I am recently learning about time-series analysis and the model diagnostics. I am facing difficulties in understanding the following points:
- Mathematically, I understand that standardizing the residuals is dividing them by the conditional or unconditional volatility. But, I am not able to intuitively understand, why we actually need the standardizing of residuals (because in practice I am reading that "residuals" should follow the white noise process - then why the scaling?) ? Like why we use standardized residuals in every tests (like Ljung-Box Test, Jarque-Bera test, etc.) or in plotting the autocorrelation and partial autocorrelation plots instead of simple residuals?
- Next is, we plot the autocorrelation and partial autocorrelation plots for the standardized residuals and their squares to study and compare them with white noise. I am not able to capture the motive of comparing the ACF or PACF plots for the square of standardized residuals too! What is the significance of analyzing the 2 plots for the squared standardized residuals?
Any pointers will be really helpful!