Forecasting the number of foreign tourist using intervention and ARCH analysis

Time series data modeling with ARIMA requires that the input time series data is stationary, ergodic, and free from outliers. The number of foreign tourists visiting Indonesia for the January 2016 – July 2021 period continued to increase until the end of 2019. Entering 2020, to be precise around March – April 2020 there was a very sharp decline in the number of foreign tourists due to the COVID-19 pandemic in Indonesia. The ARIMA method with intervention is useful for overcoming time series data modeling with interventions such as data on the number of foreign tourists to Indonesia. In this study, data modeling on the number of foreign tourists to Indonesia was carried out using intervention analysis and ARCH. From the data after the stationary process, ARIMA (1,1,0) was obtained and the intervention factor had to be added starting April 2021 or T=52. The hypothesis test of ARIMA parameters (1,1,0) plus intervention, showed that the AR1 factor was not significant while the intervention factor was very significant, so the model became ARIMA (0,1,0) plus intervention. The homogeneity test of the error with the residual squared ACF plot and the Lagrange Multiplier test (LM test) showed significant test results at lag 1 and lag 2. This indicated the presence of heteroscedasticity in the error. Heteroscedasticity often occurs in data on the number of foreign tourists who have high volatility. Residual modeling with ARCH (1.0) and ARCH (2.0) shows that the ARCH (2.0) is not significant, so the ARCH(1.0) model is used for the error. Forecasting the number of foreign tourists visiting using the ARIMA(0,1,0) plus intervention method and ARCH(1,0) shows that the model has met the assumption of homoscedasticity and has a small Mean Absolute Percentage Error (MAPE) of 8,3% so that the model is accurate.