is 'malaysia truly asia'? forecasting tourism demand from asean ...

Loganathan Nanthakumar, Thirunaukarasu Subramaniam & Mori KogidForecasting SARIMA processes is completely analogous to theforecasting of ARIMA processes. This can be expressed asARIMA(p,d,q)4 for quarterly data. Where, ‘p’ indicates the order ofautoregressive operator; ‘d’ are the differences; and ‘q’ are the orders ofmoving average operator of non-seasonal and seasonal componentsrespectively. The first two steps in identifying SARIMA models for a dataset are to find ‘d’ and to create the differenced observations:ytd s D( 1−B) ( 1−B ) X t= (7)In this study we used one-period-ahead forecasting using seasonalARIMA modelling. In order to forecast SARIMA model, the meanabsolute percentage error (MAPE) is a useful measure to compare theaccuracy of forecasts between different forecasting models since itmeasures relative performance. If an error is divided by the correspondingobserved value, we have a percentage error. In many empirical studies itappears that, models that tend to do best for within-sample data do notnecessarily forecast better in out-of-the sample. There is no strict rule forthat, but empirical experience suggests that it would be better to selectseveral models based on the Akaike Information Criterion (AIC) andevaluate these on the forecasted data. The last evaluation can be based onroot mean square error (RMSE). The RMSE can be expressed as follows:⎡m⎤2RMSE = ( 1−m) ⎢∑( ŷ n + h − yn+h ) ⎥(8)⎢⎣h=1⎥⎦Meanwhile, in previous literatures, mean absolute percentage error(MAPE) was used to determine suitable models. It worth mentioning, thatMAPE is not very useful for very small observation (Franses, 1998). TheMAPE can be expressed as follows:⎡m⎤MAPE = ( 1−m) ⎢∑( ŷn+h − yn+h )/yn+h ⎥(9)⎢⎣h=1⎥⎦Therefore, ARIMA-SARIMA model selection in this study is basedon AIC forecast evolution results, especially referring to the minimumvalue of RMSE and MAPE.374