I'm trying to fit an ARMAX model using forecast::Arima() which is using MLE (https://otexts.com/fpp3/arima-estimation.html). Thus, there is no need for normality test as required by OLS estimator. I also applied unit root test using ADF.test() on every time series variables included in the model.
My Question is,
- How do I conducted heteroscedaticity test for MLE estimator residuals?
- When I run below code to test for auto-correlations
Box.test(na.omit(r11x), lag = 1, type = "Ljung-Box") # r11x is residuals of ARMA(1,1)-X fit Box-Ljung test data: na.omit(r11x) X-squared = 0.94702, df = 1, p-value = 0.3305
means that there is no auto-correlation.
But.. when I specify the lag > 6, the test show that the auto-correlation existed.
Box.test(na.omit(r11x), lag = 7, type = "Ljung-Box") # r11x is residuals of ARMA(1,1)-X Box-Ljung test data: na.omit(r11x) X-squared = 22.508, df = 7, p-value = 0.002076
Last, is there any other diagnostic test to be conducted?