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Leading indicator tourism forecasts
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Tourism Management 24 (2003) 503–510
Leading indicator tourism forecasts Nada Kulendrana, Stephen F. Wittb,* a
School of Applied Economics, Victoria University, Melbourne, VIC 8001, Australia b School of Management, University of Surrey, Guildford, Surrey GU2 7XH, UK Received 1 September 2002; accepted 11 December 2002
Abstract Leading indicators have been widely used in general business forecasting situations, but only rarely in a tourism context. In this study leading indicator transfer function (TF) models are developed to generate forecasts of international tourism demand from the UK to six major destinations. The out-of-sample forecasting accuracy is compared with the accuracy of forecasts generated by univariate ARIMA and error correction models (ECMs). The inclusion of a causal input within an ARIMA time series framework (TF model) does not result in an improvement in forecasting performance. The time series models outperform the ECM for shortterm forecasting, but the ECM generates more accurate longer-term forecasts. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Leading indicator; Transfer function; ARIMA model; Error correction model; Forecast accuracy
1. Introduction Future changes in some aggregate economic activity (such as the demand for international tourism) are often foreshadowed by changes in other time series variables. These latter economic variables are known as leading (economic) indicators. Leading indicators have been widely used in general business forecasting situations. For a review see Lahiri and Moore (1991) and for more recent studies see Estrella and Mishkin (1998) and Qi (2001). The use of leading indicators is based on the view that market economies experience business cycles within which repetitive sequences occur. These cycles consist of expansions/contractions in various economic activities, but these expansions/contractions do not occur at exactly the same time for different activities, i.e. some economic activities are leading and some lagging. The leading indicator approach involves identifying the repetitive sequences within business cycles and using them for forecasting. Traditionally the main interest in leading economic indicator forecasting has been to *Corresponding author. Tel.: +44-1483-686323; fax: +44-1483686301. E-mail addresses: [email protected] (N. Kulendran), [email protected] (S.F. Witt).
forecast turning points in an economic activity, but ‘‘Leading indicators can be and are being used to forecast over uniform calendar time units, and not just around turning points’’ (Lahiri & Moore, 1991, p. 2). Forecasting performance assessment is therefore not restricted to the turning point outcome, but can be broadened to error magnitude measures. Thus, for example, Weller (1990) and Turner, Kulendran, and Fernando (1997) measure the accuracy of leading indicator forecasts in terms of mean absolute percentage error (MAPE). Although Sheldon and Var (1985) pointed out the need for research into the use of economic indicators in tourism forecasting, little attention has been focused upon leading economic indicators in the tourism forecasting literature. However, papers on the topic have been published recently by Turner et al. (1997) and Rossello-Nadal (2001). Wong (1997) also investigates the use of business cycles to forecast tourism demand but does not follow a leading indicator approach. Turner et al. (1997) examine various potential leading indicators (such as origin country income and exchange rate) in the context of forecasting the demand for tourism from Japan, New Zealand, the UK and the USA to Australia. They construct transfer function (TF) models incorporating these leading indicators which they use to forecast tourism demand. The accuracy of
0261-5177/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0261-5177(03)00010-4
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the TF model forecasts is compared with the accuracy of forecasts generated by univariate ARIMA and na.ıve ‘no change’ models. The Turner et al. (1997) study (which measures accuracy in terms of error magnitude) shows that the leading indicator model outperforms no change, but is inconclusive as to whether leading indicator models tend to generate more accurate tourism forecasts than univariate ARIMA models, and the concluding comments highlight the need for further research. Rossello-Nadal (2001) examines a wide range of potential leading indicators, which are taken to be indicative of either economic activity, financial activity or prices, in the context of forecasting the demand for tourism from Germany and the UK to the Balearic Islands, Spain. He constructs regression models where the leading indicators appear as independent variables, and uses the models to generate forecasts. The accuracy of these forecasts is compared with the accuracy of forecasts generated by univariate ARIMA and ‘no change’ models. The Rossello-Nadal (2001) study (which examines accuracy in terms of both error magnitude and turning points) concludes that the leading indicator model generates more accurate forecasts than no change, and is also more accurate than the ARIMA model in terms of forecasting turning points. However, the study is inconclusive as to whether leading indicator models generate more accurate tourism forecasts than univariate ARIMA models when accuracy is measured in terms of error magnitude. The purposes of this paper are as follows: first, to expand the very limited existing empirical evidence on the relative forecasting performance of leading indicator models in tourism; second, to provide a more comprehensive study than previous ones in terms of comparing in a tourism context the forecasting performances of leading indicator and error correction models (ECMs); and third, to examine a greater number of tourism demand series than in previous studies in order to permit general conclusions to be drawn from the empirical results with greater confidence.
2. Leading indicator model The time series to be examined relate to UK outbound holiday tourism demand over the period 1978–1995, and comprise quarterly observations on the number of tourist visits (V ). Six major destinations for UK tourists are considered: Germany, Greece, Netherlands, Portugal, Spain and the USA. The data are based on the results of the International Passenger Survey and relate to visits which involve at least one overnight stay. They were supplied by the Office for National Statistics. The particular data series and time period are chosen to permit a direct comparison with previous empirical results on the forecasting performance of tourism
demand models published by Kulendran and Witt (2001). Specifically, the latter study examines the forecasting accuracy of the ECM in terms of MAPE. Although the leading indicator approach is sometimes referred to as measurement without theory, economic theory does give clues as to the selection of appropriate indicators. In this study the economic variables which generally feature as explanatory variables in econometric models of international holiday tourism demand (income and holiday prices) are considered as potential leading indicators (Witt & Witt, 1995). The set of indicators therefore comprises relative price (RP) (destination country consumer price index/origin country consumer price index), exchange rate between the destination country currency and origin country currency (ER), exchange rate adjusted relative price (ERRP) ((ER) (RP)), origin country real personal disposable income (PDI), and origin country real gross domestic product (GDP). Data on consumer prices and exchange rates are published in OECD Main Economic Indicators and income data in Economic Trends. In this study the leading indicator modelling approach followed by Turner et al. (1997) is adopted, i.e. a singleinput TF modelling approach. This assumes that the values of the output series (tourism demand) are related to the values of the input series (the indicator). However, the current value of the output series is also a function of previous values of the output series (autoregressive component) and current and lagged values of a white noise process (moving average component). As the objective is to discover whether a variable is a leading indicator, tourism demand should be related to past values of the indicator. In order to discover whether an input series leads tourism demand, cross-correlation functions (which describe the extent to which two series are correlated) are examined. (All the TF model estimations in this study were carried out using the SAS program, version 8.) To avoid the problem of misleading correlations which can occur if autocorrelation is present in either the input or output series, seasonal univariate ARIMA models are fitted to each of the series and the cross-correlation coefficients (which measure the degree of association) of the two residual series are calculated (Haugh, 1976). In order for the input series to lead the output series, it is necessary to obtain statistically significant cross-correlation coefficients at positive lags. The residuals from the two series are the pre-whitened values (i.e. the values after all known patterns, such as trend, seasonality and autocorrelation, have been removed) of tourism demand and the leading indicator. To ensure stationarity in order to obtain the appropriate sample autocorrelation plots to identify the parsimonious ARIMA models, logarithmic transformations and first and seasonal differences are taken. The residuals were checked for autocorrelation at lags 6, 12, 18 and 24, but the calculated chi-square
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values for the various lags were found to be not significant at the 5% level. This indicates that the residual series do not have problems with serial correlation and are indeed white noise. The forecasting models were estimated over the period 1978 (quarter 1) to 1992 (quarter 4) and used to forecast tourist flows for one, two, four and eight quarters ahead. They were then re-estimated for the period 1978 (quarter 1) to 1993 (quarter 1), and again used to generate forecasts for one, two, four and eight quarters ahead. This process is repeated several times, adding a further observation at each stage. The latest observation used in model estimation for eight-quartersahead forecasts is 1993 (quarter 4), for four-quartersahead forecasts 1994 (quarter 4), for two-quarters-ahead forecasts 1995 (quarter 2) and for one-quarter-ahead forecasts 1995 (quarter 3). Forecasting performance is measured in terms of MAPE (Witt & Witt, 1992, Chapter 6). Table 1 shows the positive lags for which statistically significant cross-correlations were obtained (5% level) for the various destination countries. The lead time between the various indicators and tourism demand ranges from one quarter to nine quarters. However, a lead time of two quarters is considered the minimum necessary to be of practical use in forecasting tourist flows; a one-quarter lead period does not allow data on the leading indicator to become available in time to generate useful forecasts. It is clear from Table 1 that the exchange-rate-adjusted relative price is the most widely applicable leading economic indicator, playing a useful forecasting role for five of the six destination countries. The next most common indicators are exchange rate and personal disposable income (each three cases). There is just one useful leading economic indicator for Germany (ERRP), Netherlands (PDI) and Spain (ERRP), whereas for each of Greece and Portugal there are four potential leading indicator forecasting models and for the USA three. Where there are several potential models, that leading indicator model which overall generates the most accurate forecasts for a particular destination is selected; thus, the leading indicator used in the TF forecasting models for Greece and Portugal is
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PDI and for the USA is ERRP. Just two leading indicator variables are therefore selected—ERRP (three destinations) and PDI (three destinations). The choice of ERRP as a measure of tourism prices in preference to either simply exchange rate or relative price supports previous findings (Martin & Witt, 1987), and the choice of PDI as a measure of origin country income in preference to GDP supports expectations as holiday tourism is under consideration. In common with generally accepted practice in tourism demand modelling, and also in order to satisfy the assumption of constant variance of the error term, the dependent and explanatory variables are specified in logarithmic form (Witt & Witt, 1995). Single-input TF models are fitted to the differenced series on tourism demand and the chosen explanatory variable (ERRP or PDI) (see above). The lag length for the selected input series is given in Table 1. As seasonally unadjusted quarterly time series are under consideration both first (to remove trend) and fourth (to remove seasonality) differences are applied. The results are presented in Table 2. It can be seen from Table 2 that all coefficients are significantly different from zero at the 5% level for all destinations apart from Portugal (Eq. (1)). Although a statistically significant cross-correlation was obtained for a three-period lag in the case of PDI for Portugal, and this leading indicator generated the most accurate forecasts of tourism demand from the UK to Portugal, the coefficient of PDI was not statistically significant at the 5% level. In the identification of the TF model, it is necessary to apply the same pre-whitening transformation to both the input and output series in order to preserve the integrity of the functional relationship (Makridakis, Wheelwright, & McGee, 1989, p. 490). However, the seasonal pattern of the leading indicator may not be the same as the seasonal pattern of tourism demand. Therefore, the discrepancy between the significance of the cross-correlation and the coefficient of PDI may be due to the presence of different seasonal patterns in the tourism demand and PDI series (Edlund & Karlsson, 1993). The next most accurate leading indicator that resulted in a statistically significant TF for
Table 1 Positive lags with statistically significant correlations (5%), 1978–1992 Leading indicator
RP ER ERRP PDI GDP
Destination country Germany
Greece
Netherlands
Portugal
Spain
USA
— — 8 — —
4 9 6 4 —
— — 1 7 —
— 8 8 3 8
— — 7 — —
1 3 3 — 8
Notes: RP denotes relative price, ER exchange rate, ERRP exchange rate adjusted relative price, PDI personal disposable income and GDP gross domestic product.
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Table 2 Estimated TF models, 1978–1992
Notes: *denotes significant at 5% level. Figures in parentheses are t values. B is the backward shift operator. D1 and D4 represent first and fourth differences, respectively. et is white noise.
Portugal is the exchange-rate-adjusted relative price. This model is also presented in Table 2 (Eq. (2)). Diagnostic testing is a standard statistical testing procedure to determine model validity, and the diagnostic test results for the TF models show that, at the 5% significance level, there are no autocorrelation problems (chi-square test). Furthermore, the crosscorrelation coefficients between the pre-whitened input series and the TF residuals for different lags are not significant at the 5% level (chi-square test) for Germany, Greece, Netherlands, Portugal and the USA, and at the 1% level for Spain, indicating that the assumption of independence between the two series is satisfied (a necessary condition for the validity of TF models).
3. Error correction model In order to see whether the TF models compare favourably with other forecasting methods that incorporate explanatory variables, ECM forecasting performance is examined. ECMs express the current value of the dependent variable as a linear function of past values of the dependent variable, current and past values of the explanatory variables, and the previous value(s) of the error term from the cointegration relationship(s). Kulendran and Witt (2001) have generated ECM forecasts of UK outbound holiday tourism demand using the same data set as that used in this study, i.e. 1978–1992 for model estimation and 1993–1995 for outof-sample forecasting performance assessment. The error correction modelling procedure and estimation results from that study are now discussed. (For a more detailed discussion of error correction modelling see Song and Witt (2000); and for the full set of empirical results see Kulendran and Witt (2001).)
The effect of origin country population (P) on tourism demand is accommodated by modifying the forecast variable to become international demand per capita (V =P). (In order to generate forecasts of tourism demand, corresponding to the output variable from the TF model, the forecast values of V =P are multiplied by the known values of P:) Other (seasonally unadjusted) long-run demand influences included in the model are as follows. First, as holiday tourism is considered, the appropriate income variable is UK real personal disposable income per capita (PDI/P). Second, the cost of living for tourists in the destination country (proxied by the consumer price index, adjusted by the exchange rate with the origin country) relative to the cost of living for tourists in the UK (ERRP) allows for substitution possibilities between foreign tourism and both domestic and non-holiday alternatives. Third, the cost of living for tourists in the destination country relative to a weighted average (based on previous market shares) of the cost of living for tourists in the nine most popular (for UK residents) competing foreign destinations (ERRPS) permits substitution possibilities between them. Fourth, the real standard unrestricted economy airfare from the UK to the destination country (F ) is taken to be representative of general travel cost movements, since on short-haul routes airfares must be competitive with surface travel costs. Fifth, the airfare from the UK to the destination relative to a weighted average of airfares to competing foreign destinations (FS) again allows for the impact of substitutes. Shortrun influences on tourism demand are seasonality effects, together with various one-off events represented by dummy variables: the 1979 oil crisis (1979(1)–1979(4)); the bombing of Libya by the USA in 1986 (1986(2)– 1986(3)); the 1990 invasion of Kuwait by Iraq (1990(3)– 1990(4)); and the 1991 Gulf War (1991(1)–1991(3)).
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Additionally, a lagged dependent variable is included (simple dynamics). The justification for the explanatory variables included and the forms of the variables used is discussed elsewhere (Witt & Witt, 1992, 1995). UK population figures are published in the Monthly Digest of Statistics. Air fares are published in the ABC World Airways Guide/OAG World Airways Guide. As with the TF models, the dependent and explanatory variables are specified in logarithmic form. It is likely that the data series on UK outbound tourist visits exhibit trend and seasonality. Tests for stationarity are often referred to as unit root tests, and evidence of a unit root at zero frequency implies that the stochastic trend is non-stationary, whereas evidence of unit roots at semi-annual and annual frequencies implies that the stochastic seasonality is non-stationary. Hylleberg, Engle, Granger, and Yoo (1990) have proposed a strategy that tests for unit roots (i.e. how many times a series must be differenced in order to achieve stationarity, known as the order of integration) at both semiannual and annual frequencies, as well as the usual zero frequency, and this standard procedure is used to examine the time series properties of the holiday visit, income and price variables for each tourist flow. As a result first or fourth differences are taken, so avoiding the potential problem of over-differencing if both first and fourth differences are taken. The testing was carried out using MicroFit 4.0 (Pesaran & Pesaran, 1997), a computer package which was also used for subsequent estimation and testing of the cointegration relationships and ECMs. The cointegration relationships are the longrun equilibrium relationships between the economic variables that share a common trend. If variables do not move together in the long run, then there is no long-run equilibrium relationship and the variables are not cointegrated. If two variables are cointegrated and they move away from their equilibrium relationship with each other, they will return towards their equilibrium relationship, and the model of this process of reverting to the equilibrium is the ECM. The results of the unit root tests for the dependent and explanatory variables for tourism from the UK to the six destinations under consideration show that the order of integration of income as well as UK outbound tourism to Greece is I(1,1,1). This implies that the series have a unit root at zero frequency and unit roots at seasonal semi-annual and annual frequencies. In order to perform a standard cointegration test at zero frequency, the seasonal unit roots at semi-annual and annual frequencies need to be removed, so the filter S1 ðBÞ ¼ ð1 þ B þ B2 þ B3 Þ is applied, where B is the backward shift operator (Engle, Granger, & Hallman, 1989). The order of integration of UK outbound tourism to Portugal and the USA, the airfare to Germany, and the relative airfare to Spain is I(1,1,0), so these series have a unit root at zero frequency and a
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unit root at seasonal semi-annual frequency. In order to perform a standard cointegration test at zero frequency, the seasonal unit root at semi-annual frequency needs to be removed, so the filter S2 ðBÞ ¼ ð1 þ BÞ is applied to each of these series. Having identified the common trends between the tourism demand variable and the income and price variables for UK outbound tourism to Germany, Greece, the Netherlands, Portugal, Spain and the USA, Johansen’s (1988) full-information maximum likelihood is used to estimate the long-run cointegration relationships. However, it is possible to have multiple long-run relationships, and thus this possibility is first investigated using the Johansen and Juselius (1990) test. The log-likelihood ratio statistics for determining the number of long-run cointegration relationships for tourist flows to each destination show that at the 5% level there is one statistically significant long-run relationship for tourism demand to Greece, the Netherlands and Portugal, but two such relationships for tourism demand to Germany, Spain and the USA. The error terms from each of the significant estimated long-run cointegration relationships generated using Johansen’s (1988) full-information maximum likelihood uit ði ¼ 1; 2; y; 9Þ are included in the short-run dynamic ECMs which are used to generate the forecasts. The error terms allow the long-run information lost due to differencing to be reinstated in the ECMs. Ordinary least squares is used to estimate the latter for each of the UK outbound holiday flows, and the results are presented in Table 3. As each of the error terms from the significant long-run relationships is statistically significant at the 5% level in the ECMs, they are all included. In each case, up to four lags of the tourist visit, income and various price series are included, but only significant terms are retained for final estimation, with the least significant terms being deleted first. As a result, the models for the various destinations contain different explanatory variables. The effects of the special events (oil crisis, USA–Libya conflict, Iraq invasion of Kuwait, Gulf War) were examined, but none of the coefficients was statistically significant at the 5% level, and thus no special event dummy variables are included in the shortrun dynamic models. Seasonal dummies are included where appropriate (i.e. in all cases other than where fourth differencing is used); although in some cases one of the seasonal dummy variable coefficients is not statistically significant, the full set of seasonal dummies is retained. For those series which are I(1,1,1) (holiday visits to Greece and income), fourth differences (D4 ) are taken in order to achieve stationarity and estimate the short-run dynamic models. However, for those series which have a unit root at zero frequency and at seasonal semi-annual frequency (but not at seasonal annual frequency), i.e. those series which are I(1,1,0) (holiday visits to the USA and Portugal, airfare to Germany,
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Table 3 Estimated ECMs, 1978–1992
Source: Kulendran and Witt (2001). Notes: *denotes significant at 5% level. Figures in parentheses are t values. D1 and D4 represent first and fourth differences, respectively. Ut denotes error correction term. DW, Durbin–Watson statistic; LM(4), Lagrange multiplier chi-square statistic to test for fourth-order serial correlation; RESET, chi-square test of functional form; BP, Breusch–Pagan chi-square test for heteroskedasticity; Chow, post-sample predictive failure test, over period January 1993–December 1995. Critical values at 5% significance level are w2 ð1Þ ¼ 3:84 and w2 ð4Þ ¼ 9:49:
relative airfare to Spain), first differencing (D1 ) is used rather than fourth differencing (so avoiding the problem of over-differencing) in order to achieve stationarity and estimate the ECMs. The ECMs shown in Table 3 are valid because the error correction terms and the F statistics are significant, and the results of the other diagnostic tests are also generally satisfactory at the 5% level. The Durbin– Watson test indicates absence of first-order serial correlation, and the Lagrange multiplier chi-square test indicates that there is no fourth-order serial correlation. The RESET chi-square test of functional form shows a possible problem with the model for Greece, but the test result is marginal and the statistic is not significant at the 1% level. The Breusch–Pagan chi-square test for heteroskedasticity indicates a problem with the model for Greece, particularly as heteroskedasticity is still present at the 1% significance level. The Chow F test demonstrates absence of post-sample predictive failure. Therefore, the results of the diagnostic tests show that only model which is not wholly satisfactory is that for Greece.
4. Univariate ARIMA model In order to determine whether the use of leading indicators improves forecasting performance, the accuracy of out-of-sample forecasts generated by the TF models selected in Table 2 is compared with the accuracy of univariate ARIMA models. The ARIMA modelling approach expresses the current time series value as a linear function of past time series values (autoregressive component) and current and lagged values of a white noise process (moving average component). Seasonal ARIMA models are fitted to stationary time series, and seasonal data require regular and seasonal differencing to achieve stationarity. The seasonal (quarterly) ARIMA model is denoted ARIMA ðp; d; qÞðP; D; QÞ4 ; where p and P are the orders of the non-seasonal and seasonal autoregressive parameters, q and Q are the orders of the non-seasonal and seasonal moving average parameters, and d and D are the numbers of regular and seasonal differences required, respectively.
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Kulendran and Witt (2001) fit seasonal univariate ARIMA models to each of the six tourism demand series. The models estimated for the various destination countries after taking first and fourth differences are as follows: Germany (2,1,0)(0,1,1)4; Greece (1,1,0)(1,1,0)4; the Netherlands (2,1,0)(1,1,0)4; Portugal (2,1,0)(0,1,1)4; Spain (0,1,0)(1,1,0)4; and the USA (0,1,0)(1,1,0)4.
5. Forecasting performance 5.1. TF vs. univariate ARIMA model The MAPE values for the TF and univariate ARIMA (first and fourth differences) models for the period 1993–1995 are presented in Table 4. When the average MAPE values for each forecast horizon are considered, it is clear that the TF model does not outperform the univariate ARIMA model. For one, four and eight quarters ahead, the univariate ARIMA model generates more accurate forecasts than the TF model, whereas for two quarters ahead, the TF model is slightly more accurate. When individual destinations are examined, the TF model outperforms the univariate model in 50% of cases: twice for one quarter ahead, four times for two quarters ahead, and three times for both four and eight quarters ahead. It appears therefore that the forecasting performance of the two models is roughly the same, with perhaps the univariate ARIMA model generating somewhat more accurate forecasts. Certainly, the move from an ARIMA model involving a single time series to one involving two time series does not result in an improvement in forecasting performance. When the forecasting performances of the two leading indicator input variables are examined separately the results do not change. The overall MAPEs for Greece and the Netherlands are 19.1 for the TF model (PDI) and 18.5 for the univariate ARIMA model; and those for Germany, Portugal, Spain and the USA are 24.4 for
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the TF model (ERRP) and 20.2 for the univariate ARIMA model. 5.2. TF vs. ECM The relative forecasting performance results for the ECM are presented in Table 5. The MAPE values averaged across all destination countries are shown for each forecast horizon. The TF model is more accurate for short-term forecasting (one and two quarters ahead) than the ECM, whereas the ECM exhibits superior performance for near medium-term forecasting (four quarters ahead) and markedly superior performance for more distant medium-term forecasting (eight quarters ahead). These results conform to prior expectations regarding the nature of the models; time series models may be expected to generate more accurate short-term forecasts and ECMs more accurate longer-term forecasts. Indeed, for eight quarters ahead the ECM also generates considerably more accurate forecasts than the univariate ARIMA model (Tables 4 and 5).
6. Conclusions The use of leading indicator transfer function models to generate tourism demand forecasts has been Table 5 Forecasting accuracy TF vs. ECM (MAPE), 1993–1995, averaged across destinations Forecast horizon
1 2 4 8
Forecasting method
quarter quarters quarters quarters a
ECMa
TF
18.8 18.4 16.5 18.3
16.9 17.2 20.4 35.9
Source: Kulendran and Witt (2001).
Table 4 Forecasting accuracy TF vs. univariate ARIMA (MAPE), 1993–1995 Forecast horizon
1 quarter 2 quarters 4 quarters 8 quarters
Forecasting method
TF ARIMA TF ARIMA TF ARIMA TF ARIMA
Destination country Germany
Greece
Neth
Portugal
Spain
USA
Average
21.11 23.18 24.17 24.52 24.87 15.10 42.52 30.13
13.57 14.81 10.97 13.52 12.90 16.20 21.31 26.19
28.64 17.81 13.57 16.25 12.37 19.30 39.13 23.99
19.29 17.51 25.58 21.80 34.28 12.55 64.41 21.99
10.12 8.08 11.75 11.29 16.78 11.13 27.09 44.71
8.71 7.97 17.37 17.66 21.35 23.08 20.77 33.09
16.9 14.9 17.2 17.5 20.4 16.2 35.9 30.0
Notes: TF input variables: Germany, Portugal, Spain, USA exchange rate adjusted relative price; Greece, Netherlands personal disposable income.
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illustrated using data on holiday visits from the UK to six major destinations. This expands the very limited existing literature on leading indicator tourism forecasting, and is more comprehensive than previous studies in terms of both the number of tourism series examined and the inclusion of error correction models in the relative accuracy evaluation. Previous empirical forecasting comparisons of the leading indicator model with the univariate ARIMA model where accuracy is measured in terms of error magnitude have been inconclusive (Turner et al., 1997; Rossello-Nadal, 2001). By contrast, the present study has shown clearly that the leading indicator model does not outperform the univariate ARIMA model. The implication for tourism practitioners is that there is no advantage in terms of forecast accuracy in moving from a univariate ARIMA model to a more complex leading indicator model. This study has shown that, for the particular data set examined, the inclusion of a causal (explanatory variable) input within an ARIMA time series framework does not result in an improvement in forecasting performance. Now, just as the TF model allows explanatory variables to be incorporated within an ARIMA time series framework, the causal structural time series model (STSM) allows explanatory variables to be incorporated within a structural time series framework. Turner and Witt (2001) have compared the forecasting performance of the causal STSM with the univariate STSM in a tourism context, and their empirical results show that the causal STSM does not outperform the univariate STSM. The Turner and Witt results therefore support the findings of the current study that moving from a univariate to a causal time series modelling approach does not improve forecasting performance. It appears, therefore, that there is significant evidence to suggest that it is not worthwhile for tourism practitioners to attempt to use causal rather than univariate time series forecasting models. An empirical forecasting comparison of the leading indicator TF model with the ECM, using data on UK holiday tourism to six destinations, has demonstrated that the time series model is more accurate for shortterm forecasting, but the ECM is more accurate for medium-term forecasting. For the more distant medium term (eight quarters ahead) the superiority of the ECM over the ARIMA models (TF and univariate) is very clear. This suggests that time series models are likely to generate more accurate short-term forecasts of tourism demand and ECMs more accurate longer-term forecasts.
References Edlund, P., & Karlsson, S. (1993). Forecasting the Swedish unemployment rate: Var vs. transfer function modelling. International Journal of Forecasting, 9, 61–76. Engle, R. F., Granger, C. W. J., & Hallman, J. J. (1989). Merging short- and long-run forecasts: An application of seasonal cointegration to monthly electricity sales forecasting. Journal of Econometrics, 40, 45–62. Estrella, A., & Mishkin, F. S. (1998). Predicting US recessions: Financial variables as leading indicators. The Review of Economics and Statistics, 80(1), 45–61. Haugh, L. D. (1976). Checking the independence of two covariancestationary time series: A univariate residual cross-correlation approach. Journal of the American Statistical Association, 71, 378–385. Hylleberg, S., Engle, R. F., Granger, C. W. J., & Yoo, B. S. (1990). Seasonal integration and cointegration. Journal of Econometrics, 44, 215–238. Johansen, S. (1988). Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control, 12, 231–254. Johansen, S., & Juselius, K. (1990). Maximum likelihood estimation and inference on cointegration with application to the demand for money. Oxford Bulletin of Economics and Statistics, 52, 169–210. Kulendran, N., & Witt, S. F. (2001). Cointegration versus least squares regression. Annals of Tourism Research, 28, 291–311. Lahiri, K., & Moore, G. H. (1991). Leading economic indicators: New approaches and forecasting records. Cambridge: Cambridge University Press. Makridakis, S., Wheelwright, S. C., & McGee, V. E. (1989). Forecasting: Methods and applications (2nd ed.). New York: Wiley. Pesaran, M. H., & Pesaran, B. (1997). Working with Microfit 4.0: Interactive econometric analysis. Oxford: Oxford University Press. Qi, M. (2001). Predicting US recessions with leading indicators via neural network models. International Journal of forecasting, 17, 383–401. Rossello-Nadal, J. (2001). Forecasting turning points in international visitor arrivals in the Balearic Islands. Tourism Economics, 7, 365–380. Sheldon, P. J., & Var, T. (1985). Tourism forecasting: A review of empirical research. Journal of Forecasting, 4, 183–195. Song, H., & Witt, S. F. (2000). Tourism demand modelling and forecasting: Modern econometric approaches. Oxford: Pergamon. Turner, L. W., Kulendran, N., & Fernando, H. (1997). The use of composite national indicators for tourism forecasting. Tourism Economics, 3, 309–317. Turner, L. W., & Witt, S. F. (2001). Forecasting tourism using univariate and multivariate structural time series models. Tourism Economics, 7, 135–147. Weller, B. R. (1990). Predicting small region sectoral responses to changes in aggregate economic activity: A time series approach. Journal of Forecasting, 9, 273–281. Witt, S. F., & Witt, C. A. (1992). Modeling and forecasting demand in tourism. London: Academic Press. Witt, S. F., & Witt, C. A. (1995). Forecasting tourism demand: A review of empirical research. International Journal of Forecasting, 11, 447–475. Wong, K. K. F. (1997). The relevance of business cycles in forecasting international tourist arrivals. Tourism Management, 18, 581–586.
Tourism Management 24 (2003) 503–510
Leading indicator tourism forecasts Nada Kulendrana, Stephen F. Wittb,* a
School of Applied Economics, Victoria University, Melbourne, VIC 8001, Australia b School of Management, University of Surrey, Guildford, Surrey GU2 7XH, UK Received 1 September 2002; accepted 11 December 2002
Abstract Leading indicators have been widely used in general business forecasting situations, but only rarely in a tourism context. In this study leading indicator transfer function (TF) models are developed to generate forecasts of international tourism demand from the UK to six major destinations. The out-of-sample forecasting accuracy is compared with the accuracy of forecasts generated by univariate ARIMA and error correction models (ECMs). The inclusion of a causal input within an ARIMA time series framework (TF model) does not result in an improvement in forecasting performance. The time series models outperform the ECM for shortterm forecasting, but the ECM generates more accurate longer-term forecasts. r 2003 Elsevier Science Ltd. All rights reserved. Keywords: Leading indicator; Transfer function; ARIMA model; Error correction model; Forecast accuracy
1. Introduction Future changes in some aggregate economic activity (such as the demand for international tourism) are often foreshadowed by changes in other time series variables. These latter economic variables are known as leading (economic) indicators. Leading indicators have been widely used in general business forecasting situations. For a review see Lahiri and Moore (1991) and for more recent studies see Estrella and Mishkin (1998) and Qi (2001). The use of leading indicators is based on the view that market economies experience business cycles within which repetitive sequences occur. These cycles consist of expansions/contractions in various economic activities, but these expansions/contractions do not occur at exactly the same time for different activities, i.e. some economic activities are leading and some lagging. The leading indicator approach involves identifying the repetitive sequences within business cycles and using them for forecasting. Traditionally the main interest in leading economic indicator forecasting has been to *Corresponding author. Tel.: +44-1483-686323; fax: +44-1483686301. E-mail addresses: [email protected] (N. Kulendran), [email protected] (S.F. Witt).
forecast turning points in an economic activity, but ‘‘Leading indicators can be and are being used to forecast over uniform calendar time units, and not just around turning points’’ (Lahiri & Moore, 1991, p. 2). Forecasting performance assessment is therefore not restricted to the turning point outcome, but can be broadened to error magnitude measures. Thus, for example, Weller (1990) and Turner, Kulendran, and Fernando (1997) measure the accuracy of leading indicator forecasts in terms of mean absolute percentage error (MAPE). Although Sheldon and Var (1985) pointed out the need for research into the use of economic indicators in tourism forecasting, little attention has been focused upon leading economic indicators in the tourism forecasting literature. However, papers on the topic have been published recently by Turner et al. (1997) and Rossello-Nadal (2001). Wong (1997) also investigates the use of business cycles to forecast tourism demand but does not follow a leading indicator approach. Turner et al. (1997) examine various potential leading indicators (such as origin country income and exchange rate) in the context of forecasting the demand for tourism from Japan, New Zealand, the UK and the USA to Australia. They construct transfer function (TF) models incorporating these leading indicators which they use to forecast tourism demand. The accuracy of
0261-5177/03/$ - see front matter r 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0261-5177(03)00010-4
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the TF model forecasts is compared with the accuracy of forecasts generated by univariate ARIMA and na.ıve ‘no change’ models. The Turner et al. (1997) study (which measures accuracy in terms of error magnitude) shows that the leading indicator model outperforms no change, but is inconclusive as to whether leading indicator models tend to generate more accurate tourism forecasts than univariate ARIMA models, and the concluding comments highlight the need for further research. Rossello-Nadal (2001) examines a wide range of potential leading indicators, which are taken to be indicative of either economic activity, financial activity or prices, in the context of forecasting the demand for tourism from Germany and the UK to the Balearic Islands, Spain. He constructs regression models where the leading indicators appear as independent variables, and uses the models to generate forecasts. The accuracy of these forecasts is compared with the accuracy of forecasts generated by univariate ARIMA and ‘no change’ models. The Rossello-Nadal (2001) study (which examines accuracy in terms of both error magnitude and turning points) concludes that the leading indicator model generates more accurate forecasts than no change, and is also more accurate than the ARIMA model in terms of forecasting turning points. However, the study is inconclusive as to whether leading indicator models generate more accurate tourism forecasts than univariate ARIMA models when accuracy is measured in terms of error magnitude. The purposes of this paper are as follows: first, to expand the very limited existing empirical evidence on the relative forecasting performance of leading indicator models in tourism; second, to provide a more comprehensive study than previous ones in terms of comparing in a tourism context the forecasting performances of leading indicator and error correction models (ECMs); and third, to examine a greater number of tourism demand series than in previous studies in order to permit general conclusions to be drawn from the empirical results with greater confidence.
2. Leading indicator model The time series to be examined relate to UK outbound holiday tourism demand over the period 1978–1995, and comprise quarterly observations on the number of tourist visits (V ). Six major destinations for UK tourists are considered: Germany, Greece, Netherlands, Portugal, Spain and the USA. The data are based on the results of the International Passenger Survey and relate to visits which involve at least one overnight stay. They were supplied by the Office for National Statistics. The particular data series and time period are chosen to permit a direct comparison with previous empirical results on the forecasting performance of tourism
demand models published by Kulendran and Witt (2001). Specifically, the latter study examines the forecasting accuracy of the ECM in terms of MAPE. Although the leading indicator approach is sometimes referred to as measurement without theory, economic theory does give clues as to the selection of appropriate indicators. In this study the economic variables which generally feature as explanatory variables in econometric models of international holiday tourism demand (income and holiday prices) are considered as potential leading indicators (Witt & Witt, 1995). The set of indicators therefore comprises relative price (RP) (destination country consumer price index/origin country consumer price index), exchange rate between the destination country currency and origin country currency (ER), exchange rate adjusted relative price (ERRP) ((ER) (RP)), origin country real personal disposable income (PDI), and origin country real gross domestic product (GDP). Data on consumer prices and exchange rates are published in OECD Main Economic Indicators and income data in Economic Trends. In this study the leading indicator modelling approach followed by Turner et al. (1997) is adopted, i.e. a singleinput TF modelling approach. This assumes that the values of the output series (tourism demand) are related to the values of the input series (the indicator). However, the current value of the output series is also a function of previous values of the output series (autoregressive component) and current and lagged values of a white noise process (moving average component). As the objective is to discover whether a variable is a leading indicator, tourism demand should be related to past values of the indicator. In order to discover whether an input series leads tourism demand, cross-correlation functions (which describe the extent to which two series are correlated) are examined. (All the TF model estimations in this study were carried out using the SAS program, version 8.) To avoid the problem of misleading correlations which can occur if autocorrelation is present in either the input or output series, seasonal univariate ARIMA models are fitted to each of the series and the cross-correlation coefficients (which measure the degree of association) of the two residual series are calculated (Haugh, 1976). In order for the input series to lead the output series, it is necessary to obtain statistically significant cross-correlation coefficients at positive lags. The residuals from the two series are the pre-whitened values (i.e. the values after all known patterns, such as trend, seasonality and autocorrelation, have been removed) of tourism demand and the leading indicator. To ensure stationarity in order to obtain the appropriate sample autocorrelation plots to identify the parsimonious ARIMA models, logarithmic transformations and first and seasonal differences are taken. The residuals were checked for autocorrelation at lags 6, 12, 18 and 24, but the calculated chi-square
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values for the various lags were found to be not significant at the 5% level. This indicates that the residual series do not have problems with serial correlation and are indeed white noise. The forecasting models were estimated over the period 1978 (quarter 1) to 1992 (quarter 4) and used to forecast tourist flows for one, two, four and eight quarters ahead. They were then re-estimated for the period 1978 (quarter 1) to 1993 (quarter 1), and again used to generate forecasts for one, two, four and eight quarters ahead. This process is repeated several times, adding a further observation at each stage. The latest observation used in model estimation for eight-quartersahead forecasts is 1993 (quarter 4), for four-quartersahead forecasts 1994 (quarter 4), for two-quarters-ahead forecasts 1995 (quarter 2) and for one-quarter-ahead forecasts 1995 (quarter 3). Forecasting performance is measured in terms of MAPE (Witt & Witt, 1992, Chapter 6). Table 1 shows the positive lags for which statistically significant cross-correlations were obtained (5% level) for the various destination countries. The lead time between the various indicators and tourism demand ranges from one quarter to nine quarters. However, a lead time of two quarters is considered the minimum necessary to be of practical use in forecasting tourist flows; a one-quarter lead period does not allow data on the leading indicator to become available in time to generate useful forecasts. It is clear from Table 1 that the exchange-rate-adjusted relative price is the most widely applicable leading economic indicator, playing a useful forecasting role for five of the six destination countries. The next most common indicators are exchange rate and personal disposable income (each three cases). There is just one useful leading economic indicator for Germany (ERRP), Netherlands (PDI) and Spain (ERRP), whereas for each of Greece and Portugal there are four potential leading indicator forecasting models and for the USA three. Where there are several potential models, that leading indicator model which overall generates the most accurate forecasts for a particular destination is selected; thus, the leading indicator used in the TF forecasting models for Greece and Portugal is
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PDI and for the USA is ERRP. Just two leading indicator variables are therefore selected—ERRP (three destinations) and PDI (three destinations). The choice of ERRP as a measure of tourism prices in preference to either simply exchange rate or relative price supports previous findings (Martin & Witt, 1987), and the choice of PDI as a measure of origin country income in preference to GDP supports expectations as holiday tourism is under consideration. In common with generally accepted practice in tourism demand modelling, and also in order to satisfy the assumption of constant variance of the error term, the dependent and explanatory variables are specified in logarithmic form (Witt & Witt, 1995). Single-input TF models are fitted to the differenced series on tourism demand and the chosen explanatory variable (ERRP or PDI) (see above). The lag length for the selected input series is given in Table 1. As seasonally unadjusted quarterly time series are under consideration both first (to remove trend) and fourth (to remove seasonality) differences are applied. The results are presented in Table 2. It can be seen from Table 2 that all coefficients are significantly different from zero at the 5% level for all destinations apart from Portugal (Eq. (1)). Although a statistically significant cross-correlation was obtained for a three-period lag in the case of PDI for Portugal, and this leading indicator generated the most accurate forecasts of tourism demand from the UK to Portugal, the coefficient of PDI was not statistically significant at the 5% level. In the identification of the TF model, it is necessary to apply the same pre-whitening transformation to both the input and output series in order to preserve the integrity of the functional relationship (Makridakis, Wheelwright, & McGee, 1989, p. 490). However, the seasonal pattern of the leading indicator may not be the same as the seasonal pattern of tourism demand. Therefore, the discrepancy between the significance of the cross-correlation and the coefficient of PDI may be due to the presence of different seasonal patterns in the tourism demand and PDI series (Edlund & Karlsson, 1993). The next most accurate leading indicator that resulted in a statistically significant TF for
Table 1 Positive lags with statistically significant correlations (5%), 1978–1992 Leading indicator
RP ER ERRP PDI GDP
Destination country Germany
Greece
Netherlands
Portugal
Spain
USA
— — 8 — —
4 9 6 4 —
— — 1 7 —
— 8 8 3 8
— — 7 — —
1 3 3 — 8
Notes: RP denotes relative price, ER exchange rate, ERRP exchange rate adjusted relative price, PDI personal disposable income and GDP gross domestic product.
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Table 2 Estimated TF models, 1978–1992
Notes: *denotes significant at 5% level. Figures in parentheses are t values. B is the backward shift operator. D1 and D4 represent first and fourth differences, respectively. et is white noise.
Portugal is the exchange-rate-adjusted relative price. This model is also presented in Table 2 (Eq. (2)). Diagnostic testing is a standard statistical testing procedure to determine model validity, and the diagnostic test results for the TF models show that, at the 5% significance level, there are no autocorrelation problems (chi-square test). Furthermore, the crosscorrelation coefficients between the pre-whitened input series and the TF residuals for different lags are not significant at the 5% level (chi-square test) for Germany, Greece, Netherlands, Portugal and the USA, and at the 1% level for Spain, indicating that the assumption of independence between the two series is satisfied (a necessary condition for the validity of TF models).
3. Error correction model In order to see whether the TF models compare favourably with other forecasting methods that incorporate explanatory variables, ECM forecasting performance is examined. ECMs express the current value of the dependent variable as a linear function of past values of the dependent variable, current and past values of the explanatory variables, and the previous value(s) of the error term from the cointegration relationship(s). Kulendran and Witt (2001) have generated ECM forecasts of UK outbound holiday tourism demand using the same data set as that used in this study, i.e. 1978–1992 for model estimation and 1993–1995 for outof-sample forecasting performance assessment. The error correction modelling procedure and estimation results from that study are now discussed. (For a more detailed discussion of error correction modelling see Song and Witt (2000); and for the full set of empirical results see Kulendran and Witt (2001).)
The effect of origin country population (P) on tourism demand is accommodated by modifying the forecast variable to become international demand per capita (V =P). (In order to generate forecasts of tourism demand, corresponding to the output variable from the TF model, the forecast values of V =P are multiplied by the known values of P:) Other (seasonally unadjusted) long-run demand influences included in the model are as follows. First, as holiday tourism is considered, the appropriate income variable is UK real personal disposable income per capita (PDI/P). Second, the cost of living for tourists in the destination country (proxied by the consumer price index, adjusted by the exchange rate with the origin country) relative to the cost of living for tourists in the UK (ERRP) allows for substitution possibilities between foreign tourism and both domestic and non-holiday alternatives. Third, the cost of living for tourists in the destination country relative to a weighted average (based on previous market shares) of the cost of living for tourists in the nine most popular (for UK residents) competing foreign destinations (ERRPS) permits substitution possibilities between them. Fourth, the real standard unrestricted economy airfare from the UK to the destination country (F ) is taken to be representative of general travel cost movements, since on short-haul routes airfares must be competitive with surface travel costs. Fifth, the airfare from the UK to the destination relative to a weighted average of airfares to competing foreign destinations (FS) again allows for the impact of substitutes. Shortrun influences on tourism demand are seasonality effects, together with various one-off events represented by dummy variables: the 1979 oil crisis (1979(1)–1979(4)); the bombing of Libya by the USA in 1986 (1986(2)– 1986(3)); the 1990 invasion of Kuwait by Iraq (1990(3)– 1990(4)); and the 1991 Gulf War (1991(1)–1991(3)).
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Additionally, a lagged dependent variable is included (simple dynamics). The justification for the explanatory variables included and the forms of the variables used is discussed elsewhere (Witt & Witt, 1992, 1995). UK population figures are published in the Monthly Digest of Statistics. Air fares are published in the ABC World Airways Guide/OAG World Airways Guide. As with the TF models, the dependent and explanatory variables are specified in logarithmic form. It is likely that the data series on UK outbound tourist visits exhibit trend and seasonality. Tests for stationarity are often referred to as unit root tests, and evidence of a unit root at zero frequency implies that the stochastic trend is non-stationary, whereas evidence of unit roots at semi-annual and annual frequencies implies that the stochastic seasonality is non-stationary. Hylleberg, Engle, Granger, and Yoo (1990) have proposed a strategy that tests for unit roots (i.e. how many times a series must be differenced in order to achieve stationarity, known as the order of integration) at both semiannual and annual frequencies, as well as the usual zero frequency, and this standard procedure is used to examine the time series properties of the holiday visit, income and price variables for each tourist flow. As a result first or fourth differences are taken, so avoiding the potential problem of over-differencing if both first and fourth differences are taken. The testing was carried out using MicroFit 4.0 (Pesaran & Pesaran, 1997), a computer package which was also used for subsequent estimation and testing of the cointegration relationships and ECMs. The cointegration relationships are the longrun equilibrium relationships between the economic variables that share a common trend. If variables do not move together in the long run, then there is no long-run equilibrium relationship and the variables are not cointegrated. If two variables are cointegrated and they move away from their equilibrium relationship with each other, they will return towards their equilibrium relationship, and the model of this process of reverting to the equilibrium is the ECM. The results of the unit root tests for the dependent and explanatory variables for tourism from the UK to the six destinations under consideration show that the order of integration of income as well as UK outbound tourism to Greece is I(1,1,1). This implies that the series have a unit root at zero frequency and unit roots at seasonal semi-annual and annual frequencies. In order to perform a standard cointegration test at zero frequency, the seasonal unit roots at semi-annual and annual frequencies need to be removed, so the filter S1 ðBÞ ¼ ð1 þ B þ B2 þ B3 Þ is applied, where B is the backward shift operator (Engle, Granger, & Hallman, 1989). The order of integration of UK outbound tourism to Portugal and the USA, the airfare to Germany, and the relative airfare to Spain is I(1,1,0), so these series have a unit root at zero frequency and a
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unit root at seasonal semi-annual frequency. In order to perform a standard cointegration test at zero frequency, the seasonal unit root at semi-annual frequency needs to be removed, so the filter S2 ðBÞ ¼ ð1 þ BÞ is applied to each of these series. Having identified the common trends between the tourism demand variable and the income and price variables for UK outbound tourism to Germany, Greece, the Netherlands, Portugal, Spain and the USA, Johansen’s (1988) full-information maximum likelihood is used to estimate the long-run cointegration relationships. However, it is possible to have multiple long-run relationships, and thus this possibility is first investigated using the Johansen and Juselius (1990) test. The log-likelihood ratio statistics for determining the number of long-run cointegration relationships for tourist flows to each destination show that at the 5% level there is one statistically significant long-run relationship for tourism demand to Greece, the Netherlands and Portugal, but two such relationships for tourism demand to Germany, Spain and the USA. The error terms from each of the significant estimated long-run cointegration relationships generated using Johansen’s (1988) full-information maximum likelihood uit ði ¼ 1; 2; y; 9Þ are included in the short-run dynamic ECMs which are used to generate the forecasts. The error terms allow the long-run information lost due to differencing to be reinstated in the ECMs. Ordinary least squares is used to estimate the latter for each of the UK outbound holiday flows, and the results are presented in Table 3. As each of the error terms from the significant long-run relationships is statistically significant at the 5% level in the ECMs, they are all included. In each case, up to four lags of the tourist visit, income and various price series are included, but only significant terms are retained for final estimation, with the least significant terms being deleted first. As a result, the models for the various destinations contain different explanatory variables. The effects of the special events (oil crisis, USA–Libya conflict, Iraq invasion of Kuwait, Gulf War) were examined, but none of the coefficients was statistically significant at the 5% level, and thus no special event dummy variables are included in the shortrun dynamic models. Seasonal dummies are included where appropriate (i.e. in all cases other than where fourth differencing is used); although in some cases one of the seasonal dummy variable coefficients is not statistically significant, the full set of seasonal dummies is retained. For those series which are I(1,1,1) (holiday visits to Greece and income), fourth differences (D4 ) are taken in order to achieve stationarity and estimate the short-run dynamic models. However, for those series which have a unit root at zero frequency and at seasonal semi-annual frequency (but not at seasonal annual frequency), i.e. those series which are I(1,1,0) (holiday visits to the USA and Portugal, airfare to Germany,
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Table 3 Estimated ECMs, 1978–1992
Source: Kulendran and Witt (2001). Notes: *denotes significant at 5% level. Figures in parentheses are t values. D1 and D4 represent first and fourth differences, respectively. Ut denotes error correction term. DW, Durbin–Watson statistic; LM(4), Lagrange multiplier chi-square statistic to test for fourth-order serial correlation; RESET, chi-square test of functional form; BP, Breusch–Pagan chi-square test for heteroskedasticity; Chow, post-sample predictive failure test, over period January 1993–December 1995. Critical values at 5% significance level are w2 ð1Þ ¼ 3:84 and w2 ð4Þ ¼ 9:49:
relative airfare to Spain), first differencing (D1 ) is used rather than fourth differencing (so avoiding the problem of over-differencing) in order to achieve stationarity and estimate the ECMs. The ECMs shown in Table 3 are valid because the error correction terms and the F statistics are significant, and the results of the other diagnostic tests are also generally satisfactory at the 5% level. The Durbin– Watson test indicates absence of first-order serial correlation, and the Lagrange multiplier chi-square test indicates that there is no fourth-order serial correlation. The RESET chi-square test of functional form shows a possible problem with the model for Greece, but the test result is marginal and the statistic is not significant at the 1% level. The Breusch–Pagan chi-square test for heteroskedasticity indicates a problem with the model for Greece, particularly as heteroskedasticity is still present at the 1% significance level. The Chow F test demonstrates absence of post-sample predictive failure. Therefore, the results of the diagnostic tests show that only model which is not wholly satisfactory is that for Greece.
4. Univariate ARIMA model In order to determine whether the use of leading indicators improves forecasting performance, the accuracy of out-of-sample forecasts generated by the TF models selected in Table 2 is compared with the accuracy of univariate ARIMA models. The ARIMA modelling approach expresses the current time series value as a linear function of past time series values (autoregressive component) and current and lagged values of a white noise process (moving average component). Seasonal ARIMA models are fitted to stationary time series, and seasonal data require regular and seasonal differencing to achieve stationarity. The seasonal (quarterly) ARIMA model is denoted ARIMA ðp; d; qÞðP; D; QÞ4 ; where p and P are the orders of the non-seasonal and seasonal autoregressive parameters, q and Q are the orders of the non-seasonal and seasonal moving average parameters, and d and D are the numbers of regular and seasonal differences required, respectively.
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Kulendran and Witt (2001) fit seasonal univariate ARIMA models to each of the six tourism demand series. The models estimated for the various destination countries after taking first and fourth differences are as follows: Germany (2,1,0)(0,1,1)4; Greece (1,1,0)(1,1,0)4; the Netherlands (2,1,0)(1,1,0)4; Portugal (2,1,0)(0,1,1)4; Spain (0,1,0)(1,1,0)4; and the USA (0,1,0)(1,1,0)4.
5. Forecasting performance 5.1. TF vs. univariate ARIMA model The MAPE values for the TF and univariate ARIMA (first and fourth differences) models for the period 1993–1995 are presented in Table 4. When the average MAPE values for each forecast horizon are considered, it is clear that the TF model does not outperform the univariate ARIMA model. For one, four and eight quarters ahead, the univariate ARIMA model generates more accurate forecasts than the TF model, whereas for two quarters ahead, the TF model is slightly more accurate. When individual destinations are examined, the TF model outperforms the univariate model in 50% of cases: twice for one quarter ahead, four times for two quarters ahead, and three times for both four and eight quarters ahead. It appears therefore that the forecasting performance of the two models is roughly the same, with perhaps the univariate ARIMA model generating somewhat more accurate forecasts. Certainly, the move from an ARIMA model involving a single time series to one involving two time series does not result in an improvement in forecasting performance. When the forecasting performances of the two leading indicator input variables are examined separately the results do not change. The overall MAPEs for Greece and the Netherlands are 19.1 for the TF model (PDI) and 18.5 for the univariate ARIMA model; and those for Germany, Portugal, Spain and the USA are 24.4 for
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the TF model (ERRP) and 20.2 for the univariate ARIMA model. 5.2. TF vs. ECM The relative forecasting performance results for the ECM are presented in Table 5. The MAPE values averaged across all destination countries are shown for each forecast horizon. The TF model is more accurate for short-term forecasting (one and two quarters ahead) than the ECM, whereas the ECM exhibits superior performance for near medium-term forecasting (four quarters ahead) and markedly superior performance for more distant medium-term forecasting (eight quarters ahead). These results conform to prior expectations regarding the nature of the models; time series models may be expected to generate more accurate short-term forecasts and ECMs more accurate longer-term forecasts. Indeed, for eight quarters ahead the ECM also generates considerably more accurate forecasts than the univariate ARIMA model (Tables 4 and 5).
6. Conclusions The use of leading indicator transfer function models to generate tourism demand forecasts has been Table 5 Forecasting accuracy TF vs. ECM (MAPE), 1993–1995, averaged across destinations Forecast horizon
1 2 4 8
Forecasting method
quarter quarters quarters quarters a
ECMa
TF
18.8 18.4 16.5 18.3
16.9 17.2 20.4 35.9
Source: Kulendran and Witt (2001).
Table 4 Forecasting accuracy TF vs. univariate ARIMA (MAPE), 1993–1995 Forecast horizon
1 quarter 2 quarters 4 quarters 8 quarters
Forecasting method
TF ARIMA TF ARIMA TF ARIMA TF ARIMA
Destination country Germany
Greece
Neth
Portugal
Spain
USA
Average
21.11 23.18 24.17 24.52 24.87 15.10 42.52 30.13
13.57 14.81 10.97 13.52 12.90 16.20 21.31 26.19
28.64 17.81 13.57 16.25 12.37 19.30 39.13 23.99
19.29 17.51 25.58 21.80 34.28 12.55 64.41 21.99
10.12 8.08 11.75 11.29 16.78 11.13 27.09 44.71
8.71 7.97 17.37 17.66 21.35 23.08 20.77 33.09
16.9 14.9 17.2 17.5 20.4 16.2 35.9 30.0
Notes: TF input variables: Germany, Portugal, Spain, USA exchange rate adjusted relative price; Greece, Netherlands personal disposable income.
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illustrated using data on holiday visits from the UK to six major destinations. This expands the very limited existing literature on leading indicator tourism forecasting, and is more comprehensive than previous studies in terms of both the number of tourism series examined and the inclusion of error correction models in the relative accuracy evaluation. Previous empirical forecasting comparisons of the leading indicator model with the univariate ARIMA model where accuracy is measured in terms of error magnitude have been inconclusive (Turner et al., 1997; Rossello-Nadal, 2001). By contrast, the present study has shown clearly that the leading indicator model does not outperform the univariate ARIMA model. The implication for tourism practitioners is that there is no advantage in terms of forecast accuracy in moving from a univariate ARIMA model to a more complex leading indicator model. This study has shown that, for the particular data set examined, the inclusion of a causal (explanatory variable) input within an ARIMA time series framework does not result in an improvement in forecasting performance. Now, just as the TF model allows explanatory variables to be incorporated within an ARIMA time series framework, the causal structural time series model (STSM) allows explanatory variables to be incorporated within a structural time series framework. Turner and Witt (2001) have compared the forecasting performance of the causal STSM with the univariate STSM in a tourism context, and their empirical results show that the causal STSM does not outperform the univariate STSM. The Turner and Witt results therefore support the findings of the current study that moving from a univariate to a causal time series modelling approach does not improve forecasting performance. It appears, therefore, that there is significant evidence to suggest that it is not worthwhile for tourism practitioners to attempt to use causal rather than univariate time series forecasting models. An empirical forecasting comparison of the leading indicator TF model with the ECM, using data on UK holiday tourism to six destinations, has demonstrated that the time series model is more accurate for shortterm forecasting, but the ECM is more accurate for medium-term forecasting. For the more distant medium term (eight quarters ahead) the superiority of the ECM over the ARIMA models (TF and univariate) is very clear. This suggests that time series models are likely to generate more accurate short-term forecasts of tourism demand and ECMs more accurate longer-term forecasts.
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