ARIMA/SARIMA modelling is modelling of the mean level. ARCH modelling being associated with heteroscedasticity is modelling of the variance. International tourist arrivals are likely to follow a seasonal pattern and therefore should follow a SARIMA model rather than an ARCH model. Literature confirms this. Heteroscedasticity is not likely with tourist arrivals and therefore ARCH modelling is not likely to be involved.

To confirm whether there is exist the heteroscedasticity in the ARIMA/SARIMA model, you can use ARCH test on the residuals of the model. If the p-value for the test is less than the significance level, then the ARCH effect is exist in the residual, meaning that the variance of the model should be not constant. To handle the arch effect, you can use ARCH or GARCH model for the variance model, which is depends on the pacf of the squared residuals of the ARIMA/SARIMA model.

Hi,

you should in generally test your time series on heteroskedasticity. You could use graphical analysis together with the ARCH-LM test for this. If you find heteroskedasticity, an ARIMA or SARIMA model wouldn't be appropriate, since ARMA-models assume stationarity (which is not the case for heteroskedastic time series). You could either mathematically transform your time series to a stationary one or use GARCH models., although I am quite critical how good those are for forecasting purposes.

Best regards!