Diagnostic Tests and Model Selection for GARCH Fits
Summary
The document outlines checks for evaluating an ARMA-GARCH model fit. Before using GARCH, test whether the data show ARCH effects; without conditional heteroskedasticity, a GARCH model may not be needed. After fitting, inspect standardized residuals for autocorrelation, including with the Box-Ljung test, and test whether ARCH effects remain, with the Li-Mak test cited for this purpose.
It also describes sign bias testing for leverage effects and a chi-squared goodness-of-fit test comparing standardized residuals with the model’s assumed distribution. Significant leverage evidence may motivate a model such as TGARCH or EGARCH. Passing diagnostics does not prove the model will generalize: an overfit model can describe the sample well but perform poorly on new data. Information criteria can help account for model complexity, though the document does not provide a complete testing workflow or empirical comparison.
Key ideas
- Check for ARCH effects before fitting a GARCH model.
- Use autocorrelation tests on standardized residuals to detect remaining serial dependence.
- The Li-Mak test can assess whether ARCH effects remain in model residuals.
- Sign bias tests can identify leverage effects that motivate asymmetric volatility models.
- Good in-sample diagnostics do not prevent overfitting, so model selection should consider complexity.
Tags
Full text
# ruGarch - Interpret test results # ruGarch - Interpret test results I'm working on a R project, trying to calibrate a GARCH (so far, (1,1) ) model to the yields of the STOXX50 index over the last 2 years. I've tried the garch function of the tseries package, but it gave me a "false convergence" result. I tried then the ruGARCH package, and no false convergence so far, but I would like to know if my model is a good fit for the data. How can I do that ? How can I interpret the results of all the tests done (Box-Liung, etc..) ## Answer by Neeraj (score 5, accepted) https://quant.stackexchange.com/a/24296 To test for model misspeicfication: - First ensure that auto correlation of standardized residuals resulted from the ARMA-GARCH model are not significant. Further, you can use Box-Ljung test. It test joint significance of auto correlation upto lag $K$. - Leverage effect is tested by sign bias test. If $p$ value is less than .05 (assumed significance level) then it indicate presence of leverage effect in the data. In this case, try models that capture leverage effects like TGARCH, EGARCH etc. - The chi-squared goodness of fit test compares the empirical distribution of the standardized residuals with the theoretical ones from the chosen density. But before fitting GARCH model, check for ARCH effects in your data. If there is no ARCH effect then GARCH model is not required at all. ## Answer by Richard Hardy (score 2) https://quant.stackexchange.com/a/24562 First of all I would examine whether the model performs the task it is supposed to perform, i.e. account for the conditional heteroskedasticity in the data. That would amount to testing for remaining ARCH effects in the standardized model residuals by the Li-Mak test. If the model fails the test, there is evidence that it does not do its main task well. Testing for autocorrelations of the standardized residuals, leverage effects and distributional goodness of fit as suggested by @Neeraj also makes sense. However, be aware that a model that passes all test may be an overfitted model. That is, it describes the sample data well (actually, too well) but it is not likely to generalize successfully, e.g. it would not fit a new sample from the sample underlying population (or data generating process) well. Therefore, use of information criteria (which penalize overfitting) for selecting a model may be justified. References - Li, W. K., and T. K. Mak. "On the squared residual autocorrelations in non-linear time series with conditional heteroskedasticity." Journal of Time Series Analysis 15.6 (1994): 627-636.
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.