0.0009 ENE 0.0011 0.0013 0.0014 0.0013 -0.0056 -0.0058 -0.0056 -0.0055 OIL 0.0011 0.0012 0.0013 0.0012 -0.0046 -0.0046 -0.0043 -0.0043 IDM 0.0155 0.0151 0.0130 0.0142 0.0069 0.0076 0.0085 0.0091 PRM 0.0032 0.0031 0.0033 0.0030 -0.0082 0.0085 -0.0086 -0.0085 NENE -0.0017 -0.0016 -0.0013 -0.0013 -0.0018 -0.0014 -0.0010 -0.---9 Note: The C-T test results are based on the forecast performance comparison of Model 2 and Model 3. Hypothetically, a positive C-T value implies that Model 2 outperforms Model 1 and the reverse holds if the statistic is negative. Table 9: C-W Test Forecast Performance Evaluation Results (Model 1 vs Model 2) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 AGR 1.0087 1.0388 1.0669 1.0263 0.9291 1.0106 1.1067 ENE 1.7480** 1.8721** 1.8949** 1.8543** 1.1269 1.2740 1.3489** OIL 1.7303** 1.8711** 1.8905** 1.8520** 1.0431 1.1919 1.2556 IDM 3.8358** 3.8083** 3.6919** 3.7591** 3.3373** 3.4350** 3.5135** PRM 2.1672** 2.1653** 2.1933** 2.1670** 2.4761** 2.5737** 2.6448** NENE 2.0980** 2.1042** 2.0740** 2.0700** 2.0266** 2.1101** 2.2102** AGR 0.9756 0.9307 0.8808 0.9021 0.9754 0.9496 0.9650 ENE 0.3831 0.4868 0.4505 0.4543 0.2080 0.1166 0.0944 OIL 0.1487 0.3067 0.2760 0.2717 0.4377 0.3689 0.3705 IDM 0.6232 0.5857 0.5276 0.5337 0.8731 0.8759 0.8780 PRM 0.6670 0.5736 0.5272 0.5541 -0.0033 -0.0958 -0.1454 NENE 0.8997 0.8810 0.8271 0.8305 0.9194 0.9102 0.9272 AGR 1.4244* 1.4354* 1.4482* 1.4949* 1.3759* 1.5258* 1.5516* ENE -0.3304 -0.3222 -0.1722 -0.1458 0.1882 0.3865 0.5090 OIL -0.0179 0.0259 0.2112 0.20993 -0.0609 0.1705 0.2987 IDM 1.3134* 1.3351* 1.0492 1.1443 0.8193 1.0038 1.1469 PRM 0.1358 0.0672 -0.0799 -0.1722 0.3531 0.5188 0.5974 NENE 0.8017 0.7918 0.8833 0.8818 0.4998 0.6708 0.7373 AGR 0.5443 0.5470 0.4636 0.4479 0.4644 0.4278 0.4128 ENE 0.3982 0.4206 0.3887 0.3817 0.1053 0.0567 0.0261 OIL 0.3993 0.4230 0.4020 0.3924 0.1089 0.0629 0.0350 IDM 2.5992** 2.6259** 2.4238** 2.5007** 2.2202** 2.2341** 2.2516** PRM 2.3709** 2.3843** 2.3582** 2.3147** 1.4683* 1.4787* 1.4855* NENE 1.4027* 1.4156* 1.2875* 1.2890* 1.1971 1.1832 1.1901 AGR -0.0201 -0.0956 -0.0975 -0.1583 -0.0104 0.1724 0.2101 ENE 0.3883 0.3575 0.3657 0.2943 0.7462 0.9014 0.8754 OIL 0.3417 0.3232 0.3260 0.2464 0.4865 0.6767 0.6604 IDM 1.3974* 1.4010* 1.4862* 1.4932* 1.1210 1.2815* 1.2558 PRM 0.1300 0.0400 0.0485 0.0016 0.5466 0.7309 0.7760 NENE 0.3467 0.2817 0.3060 0.2394 0.2963 0.4241 0.4638 AGR 0.9984 1.1005 1.1538 1.1218 1.5954* 1.6270* 1.6324* ENE 0.0575 0.1758 0.2200 0.1214 0.4042 0.4320 0.4511 OIL 0.0293 0.1493 0.2116 0.1536 0.7287 0.7519 0.7698 IDM 2.2745** 2.1364** 2.1236** 2.1136** 1.2627 1.2627 1.2947* PRM 0.1157 0.2613 0.3192 0.2619 1.1908 1.1849 1.191 NENE -0.8220 -0.7564 -0.7173 -0.7771 0.5162 0.5623 0.5808 AGR 0.8682 0.9472 1.0756 1.1031 0.4706 0.5941 0.6830 ENE 0.9571 1.0645 1.1663 1.1115 0.5693 0.5509 0.5664

h=12 1.1848 1.4032* 1.3150* 3.6202** 2.6720** 2.3067** 0.9758 0.0623 0.3502 0.9080 -0.1887 0.9513 1.5783* 0.5453 0.3337 1.2216 0.6272 0.7581 0.3949 0.0214 0.0317 2.2584** 1.4788* 1.1809 0.3913 1.0444 0.8347 1.3852* 0.9225 0.6517 1.6368* 0.4416 0.7643 1.2921* 1.1839 0.5823 0.7138 0.5805

21


OIL 1.0397 1.1549 1.2253 1.1777** 0.6711 0.6575 0.6949 0.7021 IDM 1.9317** 1.9134** 1.7836** 1.8775** 1.7046** 1.8093** 1.9354** 2.0274** PRM 0.9609 0.9572 0.9975 0.9337 -0.1308 -0.1695 -0.1832 -0.1760 NENE -0.3147 -0.2578 -0.1818 -0.1792 -0.2232 -0.1064 0.0377 0.0966 Note: The C-W test t-statistics are based on the critical values of 1.282 and 1.645 for 10% and 5% levels of significance, respectively.

4.2.2 The role of asymmetries in the predictive model The need to account for asymmetries in the predictive model of stock returns has continued to attract a great deal of attention in the literature (see for example, Narayan and Gupta, 2015; Salisu and Isah, 2017). Hence, we attempt to assess the extent to which asymmetries matter for the commodity-stock returns nexus. This may be important particularly for countries that are more susceptible to trade shock such as the G7 economies. We herein therefore, consider whether stock returns will respond asymmetrically to positive and negative changes in commodity prices. Thus, the equation (2) (i.e. Model 2) is further extended to capture asymmetries in commodity prices. This extension is mainly motivated by the increasing evidence of asymmetric reactions of commodity prices to shocks (see Marvasti and Lamberte, 2016). The decomposition of commodity prices into positive and negative changes follows the approach of Shin et al. (2014)7 and therefore equation (2) can be extended to capture same as follows:

rt      zt1    zt1     zt    zt1      zt    zt1    r ,t t

t

t

t

k 1

k 1

k 1

k 1

where zt   zik   max(zik , 0) and zt   zik   min(zik , 0) and

(4) there

is

presence of asymmetric effect if the coefficients on Z t and Z t are statistically different, otherwise, the effects of both are considered symmetric. For consistency, the asymmetric model can be described as Model 3 and its in-sample and out-ofsample forecast results are compared with those obtained from Model 2 which can now be regarded as a restricted version of Model 38. This approach has continued to gain prominence in the literature and some of its computational advantages are rendered in Shin et al. (2014). Recent applications of the approach to model stock returns can be found in Salisu and Isah (2017) and Swaray and Salisu (2018). 8 For the want of space, the result of asymmetry is not presented but could be made available upon request. 7

22


The same test statistics (i.e. the C-T and C-W tests) are also employed for the forecast comparison and the results are presented in Tables 10 and 11. Starting with the C-T test results in Table 10, the statistics seem predominantly positive for a good number of the G7 countries. Quite obvious is the case of France, Italy, Japan and USA, where the role of asymmetries is found to enhance the forecast accuracy of commoditybased predictive model for stock returns. This evidence does seem to support the inclusion of asymmetries in the predictive model of stock returns. The results are consistent across the different sample periods, forecast horizons and variants of commodity indexes. Even in Canada and UK where the C-T test results appear mixed, there are yet substantial instances that suggest the prominent role of asymmetries in the commodity-stock model. For instance the C-T test statistics are positive for four of the commodity indexes in the case of Canada, when the sample period is 50% and three of them when the sample period is extended to 75%. For UK, the C-T test is positive for three of the predictors for 75% and two of them for 50%. On the whole, the Germany appears the only G7 country where accounting for asymmetries in the commodity prices predictability of stock returns may not likely improve the accuracy of the forecasts. Unlike the C-W test results reported in Table 9 to choose between Model 1 and Model 2 where non-rejection seems more noticeable, those presented in Table 11 largely indicate the rejection of the null. Thus, the model that accounts for asymmetries (i.e. Model 3) is more likely to forecast stock returns better than the one that ignores same (i.e. Model 2). Like the inference drawn from the C-T statistics in Table 10, the overwhelming evidence of the null rejection is more pronounced for countries like France, Italy, Japan and USA. More importantly, the results leading to this conclusion are robust to multiple data samples, different components of commodity prices, and multiple forecast horizons.

23

G7


USA

UK

Japan

Italy

Germany

France

C a n a d a

Table 10: C-T Test Forecast Performance Evaluation Results (Model 2 vs Model 3) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 h=12 AGR 0.0109 0.0117 0.0122 0.0121 -0.0025 -0.0021 -0.0019 -0.0017 ENE -0.0063 -0.0054 -0.0048 -0.0058 0.0007 0.0002 3.94E-05 -0.0017 OIL -0.0032 -0.0024 -0.0017 -0.0022 0.0019 0.0014 0.0012 0.0009 IDM 0.0038 0.0033 0.0038 0.0037 -0.0024 -0.0019 -0.0017 -0.0016 PRM 0.0045 0.0038 0.0038 0.0037 0.0047 0.0040 0.0037 0.0034 NENE 0.0082 0.0087 0.0099 0.0095 -0.0024 -0.0020 -0.0018 -0.0016 AGR 0.0084 0.0119 0.0133 0.0098 -0.0003 9.97E-05 0.0002 0.0004 ENE 0.0138 0.0157 0.0166 0.0149 0.0067 0.0060 0.0059 0.0055 OIL 0.0135 0.0155 0.0163 0.0149 0.0070 0.0064 0.0062 0.0058 IDM 0.0503 0.0533 0.0555 0.0504 0.0327 0.0330 0.0331 0.0326 PRM 0.0117 0.0151 0.0165 0.0128 0.0014 0.0013 0.0013 0.0013 NENE 0.0175 0.0215 0.0236 0.0175 0.0038 0.0042 0.0043 0.0044 AGR -0.0103 -0.0101 -0.0052 -0.0080 -0.0058 -0.0041 -0.0031 -0.0028 ENE -0.0294 -0.0298 -0.0256 -0.0275 -0.0025 -0.0023 -0.0021 -0.0021 OIL -0.0285 -0.0287 -0.0248 -0.0263 -0.0036 -0.0032 -0.0030 -0.0029 IDM 0.0091 0.0089 0.0110 0.0103 -0.0077 -0.0057 -0.0046 -0.0045 PRM -0.0069 -0.0071 -0.0016 -0.0039 -0.0041 -0.0032 -0.0026 -0.0025 NENE -0.0107 -0.0105 -0.0061 -0.0083 -0.0073 -0.0054 -0.0043 -0.0041 AGR 0.0139 0.0132 0.0150 0.0132 0.0068 0.0066 0.0066 0.0066 ENE 0.0304 0.0300 0.0267 0.0287 0.0020 0.0019 0.0018 0.0017 OIL 0.0323 0.0321 0.0281 0.0299 0.0019 0.0018 0.0017 0.0016 IDM 0.0084 0.0083 0.0106 0.0100 0.0043 0.0042 0.0041 0.0042 PRM 0.0135 0.0134 0.0150 0.0140 0.0073 0.0071 0.0069 0.0068 NENE 0.0142 0.0138 0.0157 0.0146 0.0061 0.0059 0.0059 0.0059 AGR 0.0205 0.0216 0.0206 0.0209 -0.0063 -0.0080 -0.0084 -0.0093 ENE 0.0190 0.0200 0.0188 0.0195 0.0169 0.0107 0.0100 0.0149 OIL 0.0265 0.0277 0.0264 0.0271 0.0181 0.0117 0.0113 0.0061 IDM 0.0226 0.0227 0.0238 0.0242 0.0033 0.0004 0.0003 -0.0001 PRM -0.0045 -0.0037 -0.0043 -0.0037 0.0121 0.0082 0.0073 0.0048 NENE 0.0240 0.0248 0.0245 0.0250 -0.0069 -0.0088 -0.0093 -0.0104 AGR 0.0069 0.0088 0.0091 0.0058 -0.0091 -0.0094 -0.0095 -0.0095 ENE -0.0035 -0.0033 -0.0032 -0.0034 0.0031 0.0024 0.0021 0.0021 OIL -0.0035 -0.0031 -0.0029 -0.0032 0.0026 0.0019 0.0017 0.0017 IDM 0.0167 0.0180 0.0185 0.0157 -0.0034 -0.0036 -0.0036 -0.0036 PRM -3.89E-05 0.0012 0.0015 -7.68E-05 0.0022 0.0017 0.0016 0.0016 NENE 0.0167 0.0180 0.0185 0.0157 -0.0041 -0.0042 -0.0043 -0.0043 AGR 0.0135 0.0148 0.0179 0.0162 0.0012 0.0021 0.0030 0.0032 ENE 0.0039 0.0047 0.0065 0.0066 0.0144 0.0136 0.0133 0.0129 OIL 0.0052 0.0061 0.0079 0.0080 0.0158 0.0151 0.0147 0.0143 IDM 0.0319 0.0302 0.0292 0.0290 0.0076 0.0081 0.0086 0.0081 PRM 0.0198 0.0200 0.0221 0.0213 0.0168 0.0163 0.0161 0.0161 NENE 0.0189 0.0199 0.0230 0.0211 0.0039 0.0050 0.0055 0.0055 Note: The C-T test results are based on the forecast performance comparison of Model 2 and Model 3. Hypothetically, a positive C-T value implies that Model 3 outperforms Model 2 and the reverse holds if the statistic is negative.

24

G7


USA

UK

Japan

Italy

Germany

France

C a n a d a

Table 11: C-W Test Forecast Performance Evaluation Results (Model 2 vs Model 3) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 h=12 AGR 1.7486** 1.8159** 1.8653** 1.8691** 0.2904 0.3628 0.4034 0.4361 ENE 0.0781 0.2066 0.2990 0.2554 0.4520 0.2900 0.2265 0.1651 OIL 0.0388 0.1651 0.2779 0.2476 0.8912 0.7510 0.6965 0.6345 IDM 1.0801 1.0323 1.0787 1.0801 0.3663 0.4551 0.4969 0.5078 PRM 1.4654* 1.4186* 1.4146* 1.4126* 1.4978* 1.4222* 1.3865* 1.3589* NENE 1.6540** 1.6854** 1.7586** 1.7518** 0.2568 0.3341 0.3759 0.4174 AGR 1.7758** 1.9615** 2.0606** 1.9461** 0.6241 0.7753 0.8417 0.9053 ENE 1.6603** 1.7660** 1.8338** 1.7774** 0.2080 0.1166 0.0944 0.0623 OIL 1.7016** 1.8066** 1.8647** 1.8214** 1.7750** 1.6988** 1.6813** 1.6366** IDM 4.2107** 4.3676** 4.5028** 4.2556** 4.1688** 4.1941** 4.2114** 4.1935** PRM 1.7985** 2.0346** 2.1687** 1.9805** 1.1948 1.1717 1.1603 1.1617 NENE 2.2365** 2.4341** 2.5766** 2.3911** 1.6027* 1.6758** 1.7037** 1.7210** AGR 1.1246 1.2062 1.4349* 1.4047* 0.5408 0.7430 0.8719 0.9138 ENE -0.1863 -0.1135 0.1524 0.1648 0.2323 0.2715 0.3127 0.3079 OIL -0.3677 -0.2994 -0.0292 -0.0199 -0.7994 -0.5656 -0.4326 -0.4108 IDM 2.2707** 2.2614** 2.3517** 2.3523** 1.7374** 1.8640** 1.9318** 1.9459** PRM 1.1028 1.1765 1.4527* 1.4482* 0.3926 0.5541 0.6427 0.6645 NENE 1.2276 1.2910* 1.4780* 1.4805* 0.0975 0.3730 0.5181 0.5540 AGR 2.0394** 2.0287** 2.1919** 2.0954** 1.8856** 1.8615** 1.8519** 1.8546** ENE 2.0449** 2.0550** 1.9919** 2.0630** 2.4286** 2.3755** 2.3378** 2.3179** OIL 2.1190** 2.1395** 2.0654** 2.1395** 2.3574** 2.3045** 2.2623** 2.2428** IDM 1.7378** 1.7659** 2.0160** 1.9735** 1.7655** 1.7324** 1.7235** 1.7312** PRM 1.9809 1.9986** 2.1385** 2.0814** 1.7467** 1.7198** 1.7025** 1.6953** NENE 2.0496** 2.0594** 2.2318** 2.1799 1.8287** 1.8072** 1.8001** 1.8052** AGR 2.3291** 2.4217** 2.4316** 2.5061** -0.1178 -0.3442 -0.3837 -0.5146 ENE 2.2973** 2.4202** 2.4379** 2.5636** 2.7887** 2.2378** 2.2102** 1.7866** OIL 2.7151** 2.8347** 2.8543** 2.9746** 2.8246** 2.3171** 2.3202** 1.9274** IDM 2.9002** 2.9124** 2.9892** 3.0435** 1.7447** 1.5218* 1.5324* 1.4971* PRM 0.9150 0.9912 0.9977 1.0751 2.3711** 2.0331 1.9578** 1.7472** NENE 2.4992** 2.5646** 2.5995** 2.6862** 0.1588 -0.0468 -0.0848 -0.2130 AGR 1.3268* 1.4155* 1.4481* 1.3528* 0.4593 0.4326 0.4162 0.4189 ENE 0.3997 0.4278 0.4479 0.4171 1.7565** 1.6700* 1.6510* 1.6827** OIL 0.4938 0.5553 0.5870 0.5443 1.6503** 1.5546* 1.5357* 1.5661* IDM 3.0481** 2.9245** 2.9653** 2.9284** 0.5306 0.5035 0.5004 0.4939 PRM 1.1773 1.2765 1.3206* 1.2176 1.5507* 1.4960** 1.4773* 1.4880* NENE 1.8419** 1.9097** 1.9512** 1.8637** 0.3266 0.2945 0.2821 0.2842 AGR 1.7458** 1.8369** 1.9939** 1.9655** 0.8929 1.0008 1.1050 1.1377 ENE 1.1976 1.2841* 1.4409* 1.4628* 1.7981** 1.7504** 1.7385** 1.7168** OIL 1.3029* 1.3968* 1.5579* 1.5794* 1.9766** 1.9330** 1.9090** 1.8894** IDM 2.9275** 2.8641** 2.8270** 2.8304** 1.6136** 1.6756** 1.7303** 1.6993** PRM 2.0841** 2.1125** 2.2244** 2.2094** 2.2421** 2.2125** 2.2085** 2.2093* NENE 2.0451** 2.1069** 2.2410** 2.2239** 1.3886* 1.4871* 1.5412* 1.5432** Note: The C-W test t-statistics are based on the critical values of 1.282 and 1.645 for 10% and 5% levels of significance, respectively.

25


4.2.3 The role of structural breaks in the predictive model Another important consideration relates to structural breaks. This may affect forecast results given the behaviour of stock markets to financial crisis particularly the developed and emerging stock markets (see for example, Salisu et al., 2016). The crisis was accompanied by higher volatilities in the stock markets, among other consequences and therefore accounting for such peculiarities in the estimation may influence the outcome of the forecasts markedly. Meanwhile, we are careful not to assume specific break dates, thus, we subject the data to endogenous structural break test using the Bai and Perron (2003) approach which allows for up to five breaks in the test equation. However, in order to avoid over-fitting of the predictive model with dummy variables for breaks, we restrict the included breaks to the two most significant breaks particularly in a situation where the identified number of breaks exceeds two (see for example, Narayan and Liu, 2015; Salisu and Adeleke, 2016, Salisu et al., 2016). The results of the Bai-Perrorn test are reported in Table 12. Thus, equation (2) is extended to include the estimated structural breaks as follows:

rt     zt 1    zt   zt 1    k 1k Dkt   r ,t 2

(5)

The predictive model in equation 2 becomes our Model 4, where the inclusion of structural shift in the model is denoted by Dk  1

if t  Break Date and zero

otherwise. To verify whether the inclusion of these breaks matters in the predictive model, we compare the forecast performance of Model 4 with that of Model 2 both for the in-sample and out-of-sample forecasts. Again, we define Model 4 as the larger model that nests Model 2. Where there is no evidence of structural breaks for any predictor series, the forecast comparison is not necessary. The C-T and C-W test results are presented in Tables 13 and 14 respectively and they uniformly suggest that structural breaks significantly matter in the commodity-based predictive model for stock returns. Similar to our finding when we allow for the role of asymmetries, Germany yet appears the only G7 country where accounting for structural breaks does not seem to matter.

26


Table 12: Bai-Perron (2003) Structural break date test results Break dates for 50% data sample Predictor Canada France Germany Italy Japan AGR 1984M01 1981M03 1984M09 1976M11 1970M05 1981M07 ENE 1974M10 1974M10 1984M09 1974M10 1966M03 1984M09 1981M08 1970M06 1974M11 OIL 1974M10 1980M04 1984M09 1976M11 1970M05 1984M09 1984M09 1981M08 1980M03 1984M09 IDM 1974M10 1978M01 1964M06 1974M08 No Break 1981M09 1982M04 1973M08 1981M07 1984M09 PRM 1974M10 1982M03 1969M12 1974M10 No Break 1982M08 1984M08 1981M07 NENE 1974M10 1978M01 1984M09 1974M10 1970M05 1979M10 1982M04 1981M07 1984M06 Break dates for 75% data sample AGR 1987M10 1975M11 1981M07 1975M01 1970M05 1996M12 1982M04 1987M12 1981M06 1984M01 1987M11 1994M05 ENE 1974M10 1974M10 1970M06 1987M10 1979M06 1981M07 1981M06 1992M08 1992M04 1985M12 1987M12 1996M09 OIL 1974M10 1979M06 1981M07 1974M10 1968M09 1987M10 1987M09 1987M12 1981M06 1975M02 1996M09 1992M09 IDM 1974M10 1975M11 1981M07 1974M08 1967M08 1987M12 1982M04 1987M12 1981M07 1974M01 1995M09 1989M02 1995M12 1988M07 1989M03 1996M08 1996M11 1995M07 PRM 1982M07 1981M05 1987M11 1978M01 1970M07 1995M06 1987M10 1994M04 1986M03 1992M09 1994M03 1992M11 NENE 1974M10 1975M11 1981M07 1975M01 1974M01 1981M05 1982M04 1987M12 1981M07 1992M09 1987M10 1990M11 1987M12 1996M12 1996M12 Source: Authors’ computation. The results of Bai and Perron test would be request.

UK 1975M01 1979M05 1975M01

USA No Break

1975M01 1984M05

1982M02

1975M01 1979M05

1982M07

1975M01 1979M05 1975M01 1979M05

1975M09 1982M08 1982M07

1982M07

1975M01 1981M06

1975M09 1987M10 1994M03

1975M01 1984M05

No Break

1975M01 1984M05

1980M04 1987M12 1996M12 1981M06 1987M12 1996M07

1975M01 1981M06 1988M01 1975M01

1975M01 1981M06

1975M09 1987M10 1996M12 1975M09 1987M10 1994M03

made available upon

27

G7


USA

UK

Japan

Italy

Germany

France

C a n a d a

Table 13: C-T Test Forecast Performance Evaluation Results (Model 2 vs Model 4) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 h=12 AGR 0.0020 0.0027 0.0032 0.0030 -0.0003 -0.0001 -0.0001 -9.15E-05 ENE 0.0068 0.0073 0.0076 0.0073 0.0011 0.0013 0.0014 0.0014 OIL 0.0080 0.0084 0.0087 0.0084 0.0070 0.0070 0.0070 0.0070 IDM 0.0015 0.0016 0.0017 0.0017 -0.0011 -0.0005 -0.0002 -0.0001 PRM 0.0015 0.0016 0.0017 0.0017 -0.0009 -0.0005 -0.0003 -0.0002 NENE 0.0075 0.0079 0.0082 0.0081 0.0050 0.0051 0.0052 0.0052 AGR 0.0084 0.0109 0.0121 0.0103 0.0043 0.0047 0.0049 0.0051 ENE 0.0139 0.0163 0.0172 0.0149 0.0027 0.0026 0.0026 0.0025 OIL 0.0037 0.0054 0.0060 0.0048 0.0033 0.0033 0.0032 0.0032 IDM 0.0193 0.0222 0.0238 0.0214 0.0123 0.0128 0.0131 0.0133 PRM 0.0176 0.0207 0.0220 0.0191 0.0071 0.0069 0.0068 0.0067 NENE 0.0175 0.0215 0.0236 0.0175 0.0090 0.0092 0.0093 0.0094 AGR -0.0146 -0.0145 -0.0093 -0.0114 -0.0036 -0.0027 -0.0021 -0.0020 ENE -0.0151 -0.0154 -0.0113 -0.0132 -0.0014 -0.0012 -0.0012 -0.0012 OIL -0.0154 -0.0158 -0.0118 -0.0136 -0.0007 -0.0006 -0.0006 -0.0006 IDM -0.0204 -0.0201 -0.0140 -0.0153 0.0015 0.0029 0.0035 0.0036 PRM -0.0129 -0.0131 -0.0079 -0.0099 -0.0012 -0.0015 -0.0017 -0.0017 NENE -0.0153 -0.0154 -0.0105 -0.0124 -0.0034 -0.0024 -0.0018 -0.0017 AGR 0.0354 0.0350 0.0363 0.0354 0.0136 0.0135 0.0134 0.0134 ENE -0.0003 -0.0009 -7.76E-05 -0.0009 0.0034 0.0033 0.0032 0.0031 OIL 0.0165 0.0159 0.0166 0.0157 0.0030 0.0029 0.0028 0.0027 IDM 0.0065 0.0064 0.0087 0.0081 0.0054 0.0056 0.0057 0.0057 PRM 0.0100 0.0099 0.0113 0.0103 0.0487 0.0488 0.0489 0.0489 NENE 0.0159 0.0155 0.0173 0.0166 0.0123 0.0126 0.0127 0.0127 AGR 0.0003 0.0004 0.0004 0.0004 0.0056 0.0047 0.0045 0.0038 ENE 0.0079 0.0081 0.0081 0.0083 0.0145 0.0099 0.0088 0.0048 OIL 0.0054 0.0055 0.0055 0.0056 0.0235 0.0183 0.0170 0.0122 Not applicable IDM 0.0355 0.0310 0.0301 0.0264 Not applicable PRM 0.0117 0.0075 0.0066 0.0031 NENE 0.0002 0.0003 0.0003 0.0003 0.0051 0.0030 0.0026 0.0010 AGR 0.0328 0.0328 0.0329 0.0322 0.0139 0.0139 0.0139 0.0139 ENE 0.0397 0.0397 0.0397 0.0388 0.0344 0.0341 0.0340 0.0340 OIL 0.0232 0.0231 0.0231 0.0228 0.0642 0.0636 0.0634 0.0633 IDM 0.0376 0.0375 0.0377 0.0370 0.0238 0.0236 0.0236 0.0236 PRM 0.0339 0.0337 0.0337 0.0332 0.0085 0.0086 0.0086 0.0086 NENE 0.0352 0.0350 0.0351 0.0344 0.0172 0.0172 0.0172 0.0172 Not applicable AGR 0.0063 0.0055 0.0048 0.0046 Not applicable ENE 0.0078 0.0088 0.0110 0.0101 OIL 0.0034 0.0044 0.0063 0.0057 0.0071 0.0059 0.0047 0.0042 IDM 0.0083 0.0095 0.0126 0.0120 0.0046 0.0040 0.0035 0.0034 PRM 0.0076 0.0087 0.0110 0.0102 0.0049 0.0037 0.0025 0.0021 NENE 0.0090 0.0101 0.0127 0.0120 0.0022 0.0023 0.0024 0.0024 Note: The C-T test results are based on the forecast performance comparison of Model_II & Model_IV. Hypothetically, a positive C-T value implies that Mode_IV outperformed Model_II and the reverse holds if the statistic is negative.

28

G7


USA

UK

Japan

Italy

Germany

France

C a n a d a

Table 14: C-W Test Forecast Performance Evaluation Results (Model 2 vs Model 4) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8

h=12

AGR 0.8406 0.9840 1.0837 1.0661 0.4520 0.4829 0.4980 0.5084 ENE 1.4712* 1.5470* 1.6055* 1.5686* 0.7607 0.8182 0.8507 0.8695 OIL 1.4464* 1.4878* 1.5233* 1.5055* 1.8696** 1.8752** 1.8736** 1.8718** IDM 0.7374 0.7782 0.8004 0.8053 0.5769 0.6929 0.7435 0.7701 PRM 1.7069 1.8031** 1.8725** 1.8071** -0.2103 -0.0357 0.0524 0.1303 NENE 1.5567* 1.6154* 1.6705** 1.6608** 1.7445** 1.7684** 1.7790** 1.7877** AGR 1.3362* 1.5119* 1.6156** 1.5251* 1.3442* 1.4172* 1.4511* 1.4820* ENE 1.8898** 2.0851** 2.1755** 2.0339** 1.0303 1.0129 0.9997 0.9877 OIL 0.9304 1.1293 1.2194 1.0927 1.2090 1.2014 1.1898 1.1801 IDM 2.1447** 2.3234** 2.4494** 2.3440** 2.0180** 2.0633** 2.0861** 2.1055** PRM 2.0216** 2.2186** 2.3350** 2.2048** 1.5424* 1.5207* 1.5096* 1.4974* NENE 2.1904** 2.3752** 2.5002** 2.3887** 1.7455** 1.7701** 1.7826** 1.7949** AGR 0.6854 0.7695 1.0040 1.0032 0.9284 1.0064 1.0623 1.0757 ENE 0.4773 0.5389 0.7610 0.7467 0.8835 0.9021 0.9095 0.9095 OIL 0.4486 0.5055 0.7250 0.7095 0.9337 0.9474 0.9506 0.9509 IDM 0.8960 0.9562 1.1841 1.1943 1.7374** 1.8640** 1.9318** 1.9459** PRM 0.8088 0.8847 1.1239 1.1266 0.0195 -0.0588 -0.1048 -0.1155 NENE 0.7133 0.7925 1.0117 1.0194 0.9954 1.0801 1.1374 1.1527 AGR 3.3341** 3.3323** 3.4180** 3.3911** 2.5455** 2.5361** 2.5297** 2.5251** ENE 0.6835 0.6542 0.7495 0.68231 1.2976* 1.2798 1.2592 1.2495 OIL 2.2011** 2.1747** 2.2336*** 2.1869** 1.1640 1.1430 1.1172 1.1063 IDM 1.4023* 1.4169* 1.6094* 1.5846* 1.7203** 1.7534** 1.7752** 1.7779** PRM 1.8132** 1.8287** 1.9584*** 1.8982** 4.5661** 4.5765** 4.5847** 4.5889** NENE 2.1825** 2.1847** 2.3197*** 2.2944** 2.4864** 2.5224** 2.5453** 2.5508** AGR 0.3592 0.3806 0.3845 0.4030 2.0088** 1.7620** 1.7151** 1.5063* ENE 1.4882* 1.5146* 1.5165* 1.5337* 2.6679** 2.3443** 2.2867** 2.0081** OIL 1.1934 1.2125 1.2138 1.2267 3.4899** 3.0967** 3.0074** 2.6506** Not applicable IDM 3.8676** 3.5988** 3.5539** 3.3384** Not applicable PRM 2.3832** 2.0350** 1.9723** 1.6864** NENE 0.3274 0.3419 0.3455 0.3619 2.2424** 1.8832** 1.8258** 1.5451* AGR 2.8539** 2.8763** 2.8849** 2.8605** 0.2437 2.4425** 2.4461** 2.4449** ENE 3.3023** 3.3285** 3.3366** 3.2997** 3.2839** 3.2660** 3.2615** 3.2705** OIL 2.0939** 2.0983** 2.1004** 2.0994** 3.8792** 3.8618** 3.8574** 3.8652** IDM 3.0916** 3.1123** 3.1305** 3.1121** 3.1401** 3.1268** 3.1249** 3.1329** PRM 2.6792** 2.6855** 2.6898** 2.6783** 2.7775** 2.8026** 2.8114** 2.8078** NENE 2.8701** 2.8840** 2.8927** 2.8724** 2.7759** 2.7827** 2.7862** 2.7842** Not applicable AGR 1.8767** 1.7344** 1.5937** 1.5443* Not applicable ENE 1.6123* 1.7258** 1.9196** 1.8812** OIL 1.1728 1.2880* 1.4748* 1.4465* 1.7650** 1.6199* 1.4827* 1.4367* IDM 1.7026** 1.8264** 2.0918** 2.0761** 1.5221* 1.4481* 1.3783* 1.3649* PRM 1.6340* 1.7501** 1.9652** 1.9268** 1.6680** 1.4065* 1.1657** 1.0966 NENE 1.7335** 1.8527** 2.0733** 2.0498** 1.6166* 1.6492** 1.6829** 1.6945** Note: The C-W test t-statistics are based on the critical values of 1.282 and 1.645 for 10% and 5% levels of significance, respectively.

29


4.2.4 Historical Average vs Commodity-based predictive model (Model 2) It has become a standard approach in the literature to validate the accuracy of theory-based predictive models by comparing their forecast performance with the historical average. For completeness therefore, we extend the forecast exercise in this study to capture same. The historical average is labeled as Model 5 and the results of the C-T and C-W statistics are presented in Tables 15 and 16 respectively. Judging by the former test, the commodity-based predictive model for the G7 countries resoundingly outperforms the historical average both for the in-sample and out-ofsample forecasts irrespective of the data sample, forecast horizon and commodity price index. The only notable exception is Japan where the C-T test statistics are mostly negative regardless of the parameters for robustness. Another exception is the US with negative C-T statistics for a larger data sample. In other words, for a small data sample, the theory-based model will forecast US stock returns better than the historical average and vice versa for a large data sample. Aside these two cases,

G7

commodity prices forecast stock returns more accurately than the historical average.

Italy

Germany

France

C an ad a

Table 15: C-T Test Forecast Performance Evaluation Results (Model 2 vs Model 5) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 AGR -0.0043 -0.0038 -0.0033 -0.0040 -0.0009 -0.0003 0.0003 ENE 0.0036 0.0050 0.0054 0.0048 -0.0012 -3.32E-05 0.0005 OIL 0.0025 0.0039 0.0042 0.0037 -0.0022 -0.0010 -0.0005 IDM 0.0523 0.0513 0.0480 0.0492 0.0235 0.0247 0.0256 PRM 0.0231 0.0233 0.0239 0.0231 0.0178 0.0190 0.0199 NENE 0.0112 0.0112 0.0108 0.0106 0.0069 0.0077 0.0085 AGR 0.0041 0.0040 0.0037 0.0036 0.0026 0.0025 0.0026 ENE 0.0042 0.0052 0.0054 0.0050 0.0010 0.0011 0.0012 OIL 0.0036 0.0045 0.0048 0.0043 0.0009 0.0009 0.0011 IDM 0.0017 0.0017 0.0013 0.0010 0.0023 0.0024 0.0025 PRM 0.0043 0.0038 0.0035 0.0035 0.0012 0.0012 0.0012 NENE 0.0038 0.0038 0.0034 0.0032 0.0027 0.0027 0.0028 AGR 0.0078 0.0079 0.0082 0.0085 0.0041 0.0049 0.0050 ENE 0.0044 0.0047 0.0060 0.0060 -0.0006 0.007 0.0016 OIL 0.0057 0.0060 0.0074 0.0074 -0.0016 -0.0001 0.0007 IDM 0.0039 0.0041 0.0015 0.0024 0.0008 0.0018 0.0026 PRM 0.0019 0.0019 0.0022 0.0021 0.0003 0.0012 0.0017 NENE 0.0026 0.0027 0.0033 0.0032 0.0007 0.0013 0.0016 AGR 0.0017 0.0017 0.0012 0.0009 0.0012 0.0011 0.0011 ENE 0.0131 0.0131 0.0136 0.0131 0.0044 0.0044 0.0046 OIL 0.0147 0.0146 0.0153 0.0147 0.0048 0.0049 0.0050 IDM 0.0195 0.0194 0.0148 0.0156 0.0100 0.0102 0.0103 PRM 0.0318 0.0318 0.0315 0.0301 0.0091 0.0093 0.0095

h=12 0.0009 0.0010 -6.09E-05 0.0269 0.0203 0.0094 0.0027 0.0013 0.0011 0.0026 0.0013 0.0030 0.0052 0.0018 0.0009 0.0029 0.0018 0.0017 0.0010 0.0046 0.0051 0.0103 0.0094

30

G7

USA

UK

Japan


Japan

Italy

Germany

France

C an ad a

NENE 0.0061 0.0061 0.0042 0.0039 0.0039 0.0038 0.0039 0.0038 AGR -0.0042 -0.0044 -0.0045 -0.0047 -0.0031 -0.0027 -0.0026 -0.0021 ENE -0.0130 -0.0129 -0.0129 -0.0131 -0.0079 -0.0070 -0.0073 -0.0062 OIL -0.0193 -0.0193 -0.0193 -0.0195 -0.0110 -0.0100 -0.0102 -0.0092 IDM 0.0029 0.0033 0.0038 0.0040 -0.0007 0.0001 -7.26E-05 0.0007 PRM -0.0008 -0.0009 -0.0009 -0.0010 -0.0027 -0.0020 -0.0019 -0.0013 NENE -0.0034 -0.0035 -0.0035 -0.0038 -0.0029 -0.0025 -0.0024 -0.0016 AGR 0.0051 0.0061 0.0066 0.0061 0.0085 0.0087 0.0088 0.0088 ENE 0.0037 0.0049 0.0054 0.0045 -0.0003 -1.75E-05 0.0001 6.01E-05 OIL 0.0032 0.0044 0.0050 0.0043 3.44E-05 0.0003 0.0004 0.0004 IDM 0.0156 0.0139 0.0137 0.0132 0.0020 0.0024 0.0026 0.0024 PRM 0.0011 0.0024 0.0029 0.0023 0.0033 0.0038 0.0039 0.0038 NENE -0.0083 -0.0075 -0.0071 -0.0076 0.0003 0.0005 0.0006 0.0006 AGR 0.0021 0.0025 0.0031 0.0032 0.0013 0.0018 0.0022 0.0023 ENE 0.0041 0.0047 0.0056 0.0055 -0.0038 -0.0034 -0.0028 -0.0025 OIL 0.0034 0.0039 0.0047 0.0046 -0.0035 -0.0032 -0.0023 -0.0020 IDM 0.0148 0.0146 0.0129 0.0141 0.0074 0.0082 0.0092 0.0099 PRM 0.0052 0.0055 0.0063 0.0059 -0.0055 -0.0056 -0.0054 -0.0052 NENE -0.0019 -0.0015 -0.0010 -0.0010 -0.0008 -0.0004 0.0001 0.0003 Note: The C-T test results are based on the forecast performance comparison of Model_II & Model_V. Hypothetically, a positive C-T value implies that Mode_II outperformed Model_V and the reverse holds if the statistic is negative. Table 16: C-W Test Forecast Performance Evaluation Results (Model 2 vs Model 5) 50% Data Sample 75% Data Sample Out-of-sample Out-of-sample Predictor In-sample In-sample h=4 h=8 h=12 h=4 h=8 AGR 0.9714 1.0131 1.0495 1.0104 0.9154 1.0035 1.1058 ENE 1.6715** 1.7958** 1.8363** 1.8093** 0.9762 1.1384 1.2284 OIL 1.6196** 1.7442** 1.7769** 1.7515** 0.9006 1.0533 1.1286 IDM 3.7334** 3.7237** 3.6139** 3.6790** 3.2317** 3.3328** 3.4159** PRM 2.1353** 2.1544** 2.1947** 2.1742** 2.4439** 2.5516** 2.6312** NENE 2.0372** 2.0571** 2.0346** 2.0312** 1.9796** 2.0685** 2.1744** AGR 1.1257 1.1062 1.0666 1.0749 1.0876 1.0708 1.0940 ENE 1.4041* 1.5894* 1.6357** 1.5603* 0.8785 0.9154 0.9521 OIL 1.2242 1.3680* 1.4210* 1.3553* 0.8905 0.8965 0.9314 IDM 0.7574 0.7720 0.7277 0.7066 1.0378 1.0625 1.0802 PRM 1.0036 0.9501 0.9211 0.9228 1.2694 1.2930** 1.3093* NENE 1.0273 0.9932 0.9932 0.9810 1.0459 1.0488 1.0755 AGR 1.5651* 1.5850 1.6282** 1.6784** 1.5226* 1.6891** 1.7315** ENE 1.2610 1.3055* 1.4857** 1.4999* 0.6866 0.9076 1.0454 OIL 1.4626* 1.5116* 1.6888** 1.6945** 0.5591 0.7953 0.9346 IDM 1.3230* 1.3561* 1.1039 1.1993 0.8512 1.0466 1.1986 PRM 1.1343 1.1728 1.3218** 1.2749 0.6876 0.8725 0.9697 NENE 1.0377 1.0516 1.2192 1.2234 0.7114 0.8962 0.9791 AGR 0.8027 0.8014 0.7332 0.6989 0.7821 0.7522 0.7491 ENE 2.1083** 2.1171** 2.1954** 2.1394** 1.7579** 1.7830** 1.8184** OIL 0.3993 0.4230 0.4020 0.3924 1.8279** 1.8575** 1.8983** IDM 2.7322** 2.7550** 2.5516** 2.6193** 2.3343** 2.3544** 2.3798** PRM 2.6900** 2.6954** 2.6875** 2.6308** 1.9034** 1.9312** 1.9551** NENE 1.5445* 1.5550** 1.4323* 1.4240* 1.3796* 1.3723* 1.3891* AGR -0.1176 -0.1502 -0.1541 -0.1825 -1.2276 -1.0237 -0.9765 ENE 0.4172 0.4155 0.4156 0.4037 -0.2637 -0.1561 -0.1937 OIL 0.3047 0.2977 0.2975 0.2842 -0.6511 -0.5362 -0.5689 IDM 1.2922* 1.3359* 1.3998* 1.4231* 0.6244 0.7769 0.7476

h=12 1.1900 1.2985* 1.1980 3.5273** 2.6656** 2.2764 1.1126 0.9809 0.9472 1.1281 1.3295* 1.1098 1.7630** 1.0909 0.9781 1.2766 1.0063 1.0062 0.7344 1.8355** 1.9169** 2.3916** 1.9518** 1.3843* -0.7345 -0.0532 -0.4472 0.8916

31

USA

UK


PRM 0.5537 0.5350 0.5337 0.5291 -0.3452 -0.1421 -0.0845 0.0879 NENE 0.1871 0.1642 0.1778 0.1400 -0.4839 -0.3633 -0.3178 -0.0937 AGR 1.0468 1.1622 1.2250 1.1890 1.6597** 1.6956** 1.7043** 1.7097** ENE 1.4591* 1.5858* 1.6522** 1.5700* 1.1449 1.1986 1.2330 1.2346 OIL 1.5259* 1.6405** 1.7093** 1.6521** 1.3519* 1.3958* 1.4272* 1.4298* IDM 2.2449** 2.1493** 2.1466** 2.1226** 1.1936 1.2590 1.2968* 1.2991* PRM 0.7650 0.9341 1.0134 0.9472 1.5088* 1.5212* 1.5368* 1.5346* NENE -0.5611 -0.4577 -0.4011 -0.4642 0.6630 0.7139 0.7367 0.7409 AGR 0.8139 0.9129 1.0789 1.1047 0.8316 0.9617 1.0696 1.1099 ENE 1.2694 1.3475* 1.4777* 1.4669* 1.1941 1.2281 1.2928* 1.3259* OIL 1.2169 1.2790 1.3863* 1.3784* 1.2768 1.3073* 1.3855* 1.4101* IDM 1.8758** 1.8777** 1.7746** 1.8670** 1.7527** 1.8684** 2.0122** 2.1111** PRM 1.2478 1.3005* 1.4205* 1.3735* 0.3529 0.3462 0.3652 0.3870 NENE -0.2509 -0.1523 -0.0090 -0.0037 0.2218 0.3496 0.5079 0.5736 Note: The C-W test t-statistics are based on the critical values of 1.282 and 1.645 for 10% and 5% level of significance, respectively.

5.

Concluding remarks

This study considers the role of commodity prices in the predictive model of stock returns for the most advanced economies in the world. We depart from the extant literature in the subject matter by considering some salient features that might be present in the nexus. There are three instructive findings from the study: (i) allowing for the inherent characteristics of commodity prices such as persistence, endogeneity and conditional heteroscedasticity in the predictive model for stock returns tends to enhance the forecast accuracy of the model; (ii) accounting for structural breaks and asymmetries improves the forecast performance of the commodity-based predictive model for stock returns; (iii) commodity prices forecast stock returns better than the historical average. Nonetheless, there are few instances of deviations from these findings particularly for Germany. These findings are consistent across different sample periods, multiple forecast horizons and commodity indexes. In term of policy relevance, this study has established the importance of commodity prices in predicting stock returns in the G7 countries. As such, investors are provided with alternative hedging options that could be explored in order to increase returns on investments.

32


References Ang, A. and G. Bekaert (2007). Stock return predictability: Is it there? Review of Financial Studies 20 (3), 651-707. Bai, J. and Perron, P. (2003). Computation and analysis of multiple structural change models. Journal of applied econometrics, 18(1), 1-22. Black, A.J., Klinkowska, O., McMillan, D.G. and McMillan, F.J. (2014). Forecasting stock returns: Do commodity prices help? Journal of Forecasting, 33(8), 627639. Campbell, J.Y. (1987). Stock returns and the term structure. Journal of Financial Economics, 18, 373–399. Campbell, J.Y. and Shiller, R.J. (1988). The dividend-price ratio and expectations of future dividends and discount factors. Review of Financial Studies, 1, 195– 228. Campbell, J.Y., and Thompson, S.B. (2008). Predicting excess stock returns out of sample: can anything beat the historical average? Review of Financial Studies 21, 1509–1531. Creti, A., Joëts, M. and Mignon, V. (2013). On the links between stock and commodity markets' volatility. Energy Economics 37, 16-28. Clark, T.E. and West T.D. (2007). Approximately normal tests for equal predictive accuracy in nested models. Journal of Econometrics, 138, 291–31. Cochrane, J. (2011). Discount rates: American finance association presidential address. Journal of Finance, 66, 1047–1108. Creti, A., Joëts, M. and Mignon, V. (2013). On the links between stock and commodity markets’ volatility. Energy Economics, 37, 16–28. Devpura, N., Narayan, P.K. and Sharma, S.S. (2018). Is stock return predictability timevarying? Journal of International Financial Markets, Institutions & Money, 52, 152172. Engle, R., 1982. Autoregressive conditional heteroscedasticity with estimates of the variance of the U.K. Inflation. Econometrica 50, 987–1008. Fama, E.F. and French, K.R. (1988). Dividend yields and expected stock returns. Journal of Financial Economics, 22, 3–25. Goyal, A. and Welch, I. (2003). Predicting the Equity premium with dividend ratios. Management Sciences, 49 (5), 639-654 Hjalmarsson, E. (2010). Predicting global stock returns. Journal of Financial and Quantitative Analysis, 45, 49–80. Hodrick, R.J. (1992). Dividend yields and expected stock returns: alternative procedures for inference and measurement. Review of Financial Studies, 5, 357–386. Jordan, S.J. and Vivian, A. and Wohar, M.E. (2016). Can commodity returns forecast Canadian sector stock returns? International Review of Economics and Finance, 41, 172-188. Junttila, J., Pesonen, J. and Raatikainen, J. (2018). Commodity market based hedging against stock market risk in times of financial crisis: The case of crude oil and gold. Journal of International Financial Markets, Institutions and Money, https://doi.org/10.1016/j.intfin.2018.01.002.

33


Junttila, J-P & Raatikainen, J. 2017. Haven on Earth. Dynamic Connections between Gold and Stock Markets in Turbulent Times. Available at SSRN: https://ssrn.com/abstract=2916073. Kellard, N.M., Nankervis, J.C. and Papadimitriou, F.I. (2010). Predicting the equity premium with dividend ratios: reconciling the evidence. Journal of Empirical Finance, 17, 539–551. Lewellen, J. (2004). Predicting returns with financial ratios. Journal of Finance and Economics, 74, 209–235. Marvasti, A. and Lamberte, A. (2016). Commodity price volatility under regulatory changes and disaster. Journal of Empirical Finance, 38(A), 355-361. Narayan, P.K. and Liu, R. (2015). A unit root model for trending time-series energy variables. Energy Economics, 50 (1), 391-402 Narayan, P.K. and Gupta, R. (2015). Has oil price predicted stock returns for over century? Energy Economics, 48, 18–23. Narayan, P.K. and Liu, R. (2011). Are shocks to commodity prices persistent? Applied Energy, 88(1), 409-416. Narayan, P.K. and Sharma, S.S. (2014). Firm return volatility and economic gains: The role of oil prices. Economic Modelling, 38, 142–151. Ntantamis, C. and Zhou, J. (2015). Bull and bear markets in commodity prices and commodity stocks: Is there a relation? Resources Policy, 43, 61-81. Öztek, M. F. and Öcal, N. (2017). Financial crises and the nature of correlation between commodity and stock markets. International Review of Economics & Finance, 48, 56-68. Phan, D.H.B., Sharma, S.S. and Narayan, P.K. (2015). Stock Return Forecasting: Some New Evidence. International Review of Financial Analysis, 40, 38-51. Rapach, D.E., Wohar, M.E. and Rangvid, J. (2005). Macro variables and international stock return predictability. International Journal of Forecasting, 21, 137–166. Reboredo, J.C. and Ugolini, A. (2017). Quantile causality between gold commodity and gold stock prices. Resources Policy, 53, 56-63. Salisu, A.A and Adeleke, A.I. (2016) Further application of Narayan and Liu (2015) unit root model for trending time series, Economic Modelling, 55(3) 305-314 Salisu, A.A. and Isah, K. (2017). Revisiting the oil price and stock market nexus: A nonlinear Panel ARDL approach. Economic Modelling, 66(C), 258-271. Salisu, A.A. and Isah, K. O. (2018). Predicting US inflation: Evidence from a new approach. Economic Modelling, 71, 134-158. Salisu, A.A., Ndako, U.B., Oloko, T.F. and Akanni, L.O. (2016). Unit root modelling for trending stock market series. Borsa Istanbul Review, 16(2), 82-91. Shin, Y., Yu, B. and Greenwood-Nimmo, M. (2014) 'Modelling asymmetric cointegration and dynamic multipliers in a nonlinear ARDL framework', in Anonymous Festschrift in Honor of Peter Schmidt. Springer, pp. 281-314. Swaray, R. and Salisu, A.A. (2018). A firm-level analysis of the upstreamdownstream dichotomy in the oil-stock nexus? Global Finance Journal, 37, 199–218. Tang, K and Xiong, W. (2012). Index investment and the financialization of commodities. Financial Analysts Journal, 68(6), 54.

34


Wen, X. and Nguyen, D.K. (2017). Can investors of Chinese energy stocks benefit from diversification into commodity futures? Economic Modelling, 66, 184200. Westerlund, J. and Narayan, P.K. (2012). Does the choice of estimator matter when forecasting returns? Journal of Bankingand Finance, 36, 2632–2640. Westerlund, J. and Narayan, P.K. (2015). Testing for predictability in conditionally heteroskedastic stock returns. Journal of Finance and Economics, 13(2), 342– 375.

35


APPENDIX Figure 1: Trends in G7 Stock Prices and Agricultural Commodities FRANCE

CANADA

GERMANY 5.0

5.0

4.5 5

4.0

4.5

4.0

3.5

4 3.0

2

3.0

3

3.0

1 60

65

70

75

80

85

90

LCAN

95

00

05

10

60

15

3.5 4

3

2

1

4.0 5

3.5

3

4.5 6

6 5

4

5.0

65

70

75

80

85

90

LFRC

LAGR

ITALY

95

00

05

10

2

15

60

65

70

75

80

LAGR

85

JAPAN

6

90

LGRM

95

00

05

10

15

LAGR

UK

5.0

5.0

5.0

4.5

4.5

4.5

4.0

6

4.0

4.0

5

5 3.5

5

3.5

3.0

4

3.0

4

3.5

3

3.0

4 3

2 2

3

1

2

1 60

65

70

75

80

85 LITL

90

95

00

05

10

15

60

65

70

75

80

LAGR

85

90

LJPN

95

00

05

10

0

15

60

LAGR

65

70

75

80

85 LUK

90

95

00

05

LAGR

USA 5.0

4.5 6 5

4.0

4

3.5

3 3.0 2 1 60

65

70

75

80

85 LUS

90

95

00

05

10

15

LAGR

36

10

15


Figure 2: Trends in G7 Stock Prices and Energy Commodities GERMANY

FRANCE

CANADA

4 3

5

5

5 5

6

6

6

6

6

4

4

5

3

4

2

3

5

4 2

1

3 0 2

2 4

1

3

1

0

0

3

2 2

1

1 60

65

70

75

80

85

90

LCAN

95

00

05

10

60

15

65

70

75

80

85

90

LFRC

LENE

95

00

05

10

60

15

4

6 5

2 4

1

3

85 LITL

90

95

00

05

10

15

00

05

10

15

LENE

5

5

4

4 6

5

4

3

5

2

4

1

3

3 2 1

0

0

2 1 0

2

1

95

6

3

2

90

6

0

80

85

UK

3

75

80

LGRM

5

70

75

LENE

6

65

70

JAPAN

ITALY

60

65

60

65

70

75

80

85

90

LJPN

LENE

95

00

05

10

60

15

65

70

75

80

85 LUK

LENE

90

95

00

LENE

USA 6 5 6

4

5

3

4

2 1

3

0 2 1 60

65

70

75

80

85 LUS

90

95

00

05

10

15

LENE

37

05

10

15


Figure 3: Trends in G7 Stock Prices and Oil Commodities FRANCE

CANADA

GERMANY 5

5 4

5

4

3

3

3

5 4

4

6

6

5

5

2

2

2

4 1

3

4

1

1

3 0 2

0

3

2 1

1 60

65

70

75

80

85

90

95

LCAN

00

05

10

60

15

65

70

75

80

85

90

LFRC

LOIL

ITALY

95

00

05

10

2

15

60

5 4 3

LITL

90

95

00

05

10

15

00

05

10

15

LOIL

4

4 3

3

6

5 2

2

4 1

1

3 0

0

2

3

1

95

4

0

2

90

5

4

85

85

5

1

80

80

UK

5

75

75

LGRM

2

70

70

5

3

65

65

LOIL

JAPAN

6

60

0

1

2

0 60

65

70

75

80

85

LOIL

90

95

LJPN

00

05

10

15

60

LOIL

65

70

75

80

85 LUK

90

95

00

05

LOIL

USA 5 4

6

3

5

2

4

1

3

0

2 1 60

65

70

75

80

85 LUS

90

95

00

05

10

15

LOIL

38

10

15


Figure 4: Trends in G7 Stock Prices and Industrial Metal Commodities CANADA

FRANCE 5.0

4.5

4.5

4.0

5

3.5 4

GERANY

5.0

6

4.0

5

3.5

3.0 2.5

3

2.0 2

5.0 4.5 6 4.0

3.0 4

2.5

2.5

3 2.0

60

65

70

75

80

85

90

95

LCAN

00

05

10

1

15

2.0

3

2

1

3.5

5

3.0

4

60

65

70

75

80

85

LIDM

90

LFRC

ITALY

95

00

05

10

2

15

60

65

70

75

80

LIDM

85 LGRM

95

00

05

10

15

LIDM

UK

JAPAN 5.0

5.0

5.0

4.5

4.5

4.5

4.0

6

90

3.5 5 3.0

4.0

4.0 6

5

3.5

5

3.0

4

2.5

3

2.0

2

3.5 3.0 2.5

4

2.5

2.0

4

3

2.0 3

2 1 60

65

70

75

80

85 LITL

90

95

00

05

10

15

1 0

2 60

65

70

75

80

85

LIDM

90

LJPN

95

00

05

10

60

15

65

70

75

80

85 LUK

LIDM

90

95

00

05

10

LIDM

USA 5.0 4.5 6

4.0

5

3.5

4

3.0 2.5

3

2.0 2 1 60

65

70

75

80

85 LUS

90

95

00

05

10

15

LIDM

39

15


Figure 5: Trends in G7 Stock Prices and Precious Metal Commodities CANADA

GERMANY

FRANCE 8 7

5

6 5

4

4

7

2

7 6

6 6

6

5

5

5

5

4 4

3 3

8

8

3 2

1 65

70

75

80

85

90

LCAN

95

00

05

10

4

3

3

2

1 60

4

3

15

60

65

70

75

80

LPRM

85

90

LFRC

ITALY

95

00

05

10

60

15

65

70

75

80

85

90

95

LGRM

LPRM

00

05

10

15

LPRM

UK

JAPAN 8 8

8

7

7

7 6

6

5

5

4

4

3

3

6

2

6 5

5

6 5 5 4 4

4

3

3

2

4

3

3

1

1 60

65

70

75

80

85

90

95

00

05

10

15

0

2 60

LITL

65

70

75

80

85

90

95

00

05

10

60

15

65

70

75

80

85

90

95

00

05

LPRM LJPN

LUK

LPRM

LPRM

USA 8 7

6

6

5

5

4

4

3

3

2 1 60

65

70

75

80

85 LUS

90

95

00

05

10

15

LPRM

40

10

15


Figure 6: Trends in G7 Stock Prices and Non-Energy Commodities CANADA

FRANCE

GERMANY

5.0

5.0

4.5 4.0

5

3.5

4

4.5 4.0

5 4

2.5

3

3.5 3.0

3

1 60

65

70

75

80

85

90

95

LCAN

00

05

10

15

65

70

75

80

85

LNENE

90

95

LFRC

5

00

05

10

15

4 3

75

80

85

1 95

00

05

10

15

90

95

00

05

10

15

LNENE

UK 5.0

4.5

4.5

4.5

4.0

6

3.5 3.0

4 2.5 3

2

LITL

70

5.0

2.5

90

65

LGRM

3.0

85

2.5

60

5

80

3

LNENE

3.5

75

3.0

5.0

4.0

70

4

JAPAN

6

65

3.5

2 60

ITALY

60

4.0 5

2.5

2

1

4.5 6

6

3.0

2

5.0

4.0 5 3.5 4 3.0 3 2.5 2 1

2

0 60

65

70

75

80

LNENE

85

90

LJPN

95

00

05

10

15

60

LNENE

65

70

75

80

85 LUK

90

95

00

05

10

LNENE

USA 5.0 4.5

6

4.0

5

3.5

4

3.0

3

2.5

2 1 60

65

70

75

80

85 LUS

90

95

00

05

10

15

LNENE

41

15