I am curious how to check whether an already fitted GARCH or ARIMA model with GARCH variance adequately captures the data it is fitted to, not whether one GARCH model is a better fit than another.
For example, after fitting an ARIMA model with constant variance to a time series Y, we can use the infer function with the data set Y and the fitted ARIMA model to retrieve the residuals, which, if the model is an adequate fit, should be a white noise process.
I am unsure how, after fitting a GARCH model with the estimate function, I can check the adequacy of the fit by, say, looking at the residual series. When the infer function is used with a GARCH model, it does not return a residual series so it seems similar analysis to that above may not be able to be performed. Please offer suggestions on how a fitted GARCH model may be tested to see whether it adequately describes (is fit to) a dataset. Thank you.
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