Let's say you fit an ARMA-GARCH model to financial data and find that the standardised residuals are non-Gaussian through the Kolmogorov-Smirnov test. These residuals have mean -0.002 and standard deviation 0.997.

From this reference one cannot use the Ljung-Box test of autocorrelation in my residuals because the data needs to be Gaussian and mean-zero (it is mean zero). What test can be used then to check for remaining autocorrelation and heteroskedasticity?

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    $\begingroup$ I think the reference is incorrect about the need for normality for the Ljung-Box test. On raw data, the test functions well regardless of normality. On (standardized) model residuals from ARMA-GARCH, it might be inappropriate, again, regardless of normality. See Testing for autocorrelation: Ljung-Box versus Breusch-Godfrey. $\endgroup$ – Richard Hardy Jan 20 '19 at 16:36

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