Diagnostic tests for GARCH model goodness of fit

To check whether the fitted GARCH model is any good, we need to apply a range of diagnostic tests to ensure that the model captures the intended behavior.

• LJUNG-BOX TEST (aka., white-noise test) - The Ljung-Box test provides a means of testing for auto-correlation within the GARCH model’s standardized residuals.
• ARCH LM TEST, Similar to the Ljung-Box Test, the ARCH LM test provides a means of testing for serial dependence (auto-correlation) due to a conditional variance process by testing for auto-correlation within the squared residuals.
• NYBLOM STABILITY TEST - The Nyblom stability test provides a means of testing for structural change within a time series.
• SIGN BIAS TEST - Engle & Ng sign bias tests provide a means of testing for misspecification of conditional volatility models.
• ADJUSTED PEARSON GOODNESS-OF-FIT TEST - The adjusted Pearson goodness-of-fit test compares the empirical distribution of the standardized residuals with the selected theoretical distribution.

Aside from the Ljung-Box test, NumXL should support the remaining diagnostics tests: ARCH LM, NYBLOM, Bias-sign, and Adjusted Pearson goodness of fit.