Why does auto arima generate a best model with q order exceeding my pre-set range?

Question

I would like to create an auto arima model to automatically select the best parameter values. The value range that I set for q is [1,2]. However, the best q value generated by auto arima is 0. Does anyone know why it is?

Below is my code

sarimax_model = auto_arima(df_x_train['y'],exogenous=df_x_train[['black_friday_ind','holiday_season_ind','covid_ind']],start_p=0,d=1,start_q=1,max_p=1,max_d=1,max_q=2, start_P=0,D=1,start_Q=1,max_P=1,max_D=1,max_Q=1, m=seasonal_periods, information_criterion='aic',stepwise=True)

This is the best model generated by auto arima

Answer 1

You are testing via AIC (Akaike Information Criterion) and the lowest AIC is the best model for automated model selection. So, you see 0 for q order. If you can share sarimax_model.summary() then we can see the lowest AIC.

But, you need to be careful with automated model selection. It is very dependent on your input data and the parameters are given to the function. Parameters need to match with the data (seasonality, seasonal period, seasonal difference order, etc).

You can verify your P and Q orders manually via ACF and PACF plots and also good to check diagnostic plots for normality and correlation of residuals.