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I am using Bayesian MCMC estimation methods for GARCH models and I want to check, if model residuals are uncorrelated. In classical frequentist approach, one would use standard Ljung-Box test to check this. But with MCMC estimation, I have 10,000 volatility samples (so 10,000 residuals) for each observation. So is there any sufficient method how to perform some correlation test in Bayesian sense?

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  • $\begingroup$ The Bayesian approach is usually not to test but to model. That is, one would include an AR coefficient or some more general term in the likelihood and see if it improves the model. $\endgroup$
    – Durden
    Commented Jun 17, 2023 at 19:47

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