Applied Economics Letters, 2005, 12, 537–543
Evidence on the seasonality of stock market prices of firms traded on organized markets Jeffrey Jarrett* and Eric Kyper University of Rhode Island, College of Business Administration, 7 Lippitt Road, Ballentine, Kingston, RI 02881, USA
Studies of capital market efficiency are important because they infer that there are predictable properties of the time series of prices of traded securities on organized markets. The weak form of the efficient markets hypothesis is put in dispute by the results of this study. Furthermore, this study of individual securities prices of US traded securities corroborates previous findings of studies of stock market indexes both in the USA and for foreign stock exchanges that seasonality is present in the times of securities prices.
I. Introduction The purpose of this paper is to clarify the existence of time series characteristics of stock prices of securities marketed on organized exchanges. This study differs from previous studies where the focus was on index numbers of stock market prices rather than the actual prices of traded securities. Furthermore, this study is important because of the theory of market efficiency. Capital market efficiency is an important research topic since Fama (1955, 1970) explained these principles as apart of the efficient market hypothesis. Following Fama’s work many studies were devoted to investigating the randomness of stock price movements for the purpose of demonstrating the efficiency of capital markets. In recent years, other studies demonstrated market inefficiencies by identifying systematic variations in stock returns. Some of these systematic variations, or anomalies as they are referred to are small firm effects, investment recommendations, and extraordinary returns to the time or the calendar effect. Calendar or time effects contradict the weak form of the efficient market hypothesis. The weak form
refers to the notion that the market is efficient in past price and volume information and stock movements cannot be predicted using this historic information. If no systematic patterns exist, stock prices are time invariant. On the other hand, if seasonality effects in organized stock markets exist, market inefficiency is present and investors should be able to earn abnormal rates of return not in line with the degree of risk they undertook (Francis, 1993). The expansion of time series analysis as a discipline permits analysis of stock market prices in ways not heretofore explored. However, peculiar problems arise when seasonality is present in stock price data. It is known that stock prices have some seasonality known as monthly effects. For example Wachtel (1942) found the mean rate of return on stocks in January is higher than in other months. In addition verified the presence of monthly effects in stock markets in 17 nations, finding evidence of the January effect during the 10-year sample period, from 1970 to1979. (See similar studies by Ariel, 1987; Lakonishok and Smidt, 1989; Peiro, 1994; Boudreaux, 1995; Hamori and Tokihisa, 2002). Other studies focused on the time series behaviour on stock markets
*Corresponding author. E-mail: Jeff
[email protected] Applied Economics Letters ISSN 1350–4851 print/ISSN 1466–4291 online # 2005 Taylor & Francis Group Ltd http://www.tandf.co.uk/journals DOI: 10.1080/13504850500123288
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538 focused the volatility of Pacific Basin stock markets and their linkage of stock returns in Pacific Basin nations. Ng et al. (1991) explored lead–lag relationships among these stock returns. Cho et al. (1986) and Campbell and Hamao (1992) explored the integration of the equity markets with other national markets. Finally, Chen et al. (1995) studied the impact of futures trading on market volatility in the Tokyo Stock Exchange. Only a few studies focused on the investigation of time series components of equity prices and the predictability of these prices. Ray et al. (1997) investigated a sample of 15 firms and found both permanent and temporary systematic components in individual time series of stock market prices of firms over a lengthy period of time. Moorkejee and Yu (1999) investigated the seasonality in stock returns on the Shanghai and Shenzen stock markets. They documented the seasonal patterns existing on these exchanges and the effects these factors have on risk in investing in securities listed on these exchanges. In addition they showed that risk in investing is related to the predictability of security prices. Last, Rothlein and Jarrett (2002) investigated the existence of seasonality present in Japanese stock prices, which affect the prices of these securities. They documented the evidence of seasonality in the prices of 55 randomly selected Tokyo Stock Exchange firms over a lengthy period of 18 years (1975 through 1992). In addition, they indicated the accuracy of forecasts or predictions of these firms’ prices are seriously decreased if the seasonal or monthly effects in the time series is not recognized.
II. Methodology and Results The sample includes monthly closing stock prices for 62 randomly selected firms listed on organized exchanges in the USA (NYSE and NASDAQ). Only firms having the complete sets of time series data that covered the study period (April 1992 – September 2002). The study period was lengthy enough to minimize any effects of short-term economic fluctuations. Table 1 contains a list of those firms included in the sample.
III. The Analysis and Results The Census X-12 ARIMA Time Series Decomposition Program analyses the monthly closing prices by assuming that the systematic components are multiplicative in nature. This is consistent with previous
Table 1. Sample: firm with symbol designation abv adrx ahc aig ald amat bmy c cat cers cmcsk cohr cost csco cvs cvx cytc dj f fbf
fdc fnm fox fre g ge hal has hb hd hlt hpq intc jdsu jnj jpm klac ko l lmt low
mcd mdt medi msft mwd nok orcl pfe pmcs rdn sunw t tpth txu unh unp utx vz wmb wmt yhoo
studies noted before and others not noted which assume a relationship between systematic components of a time series. Also, the seasonality component measured is a moving and not stable component, which is more consistent with then the actual economic behaviour of seasonality. In addition, The X-12 procedure is superior to the older Census X-11 procedure, which had a bias in the direction of the centre of the database. The X-12 procedure corrects this by expanding the database by ARIMA modelling which is an automatic feature of the system. Closing prices of securities were investigated because previous studies investigated closing prices. Their rationale was closing prices are consistent with models designed to relate risk, forecasting accuracy and predictability. In addition, it is most consistent with the needs for explaining the weak form of the efficient markets hypothesis as noted before. Significance tests were executed for both stable and moving seasonality. Tests for seasonality assuming stability indicated for the 63 firms that 28 time series were significant at significance levels of ¼ 0.001 or less (that is one chance in a thousand of making a Type I error). Since it is possible that not all of the assumptions of parametric procedures are present, the Kruskal–Wallis (non-parametric procedure) test was executed assuming stable seasonality and found that 39 time series were significant at ¼ 0.01 or less. Thus, 44.4% of the time series were significant at 0.001 for the parametric test and 61.9% of the time series were significant at 0.01 for the non-parametric procedure. Clearly there is evidence of seasonal for
Seasonality of stock market prices
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Table 2. Test of significance before and after seasonal adjustments (F and Kruskal–Wallis Values–see note for significance)
Firm symbol
Seasonality assuming stability (F-value)
Non-parametric test for the presence of seasonality assuming stability (Kruskal–Wallis)
Moving seasonality test (F-value)
Residual seasonality all years (F-value)
Residual seasonality last 3 years (F-value)
abv adrx ahc aig ald amat bmy c cat cers cmcsk cohr cost csco cvs cvx cytc dj f fbf fdc fnm fox fre g ge hal has hb hd hlt hpq intc jdsu jnj jpm klac ko l lmt low mcd mdt medi msft mwd nok orcl pfe pmcs rdn sunw t tpth txu unh unp utx vz wmb wmt yhoo
1.218 137*** 3.629 221*** 4.400 577*** 0.943 731 1.487 471 4.400 577*** 6.253 34*** 1.091 13 1.5373 352*** 2.206 204 4.581 408*** 5.420 118*** 1.486 709 5.296 709*** 3.134 07*** 5.233 416*** 2.551 259 3.418 801*** 7.045 888*** 3.726 28*** 3.926 871*** 0.846 37 2.382 1.441 47 1.434 769 2.817 314 5.494 413*** 4.865 328*** 4.008 917*** 3.017 149 4.249 033*** 8.908 999*** 3.794 787*** 0.900 495 0.903 591 4.407 997*** 3.500 845*** 1.850 988 3.226 568 2.572 029 3.911 407*** 4.379 908*** 3.657 468*** 2.657 079 2.680 601 1.511 881 1.874 167 2.506 472 0.645 011 0.875 541 0.856 083 1.067 866 1.589 576 2.199 799 3.078 374*** 2.459 166 2.532 53 4.632 127*** 2.466 203 2.092 748 1.482 431 2.745 606
17.559 28.6121** 42.092 47** 17.075 57 19.043 12 42.092 47** 59.061 85** 10.4187 53.032 57** 21.886 38 44.488 11** 68.537 86** 14.728 73 41.463 75** 30.995 34** 51.552 49** 27.355 38** 36.442 25** 62.747 14** 41.531 22** 32.090 23** 13.551 52 20.933 95 16.038 93 14.676 66 30.966 51** 52.003 18** 58.981 84** 38.6694** 30.936 08** 43.747 15** 67.935 15** 42.818 05** 10.400 96 9.800 297 44.837 45** 34.4703** 19.453 31 28.729 87** 29.792 58** 40.052 32** 50.796 71** 35.382 38** 37.099 53** 36.286 91** 17.286 68 16.165 28 26.149 01** 12.853 25 11.443 89 8.577 521 12.446 43 12.262 36 18.916 55 36.937 47** 23.042 76 29.5452** 57.775 35** 24.811 33** 30.789 01** 21.730 08 28.332 41**
1.477 708 2.220 402 3.336 302** 1.466 048 1.299 468 3.336 302** 1.824 742* 2.982 542** 1.132 049 0.384 115 2.665 839** 3.482 086** 4.356 625** 2.485 851* 3.152 46** 1.707 326 4.654 27** 1.069 75 3.945 472** 3.219 328** 4.427 971** 3.847 823** 2.119 065 2.851 692** 4.409 819** 1.983 873* 4.535 197** 1.631 787 1.738 279 2.284 902** 2.611 295** 2.722 957** 1.377 37 0.975 709 1.652 036 5.083 088** 2.460 166* 3.624 519** 1.553 191 4.640 389** 3.154 682** 1.493 995 0.833 753 2.172 412* 1.540 264 3.274 444** 3.757 572** 2.909 43** 1.723 273 3.437 484** 1.104 076 1.863 823* 4.994 398** 0.408 088 2.763 445** 2.873 208** 1.516 485 2.741 369** 2.754 166** 2.169 96* 1.516 373 0.703 977
0.26 0.2 0.45 0.24 0.39 0.2 0.34 0.16 0.13 0.37 0.44 0.75 0.26 0.11 0.22 0.55 0.52 0.31 0.21 0.18 0.39 0.25 0.22 0.42 0.27 0.21 0.16 0.22 0.34 0.43 0.17 0.18 0.24 0.34 0.08 0.22 0.25 0.61 0.12 0.1 0.6 0.14 0.15 0.14 0.22 0.45 0.15 0.06 0.11 0.33 0.37 0.23 0.12 0.33 0.53 0.19 0.25 0.51 0.33 0.32 0.8 0.2
0.45 0.22 0.12 0.49 0.23 0.35 0.72 0.16 0.25 0.61 0.72 0.77 0.18 0.1 0.26 0.71 0.45 0.44 0.21 0.41 0.67 0.37 0.16 0.24 0.61 0.16 0.7 0.15 0.19 0.39 0.3 0.48 0.45 0.28 0.08 0.39 0.46 0.2 0.22 0.15 0.36 0.58 0.12 0.08 0.33 0.45 0.25 0.07 0.26 0.27 0.17 0.16 0.42 0.63 0.51 0.43 0.34 0.44 0.53 0.42 0.66 0.2
Note: Signifiance level *** ¼ 0.1%; ** ¼ 1%; * ¼ 5%.
540
Table 3. Final seasonal factors one-year ahead forecast (all firms) Oct. 2002
Nov. 2002
Dec. 2002
Jan. 2003
Feb. 2003
Mar. 2003
Apr. 2003
May 2003
June 2003
July 2003
Aug. 2003
Sep. 2003
abv adrx ahc aig ald amat bmy c cat cers cmcsk cohr cost csco cvs cvx cytc dj f fbf fdc fnm fox fre g ge hal has hb hd hlt
94.688 94.425 92.639 102.697 96.929 92.639 84.353 99.235 94.913 101.714 98.914 79.134 93.066 96.677 100.419 99.235 102.220 95.755 100.320 95.746 94.263 107.504 88.483 105.915 96.714 100.493 97.288 94.258 101.967 93.164 86.944
101.346 94.505 92.138 104.676 98.676 92.138 83.106 98.865 96.156 94.477 100.676 89.442 100.993 99.449 98.082 97.853 98.099 96.793 94.683 99.820 93.683 105.660 91.584 102.997 101.992 97.381 93.640 99.147 105.043 98.399 98.339
105.970 85.982 95.949 105.072 98.211 95.949 87.898 101.093 99.465 107.239 105.158 84.095 106.205 103.479 105.607 99.346 112.444 102.150 96.485 100.707 100.694 106.987 94.256 102.555 107.272 101.124 88.450 94.646 103.987 107.871 96.889
97.954 92.411 90.290 98.021 102.633 90.290 100.463 103.681 96.306 114.799 106.756 106.910 115.226 116.473 98.791 95.302 102.665 96.776 101.729 96.599 107.259 104.826 95.024 107.945 103.198 96.979 81.949 98.881 100.980 103.293 100.232
97.798 92.719 91.747 98.038 100.416 91.747 104.630 95.836 94.264 104.774 104.600 107.185 109.229 95.498 100.559 96.423 111.177 98.943 99.439 100.243 102.962 100.462 98.458 101.166 103.684 98.449 91.280 93.232 99.497 102.538 97.848
103.449 90.407 105.222 98.852 101.858 105.222 115.014 106.042 101.027 111.439 102.046 104.767 110.029 99.479 101.444 101.647 92.841 103.778 104.322 98.172 101.964 99.120 104.083 98.906 105.752 106.126 97.937 102.668 101.315 102.138 98.009
106.137 92.210 108.328 97.069 101.295 108.328 120.036 99.011 106.407 83.821 98.069 107.745 100.833 93.050 112.280 103.806 100.335 100.057 113.807 102.553 106.762 98.501 99.467 101.935 102.924 101.587 108.270 105.240 99.954 103.659 107.704
98.832 104.148 111.776 96.147 97.800 111.776 108.979 102.627 107.220 92.720 98.901 106.109 97.591 99.481 107.722 105.516 101.794 104.937 103.441 105.988 105.380 97.984 105.935 99.548 100.200 101.849 121.476 109.593 97.379 98.701 105.659
99.244 116.698 104.229 99.812 96.292 104.229 112.422 104.700 103.317 100.472 100.796 117.263 99.707 97.622 99.103 102.544 98.451 106.546 103.084 105.327 103.221 94.868 110.672 95.117 99.620 101.846 108.250 103.662 98.401 97.426 107.008
103.555 110.084 100.046 100.114 101.096 100.046 98.714 99.190 102.738 100.864 90.472 100.502 90.290 100.692 91.027 97.869 89.317 100.143 99.860 99.363 99.962 97.470 108.173 97.267 92.777 98.427 104.327 100.168 95.028 101.505 107.121
96.206 113.897 106.917 99.231 102.830 106.917 95.718 97.930 101.817 96.590 95.136 98.815 89.208 102.852 91.565 101.828 95.991 97.857 92.269 97.894 95.980 89.723 103.519 90.172 93.284 100.800 108.380 103.252 96.168 95.212 99.987
94.985 113.303 99.993 100.905 101.884 99.993 89.426 92.256 95.841 90.370 98.463 99.468 88.121 95.396 93.162 98.393 94.626 96.328 90.989 97.941 88.214 97.231 100.346 96.728 93.026 95.191 98.694 95.566 100.813 96.398 94.667
J. Jarrett and E. Kyper
Firm
89.743 90.688 98.174 103.626 96.958 82.293 103.156 90.426 106.747 100.100 97.617 95.806 102.095 93.233 93.483 95.410 91.254 100.433 91.310 102.054 103.567 87.738 83.574 100.124 96.791 100.088 92.215 101.545 97.319 96.299 79.979
94.462 95.042 91.201 105.573 97.496 83.692 105.640 89.402 95.080 89.944 103.541 99.960 94.015 96.639 100.177 103.369 93.126 101.227 77.708 97.114 102.568 92.759 103.384 98.694 99.532 99.015 94.774 104.812 90.166 102.226 89.493
96.233 91.202 105.994 103.865 98.333 94.816 104.153 100.457 92.677 101.130 100.685 110.308 110.424 101.151 103.965 117.728 104.819 98.711 90.820 103.163 113.718 103.261 102.165 105.006 98.698 98.911 97.940 99.094 99.081 103.587 109.155
104.291 107.602 111.181 96.373 100.353 108.774 103.653 102.635 95.277 104.719 99.329 106.852 95.368 106.317 100.896 109.674 114.081 102.483 113.207 91.672 107.352 110.015 95.270 101.644 95.859 101.698 98.528 104.056 93.362 102.012 117.545
98.571 96.428 92.327 97.790 102.484 109.182 94.891 101.596 98.736 103.214 99.910 101.271 107.069 99.152 97.199 104.074 112.207 103.818 79.942 91.543 93.713 106.279 101.881 98.004 93.660 99.324 103.977 99.156 105.867 102.240 100.131
100.537 100.258 114.864 95.686 104.369 111.205 92.283 102.471 96.751 103.070 101.024 99.865 95.546 108.455 112.320 112.314 96.037 98.175 87.256 96.416 100.140 105.906 138.377 94.658 96.705 102.718 106.381 96.663 111.313 103.906 113.172
101.796 106.949 101.852 98.767 102.892 119.179 96.840 103.019 104.325 101.716 101.906 99.161 89.581 99.334 100.637 103.927 95.398 101.400 108.860 103.202 96.684 105.217 98.990 100.794 104.372 106.648 106.925 103.677 106.668 101.263 98.564
108.799 96.852 101.527 99.432 105.475 100.833 101.070 106.357 102.346 104.312 106.050 98.553 90.397 99.833 101.528 96.441 86.222 100.985 95.631 109.761 93.407 97.749 109.016 104.118 105.398 105.163 105.175 101.564 110.688 100.164 96.115
106.855 100.575 99.227 99.828 102.563 109.239 101.536 109.257 101.372 103.991 99.464 98.439 111.484 109.630 102.194 99.360 106.544 102.166 95.647 101.633 92.654 96.765 123.647 102.246 107.354 103.440 102.126 100.817 99.274 101.422 106.126
100.159 107.128 95.234 98.661 100.792 102.388 99.826 102.200 101.780 95.340 98.256 96.483 97.080 98.865 99.769 89.514 106.976 96.995 112.376 103.766 90.904 94.078 82.596 94.937 101.807 99.249 102.295 96.018 99.573 103.614 104.741
103.638 105.868 99.316 99.951 98.615 91.640 98.063 99.456 98.810 95.900 96.624 97.662 102.617 97.672 96.358 86.718 96.703 96.638 126.399 101.206 97.109 97.818 85.669 101.539 102.559 94.865 95.323 91.974 98.851 91.229 87.199
95.344 101.790 89.552 100.989 89.786 87.835 99.331 92.598 105.907 97.238 96.110 95.741 104.480 89.372 92.465 81.285 96.028 97.032 122.287 99.162 109.752 102.782 75.837 98.215 98.030 88.757 94.076 100.651 87.329 92.304 98.131
Seasonality of stock market prices
hpq intc jdsu jnj jpm klac ko l lmt low mcd mdt medi msft mwd nok orcl pfe pmcs rdn sunw t tpth txu unh unp utx vz wmb wmt yhoo
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542 the great proportion and perhaps a majority of the sampled firms’ time series over the period of the study (see Table 2). For the moving seasonality test, 31 time series contained evidence of seasonality at ¼ 0.01 or less and an additional seven time series were significant at ¼ 0.05. Thus 38 (60.3%) of the time series contain evidence of moving seasonality, a clear majority of the time series studied (see Table 2). In turn, each time series was estimated and adjusted individually by the same Census X-12 Procedures and Decomposition Analysis. The seasonally adjusted time series were, in turn, tested for residual seasonality, that is the seasonal component not accounted for by methods for estimating stable and moving seasonality. For all 63 firms, there was no evidence of residual seasonality for all years studied and also for the last three years studied. The F-values computed for the stable and residual seasonality component in Table 2 should be noted. Also note that all F-values are less than unity indicating that the variation in time series values associated with the seasonal component was a small value in comparison with the unexplained or residual variation. The seasonal component was correctly estimated by the X-12 method and procedures and the final seasonal factors for one-year ahead forecasts are presented in Table 3. Last, it was investigated whether there were differences among the monthly seasonal factors. That is, can the hypothesis that there is no difference in the means of the seasonal factors for 12 months of the one-year ahead forecast be rejected? Logically, if this hypothesis is not rejected, the previous findings that seasonal variation was present cannot be corroborated. At ¼ 0.01 or less, the hypothesis was rejected. Since the assumption of homoscedasticity of variances may not be stable for the entire time period studied; the non-parametric Kruskal–Wallis one-way analysis of variance was performed, which corroborated the previous result.
IV. Conclusions It is well documented that there are monthly effects in the closing prices of US stocks. In this study, the existence of seasonal components in closing prices have been indicated substantially of a randomly selected set of firms traded on organized market exchanges in the USA. The results corroborate results of other past studies of international markets and previous studies of markets in the USA where time series monthly components are present in
closing prices and indexes of prices of securities. If seasonality in closing prices exists, it is possible to forecast the seasonal pattern, and thus investors can benefit from this information. Furthermore, the results indicate that the weak form of the efficient markets hypothesis is in question when decisions must be made concerning investing in stock market securities. Seasonality is neither random nor stochastic and it is possible to predict seasonal patterns with accuracy. It is suggested, for purposes of prediction that forecasters predict systematic time series components of closing prices. In addition, the importance of stock returns and portfolio risk cannot be understated. These factors coupled with recognition of systematic time series components in stock prices can improve forecasting for prices of individual securities.
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Seasonality of stock market prices Peiro, A. (1994) Daily seasonality in stock returns: further international evidence, Economics Letters, 45, 227–32. Ray, B., Chen S. and Jarrett, J. (1997) Identifying permanent and temporary components in Japanese stock prices, Financial Engineering and the Japanese Markets, 4, 233–56.
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