A few more noteworthy points about ARCH models:

• Selecting the zero-mean process is useful when working on residuals from a separately estimated model.
• To detect ARCH effects, we can look at the correlogram of the squared residuals from a certain model (such as the ARIMA model). We need to make sure that the mean of these residuals is equal to zero. We can use the Partial Autocorrelation Function (PACF) plot to infer the value of q, similarly to the approach used in the case of the Autoregressive (AR) model (please refer to the Modeling time series with ARIMA class models recipe in Chapter 3, Time Series Modeling, for more details).
• To test the validity of the model, we can inspect whether the standardized residuals and squared standardized residuals exhibit no serial autocorrelation (for example, using the Box-Pierce test—acorr_ljungbox from statsmodels). Also, we can employ the Lagrange Multiplier (LM) test to make sure that the model captures all ARCH effects (het_arch from statsmodels) .