A practitioners guide to time-series methods for ...

Tourism Management 22 (2001) 403}409

A practitioners guide to time-series methods for tourism demand forecasting * a case study of Durban, South Africa C.J.S.C. Burger , M. Dohnal, M. Kathrada*, R. Law Ecotourism Research Unit, Technikon Natal, P.O. Box 953, Durban 4001, South Africa Faculty of Business and Management, Institute for Applied Studies, Technical University of Brno. Technika 2, 616 69, Brno, Czech Republic Department of Hotel and Tourism Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Received 5 May 1999; accepted 17 October 2000

Abstract This paper compares a variety of time-series forecasting methods to predict tourism demand for a certain region, and is meant as a guideline for tourism forecasters at the commencement of any study who do not have access to large databases in order to create structural models. This study has been conducted at a metropolitan level to forecast the US demand for travel to Durban, South Africa. A brief description of the tourism attractions and context of this area is provided to give a qualitative feel of the system prior to the modelling process. A variety of techniques are employed in this survey, namely namK ve, moving average, decomposition, single exponential smoothing, ARIMA, multiple regression, genetic regression and neural networks with the latter two methods being the non-traditional techniques. O$cial statistical data from 1992 to 1998 was used in this study. The actual and predicted number of visitors are then compared. The survey shows that the neural network method performs the best. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Tourism forecasting; Durban; Genetic regression; Neural networks

1. Introduction Global consumer trends indicate that tourists are becoming more discerning in their choice of destinations. They are furthermore becoming less predictable and more spontaneous in terms of their consumption patterns. It can be claimed that the need for stimulation and new experiences are now the most important motivators for tourism trips. In this respect Africa has much to o!er as a future tourist destination, provided that it is cured of ethnic wars, mismanagement and corruption. Tourism depends entirely on the quality of the resources and political stability of the destination visited. The &magic' of Africa is still perceived as a strong selling point and European and American tourists are attracted due to its uniqueness, which should be kept intact to preserve biodiversity.

* Correspondence address. Ecotourism Research Unit, Technikon Natal, P. O. Box 953, Durban 4001, South Africa. Tel.: #27-31-26116591; fax: #27-31-203-6633. E-mail address: [email protected], [email protected] (M. Kathrada).

South Africa, so much a part of Africa, can play an important role in the growth and development that tourism can o!er to improve the quality of peoples' lives, both as an &escape' for tourists and as a source of employment and income for local communities. South Africa has a well-established network of national and private nature reserves that cater for the environmentally sensitive visitor. The World Tourism Organisation, in its 1995 review of African tourism, considered South Africa to be òne of the most promising tourism destinations on the African continenta (South Africa, 1996). However, South Africa has not yet been able to realise its full potential in tourism and the contribution of tourism to employment, small business development, income and foreign exchange earnings remains limited (South African Government, 1996). Tourism has become a very competitive business. The competitive advantage no longer lies in natural resources only, but increasingly in the level of technology, information and innovation o!ered. Therefore, the future of South African tourism will not be determined by wildlife parks, beautiful scenery, cultural diversity or other resources, but rather by how well such resources are managed and to what extent they complement human skills and innovations.

0261-5177/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 1 - 5 1 7 7 ( 0 0 ) 0 0 0 6 8 - 6

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C.J.S.C. Burger et al. / Tourism Management 22 (2001) 403}409

The African market only grew slightly in 1995 by 1.7 per cent in terms of arrivals and 6 per cent in terms of receipts while Southern Africa was the fastest growing destination in Africa as this region's arrivals increased by 17 per cent and receipts by 10.5 per cent (Caras, 1998). KwaZulu-Natal (Durban lies in this province in South Africa) dominates the domestic tourism market with a market share of 26 per cent (Caras, 1998). Durban and the adjacent areas capture a large proportion of this. KwaZulu-Natal already attracts the third highest number of international tourists (only Gauteng and the Western Cape are visited more often). Foreign visitors spend on average 5 nights in the Durban area and 7 nights in the rest of the province. Cape Town, the rest of KwaZulu-Natal, Johannesburg and the Eastern Cape (in that order) achieve higher average length of stays than Durban (Muller, Haynes, Totman, & Ferendinos, 1998). The average number of days spent by foreign tourists in KwaZulu-Natal increased from 5.05 in 1996 to 7.40 in 1998, but dropped from 6.30 to 5.30 in Durban. Foreign tourists who visit KwaZulu-Natal spend an average of R175 000 per individual while they are in the province. This implies that this province's foreign tourism market is worth in the order of 2 billion Rand or about 300 million US dollars (KwaZulu-Natal Tourism Authority, 1999). In 1999 about 8 million domestic tourists visited KZN while the number of international tourists was about 450 000. It is expected that there will be a 13 per cent increase in international tourists in the year 2000, while domestic and continental tourist arrivals will grow by 3 per cent and 10 per cent, respectively (KwaZulu-Natal Tourism Authority, 1999). Tourism has a signi"cant impact on local economies, directly and indirectly. Since 1995 a steady growth in job creation has underlined the importance of tourism as a job creator. In simple terms, it has been estimated that, for every eight tourists visiting South Africa, one permanent job is created (SATOUR Media Release, 2000). Durban has wonderful natural assets like a warm and sunny all-year-round climate, sub-tropical vegetation, world-class beaches and marine life. The rich historical and cultural background, an impressive hotel base and one of the largest conference centres on the continent are strong selling points to attract foreign visitors. It is also the gateway to one of the most ecologically varied destinations in the world and the newly declared World Heritage Site of St Lucia Wetland. On the negative side, foreign and even local tourists still perceive Durban and KwaZulu-Natal as a security risk and a lack of safety standards is discouraging tourist mobility in many areas of the city and the province. Extensive measures are being taken to rectify this problem (KwaZulu-Natal Tourism Authority, 1999). Forecasting plays a signi"cant role in tourism planning and it is crucial for the private sector in avoiding shortages or surpluses in goods and services. Tourism

investment should be based on professional business planning, long-term operating viability and an achievable vision of the industry's future (Lundberg, Krishnamoorthy, & Stavenga, 1995). The tourism industry needs to reduce the risk of poor decisions. One important way to reduce this risk is by discerning future events or environments more clearly (Smith, 1995). The bene"ts of accurate forecasts are well documented in forecasting literature (Frechtling, 1996; Smith, 1995). Accurate forecasts are valuable to both the private and the public sectors. Forecasting expenditure, for example, is valuable in "nding tourism's relative contribution to income or GDP; forecasting tourist numbers is more helpful in assessing the impact that tourism will make on resources (Bull, 1995). The value of forecasting models rests on their ability to make accurate forecasts. However, as Dharmaratne, (1995) pointed out, most previous forecasting models have failed to perform empirical tests of theoretical speci"cations. Forecasts are only as good as the assumptions of the model used. It is important to know what these assumptions are so that should any of these assumptions prove to be incorrect, forecasts can be re-evaluated. The major problem, however, is the unpredictability of economic trends and outside events and crises such as strikes, crime, disease outbreak, wars or disasters. There is no one, distinct, optimal set of tourism forecasting methods. Rather, quantitative and qualitative techniques developed to forecast variables of interest to business managers and public planners have been used to forecast phenomena of interest to those interested in tourism (Frechtling, 1996). The challenges of successful forecasting are more than just the technical di$culties of developing an accurate model. Forecasting models must be developed with a clear understanding of both the nature of the situation for which a forecast is desired and the resources available for making the forecast (Smith, 1995). It is important to ensure that the variable selected relates directly to the forecast data needed (Sheldon, 1993). This does not mean that forecasts are useless, but that those who use them should be constantly monitoring their operating environment to detect any factors that indicate any inconsistent or irregular patterns. In many instances forecasters and policy makers "nd it di$cult to develop a structural model of the system they are dealing with. The problem is mainly due to the many factors that in#uence the system and acquiring data for all these factors is very di$cult especially when dealing with government authorities. Hence, sometimes qualitative models have to be built to gain insight into the system (Kathrada, Burger, & Dohnal, 1999). In these situations time-series forecasting can give valuable projections although it must be emphasised that these projections are short term only. Chaos theory has largely shown that long-term forecasting is a futile e!ort. Time series


methods are also easy to implement. Cyclical and seasonal e!ects can distinctly be seen in time series data as well as long-term upward or downward trends. This paper reports a study that was undertaken using time-series data of tourist arrivals from the US to Durban, South Africa over the time period 1992}1998 in an attempt to create models that can predict the expected number of tourist arrivals over de"ned future periods.

2. Modelling methods Monthly data over the time period 1992}1998 was obtained from the national tourism authority SATOUR. Fig. 1 shows the actual data used in the model building process, and illustrates the high degree of nonlinearity, seasonality and upward trend in time. Ten per cent of the data were selected randomly to be used as a validation set for all the models in order to provide a fair comparison of the e!ectiveness of the models built. The rest of the data were used in constructing the models. The modelling methods used are namK ve, moving average (3 and 6 months), decomposition, single-exponential smoothing, ARIMA models, multiple regression, genetic regression and neural networks. The "rst "ve models are of the type commonly used in the tourism industry (Frechtling, 1996; Witt & Witt, 1992). The namK ve model operates on the assumption that the number of visitors at time t is the same as the value at time t!1, denoted by ¸ . R\ F "¸ . R R\

(1)

405

The moving-average model uses the average of the last 3 months as a forecast value: F "(¸ #¸ #¸ )/3. R R\ R\ R\

(2)

The decomposition method involves "rst creating a 12 month moving average that is then centred after which seasonal ratios are calculated. The actual rates are then divided by these ratios to give a forecast one year into the future. The following set of equations describe the decomposition method. Frechtling (1996) has a detailed spreadsheet method outlining the procedure. A12 "Average(¸ , 2, ¸ #11) t"1, 2, n!12, R R R C12 "Average(A12 #A12 ) t"1, 2, n!6, R R R> sr "¸ /C12 G R> R

t"1, 2, n!6, i"1, 2, n!12,

SR "Average(sr , sr , sr , sr , sr ) G R R> R> R> R> t"1, 2, n!6, i"1, 2, 12, F "¸ /SR R> R G

t"1, 2, n!12, i"1, 2, 12.

(3)

In the exponential smoothing model, the number of tourists for the next month is predicted using F "F (x)#¸ (1!x) 0(x(1 (4) R R\ R\ to "nd a best "t value of x. An extension to singleexponential smoothing models is the ARIMA type models (Duke University Department of Statistics, 2000; Montgomery & Zarnowitz, 1998). ARIMA is an acronym for Àuto-Regressive Integrated Moving-Averagea.

Fig. 1. USA visitor arrivals to Durban, South Africa.

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Lags of the di!erenced series appearing in the forecasting equation are called àuto-regressivea terms, lags of the forecast errors are `moving averagea terms, and a time series which needs to be di!erenced to be made stationary is said to be an ìntegrateda version of a stationary series. Random-walk and random-trend models, autoregressive models, and exponential smoothing models (i.e., exponential-weighted moving averages) are all special cases of ARIMA models. A non-seasonal ARIMA model is classi"ed as an ÀRIMA (p, d, q)a model, where E p is the number of autoregressive terms, E d is the number of non-seasonal di!erences, and E q is the number of lagged forecast errors in the prediction equation. ARIMA (0, 1, 0) is a random walk function F "#¸ , R R\

(5)

where the constant term is the average di!erence in >. Since it includes (only) a non-seasonal di!erence and a constant term, it is classi"ed as an ÀRIMA (0, 1, 0) model with constant.a ARIMA (1, 1, 0) is a di!erenced "rst-order autoregressive model: If the errors of the random walk model are autocorrelated, the problem may be addressed by adding one lag of the dependent variable to the prediction equation. This would yield the following prediction equation: F "#¸ # (¸ !¸ ), R R\ R\ R\

(6)

where is optimally found from a solver as found in most spreadsheets. ARIMA (0, 2, 1) or (0, 2, 2) without a constant is termed linear exponential smoothing. Linear exponential smoothing models are ARIMA models which use two non-seasonal di!erences in conjunction with MA terms. The second di!erence of a series > is not simply the di!erence between > and itself lagged by two periods, but rather it is the "rst di!erence of the "rst di!erence, i.e. the change-in-the-change of > at period t. A second di!erence of a discrete function is analogous to a second derivative of a continuous function: it measures the àccelerationa or `curvaturea in the function at a given point in time. The ARIMA (0, 2, 2) model without a constant predicts that the second di!erence of the series equals a linear function of the last two forecast errors. This is essentially the same as Brown's linear exponential smoothing model, F "2¸ !¸ !2(1!a)E #(1!a)E . R R\ R\ R\ R\

(7)

The other standard technique used is multiple regression. Here the input variables are the previous 12 months and the output variable the following month. The same vari-

able selection style was used for the genetic regression technique and the neural network. The multiple regression equation generated is of the form F "a #a ¸ #a ¸ #a ¸ #a ¸ R R\ R\ R\ R\ #a ¸ #a ¸ #a ¸ #a ¸ #a ¸ R\ R\ R\ R\ R\ #a ¸ #a ¸ #a ¸ . R\ R\ R\

(8)

The multiple-regression technique is used here mainly to compare its e!ectiveness against the neural network as both are essentially interpolating tools. This is done so as to justify whether or not a more sophisticated technique like neural networks should be used whereas multiple regression is relatively quick and easy to implement. The input to the neural network model is the same as the input to the multiple regression procedure. A short discussion is given as follows on the non-traditional techniques used. 2.1. GMDH (Group method of data handling * genetic regression) algorithm 2.1.1. Polynomial support Function This method involves sorting, that is successive testing of models selected out of a set of candidate models according to a speci"ed criterion. Nearly all known GMDH algorithms use polynomial support functions. General connection between input and output variables can be found in the form of a functional Volterra series, whose discrete analogue is known as the Kolmogorov}Gabor polynomial (Lemke & Mueller, 1997; Ivakhnenko & MuK ller, 1995), + + + y"a # a x # a x x G G GH G H G G H + + + # a xx x , GHI G H I G H I

(9)

where X(x , x ,2, x ) is the vector of input variables + and A(a , a ,2, a ) is the vector of the summand coe$ + cients. The complexity of the model structure is estimated by the number of polynomial terms used. The sorting procedure consists in computing the criterion as the structure of the model gradually changes. The input data sample is a matrix containing N levels (points) of observations over a set of M variables. The sample is divided into two parts. Two-thirds of points having a high variance make up the learning sub-sample N , and the remaining one-third of points from the check sub-sample N . The learning sample is used to derive estimates for the coe$cients of the polynomial, and the check sub-sample is used to choose the structure of the optimal model, that is, one for which the regularity


criterion AR(s) takes on a minimal value

3. Results and analysis

1 , AR(s)" (y !>K (B))Pmin. (10) G G N G To obtain a smooth exhaustive-search curve, which would permit one to formulate the exhaustive-search termination rule, the exhaustive search is performed on models classed into groups of an equal complexity. The "rst layer uses the information contained in every column of the sample, that is, the search is applied to models of form: y"a #a x (i"1, 2, M). (11) G The output variable must be speci"ed in advance by the experimenter. Only a small number of variables (usually, F"3), showing the best results in the "rst layer, are allowed to form second-layer candidate models of the form y"a #a x #a x G H

( j"1, 2, M).

407

(12)

2.2. Neural networks Neural networks are being increasingly used in various industries with many recent applications in the tourism industry (Law & Au, 1999; Uysal & Sherif El Roubi, 1999). A brief account of neural networks is given here. A more in depth account can be obtained from Masters (1993). In recent years the application of arti"cial neural networks has been the subject of much study. This new interest in approach to modelling is due to the fact that neural networks generally have high degrees of freedom, thus they can capture the non-linearity of a process being studied much better than regression techniques. In addition, neural networks have the ability to model systems with multiple inputs and multiple outputs. Arti"cial neural networks are composed of many elements called neurons. Neural networks have one input layer, one output layer and one or more hidden layers. A set of input and output variables are entered and the network attempts to map (train) the process by which the input variables are linked to the output variables. Neural networks are trained by adjusting the connection weights (= ) by some suitable optimisation GHI algorithm such as genetic optimisation or simulated annealing so that the di!erence between the predicted and the observed outputs is made as small as possible. A common algorithm used for training is the backpropagation algorithm with momentum. The output from one neuron is calculated by applying a transfer function to the weighted summation of its input to give an output, which in turn can serve as inputs to other neurons. Commonly used transfer functions in the hidden layer is the sigmoid function which gives values in the range from 0 and 1 while it is common to have a linear function in the output layer.

The accuracy of the models discussed was assessed using the mean absolute percentage error (MAPE) and the Pearson product moment correlation coe$cient (r): MAPE"X !> /n;100% (i"1, 2, n) G G

(13)

r"[n(X > )!(X )(> )]/([nX!(X )] G G G G G G ;[n>!(> )] (i"1, 2, n). (14) G G Table 1 shows the empirical results of the di!erent models. The namK ve, moving average and single-exponential models perform fairly similarly and with reasonably good accuracy. Similar results in using these models were obtained by (Law & Au, 1999). The best value of x obtained in the single-exponential smoothing was 0.2. The decomposition method performed poorly (r!0.791). This is probably due to the fact that decomposition method cannot calculate reasonable seasonable ratios on such a highly non-linear dataset, which is showing an increasing trend. The ARIMA models all performed similarly indicating very much that once they are e!ective in removing the seasonal component. The MAPE achieved is approximately 11.4 per cent and r of 0.995 for all the ARIMA models. The ARIMA (0, 1, 0) had a of 190, showing that the data is fairly stationary, hence the reason for all the ARIMA models behaving similarly. The ARIMA (1, 1, 0) had a of !0.17 and the ARIMA (0, 2, 2) had and a of 1.445. In these cases the values of and a were found using the built in solver in a spreadsheet program. In comparing the two regression procedures, multiple regression (MAPE!7.20) produces better results than the GMDH regression procedure (MAPE!20.58). This is mainly due to the GMDH algorithm setting aside a large part of the input data for the validation set hence

Table 1 Accuracy comparison in sample for di!erent time-series models

NamK ve 3-month MA 6-month MA Single-exponential smoothing (0.2) Decomposition ARIMA (0, 1, 0) ARIMA (1, 1, 0) ARIMA (0, 2, 2) GMDH Multiple regression Neural networks (1 month forecast) Neural networks (3 month forecast) Neural networks (6 month forecast) Neural networks (12 month forecast)

r

MAPE

0.908 0.853 0.907 0.870 0.791 0.995 0.995 0.993 0.702 0.944 0.979 0.779 0.789 0.892

11.24 12.85 10.89 10.04 20.56 11.30 11.33 11.50 20.58 7.20 5.07 14.37 15.56 11.00

408


not being able to completely follow all the patterns that are evident in this relatively small dataset. GMDH algorithms work best for large datasets involving industrial online applications. The neural network performs the best achieving the highest r (0.979) and lowest MAPE (5.07%). This can be attributed to the complexity of neural network models, in that they have a high degree of freedom, due to the large number of interconnections between the nodes. Hence there is a larger parameter space that can be searched in order to obtain a higher r. Regression models are constrained by the number of coe$cients in the model, which is usually small. The neural network outperforms the multiple regression procedure by an MAPE of just over 2 per cent. Thereafter an attempt was made to forecast 3, 6 and 12 months into the future using the neural network, since this was the best performing model. This yielded interesting results. The prediction for 3 and 6 months into the future was poorer that the prediction one month in the future, which is intuitive as usually the uncertainty into the future increases with time. However the prediction for 12 months into the future was better that the 3 and 6 month prediction. Here it must be noted that, since the neural network was trained on the last 12 months of visitor arrivals as an input, a similar pattern due to seasonal variations would be expected 12 months into the future. Hence the better performance of the network arises form an inherent bias within the model. Depending on the desired level of accuracy, relatively simple models can be initially used to obtain a &quantitative feel' of their predictive strengths, and serve as a basis for comparing against other more complex models. In practice, it is suggested that several simple spreadsheet models be built and if the results are not satisfactory, then more complex models like neural networks can be used.

A tourist forecaster or policy maker can at least make a good estimate of visitor arrivals in the absence of structural data by just using the available time series data. Relatively simple methodologies can be used on a spreadsheet and can give reasonable estimates albeit a short time period into the future. More complex methods like neural networks can give reasonable estimates further into the future. From the point of view of Durban, the forecaster has a con"dent estimate of the visitor arrivals that subsequently can be used in reports to decision makers. Moreover the model is such that it can easily be updated as time goes on; hence a constant track can be kept of the expected number of visitor arrivals. The models can be extended to cover more regions or even predict the total expected number of visitor arrivals. The neural network performed best of all the methodologies and it is suggested that this method be used in time series forecasting as the innate model complexity is far better able to handle non-linear behaviour. It was also found that the longer the forecasting period the poorer will be the prediction, but, interestingly, if the forecast period is exactly one year into the future the network performs fairly well, due to repetitions of expected similar seasonal patterns occurring. While positive research "ndings have been obtained, further work needs to be done to generalise the "ndings to other tourist receiving destinations. That is, future studies can employ the same forecasting models, but with di!erent data series, for forecasting accuracy testing. Moreover, additional forecasting techniques can be incorporated into future studies, particularly chaos theory if large enough data sets are available (Kantz & Schreiber, 1997). It would also be interesting to compare the accuracy of time-series models with casual regression models. References

4. Conclusions This research has attempted to examine the forecasting accuracy of various time series tourism forecasting models. Tourist arrivals from the United States to Durban in South Africa were used for model calibration and testing. The Pearson product moment correlation coe$cient and mean absolute percentage error were adopted as the measurements for forecasting accuracy. Experimental results indicated that the neural network attained the highest forecasting accuracy among all the involved models. Time series analysis can be a valuable tool for tourism forecasters at the beginning of a forecasting project. It allows the forecaster to view trends in visitor behaviour, both long-term and cyclical. The various methods outlined in this paper have tried to capture these trends to predict the number of visitor arrivals.

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