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Loganathan Nanthakumar, Thirunaukarasu Subramaniam & Mori Kogid376Table 2 Regression Results and Diagnostic Tests for SARIMAModelsModelsSARIMA(1,1,1)Season-ISeason-IISeason-IIIAR(1)MA(1)AIC valueSARIMA(1,1,2)Season-ISeason-IISeason-IIIAR(1)MA(1)MA(2)AIC valueARIMA(2,1,2)Season-ISeason-IISeason-IIIAR(1)AR(2)MA(1)MA(2)AIC valueCoefficient0.08 (0.24)-0.03 (0.64)0.08 (0.21)0.74 (0.00)*-0.99 (0.00)*-0.680.09 (0.21)-0.02 (0.68)0.09 (0.22)0.81 (0.00)*-1.13 (0.00)*0.14 (0.45)-0.640.08 (0.39)-0.02 (0.68)0.08 (0.40)-0.14 (0.56)0.56 (0.00)*-0.24 (0.38)-0.74 (0.01)*-0.68ARCH-LMTest (a)3.91(0.05)2.21(0.14)1.11(0.29)H o : No serial H o :correlation (b) NormalityTest (c)0.93(0.40)1.12(0.33)1.48(0.24)23.63(0.00)*31.99(0.00)*42.14(0.00)*Note: (a), (b) and (c) indicates Autoregressive conditional heteroscedasticity (ARCH) LMtest, Breusch-Godfrey (BG) serial correlation test and Jarque-Bera (JB) normalitytest. Figures in ( ) indicates probability values. Asterisks (*) denote statisticallysignificant at 1% significance levels. Season-1 (April-June), Season-2 (July-September), Season-3 (October-December)The flow of ACF and PACF shows the autoregressive effects withfirst difference of the historical data. Table 2 indicates AIC values and thedecision to select the most suitable model is by comparing the value ofAIC to the ARIMA models used in this study. The smaller the value ofAIC, the better is the fit in the ARIMA model used. ThereforeARIMA(2,1,2) is relevant because the value of AIC is smaller comparedto ARIMA models. Besides that, diagnostics tests are applied in this studyto determine whether the estimated models deviate from the assumptions
TOURISMOS: AN INTERNATIONAL MULTIDISCIPLINARY JOURNAL OF TOURISMVolume 7, Number 1, Spring-Summer 2012, pp. 367-381UDC: 338.48+640(050)of standard linear regression model. Further, we tested for autoregressiveconditional heteroscedasticity (ARCH), serial correlation using Breusch-Godfrey (BG) test; and normality using Jarque-Bera (JB) test. Ascorrelogram of squared residuals from ARMA(2,2) shows autocorrelationpattern in squared residuals which could be attributed to volatilityclustering, to test the presence of ARCH effect, we compute ARCH-LMtest.The results in Table 2 do not indicate any ARCH effects in all modelsestimated. The Breusch-Godfrey (BG) test of serial correlation indicatesthat serial correlation hypothesis cannot be rejected in all three SARIMAmodels. Meanwhile, normality test using Jarque-Bera (JB) indicates thatnormality in the errors is rejected in all SARIMA models. This indicatesthat all three models are not normally distributed because of someseasonal effects. One interesting results that can be derived from Table 2is that, although seasonal effects have been taken into account in everySARIMA models, the results does not display any significant seasonaldummy effects, either positively or negatively.To choose suitable SARIMA model for this study, we use theinequality coefficients technique. The inequality coefficient ofSARIMA(2,1,2) model are marginally smaller than those of theSARIMA(1,1,1) and SARIMA(1,1,2). Therefore ARIMA(2,1,2) is thebest SARIMA model for this study. For one-step-ahead forecasting whichis applied in this study, the MA(2) model is found to be the best becausethe values of RMSE and MAPE are the lowest as in Table 3 below.Table 3 Summary of Forecast Evolutions of SARIMA ModelsSARIMA ModelsInequality Coefficient SARIMA(1,1,1)SARIMA(1,1,2)SARIMA(2,1,2)RMSE 0.17 0.17 0.16MAE 0.13 0.13 0.12MAPE 302.39 311.97 292.88Theil Coefficient 0.71 0.70 0.68It is clear that the dummy variables which represent seasonalityeffects do not give any clear evidence for ASEAN tourist arrivals toMalaysia. Therefore, in order to forecast ASEAN tourist arrivals usingone-period-ahead approach, this study used only ARIMA(2,1,2) modelwithout any seasonal effect to identify the autoregressive (AR) andmoving average (MA) effects. The ARIMA(2,1,2) model that had been377
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