I am trying to fit an ARFIMA(p,d,q)-GARCH(1,1) model to an asset returns time series. I start with an ARFIMA(0,0,0)-GARCH(1,1). The diagnostics tests like persistence requirement, Ljung Box test for standardised residuals, squared standardised residuals, ARCH LM Test, goodness of fit test all seem to pass.

When I start adding ARFIMA parameters, the Loglikelihood starts increasing (and AIC falling), but in ALL these cases Ljung Box test for standardised residuals fails with very small p-values (even upto ARFIMA(10,d,10)).

My return series is already stationary as per adf test.

I am trying to understand this intuitively. I am not fitting any equation for the mean and modeling only the volatility. Is this ok ? Essentially, if I force an ARMA structure on the time series, I am introducing an auto correlation artificially ?

Please advise.


  • $\begingroup$ What do you mean you fit ARFIMA to a return series? If you have a return series it means you already picked d to be 1. It is too late to apply ARFIMA. $\endgroup$ – Cowboy Trader Nov 27 '18 at 18:17
  • $\begingroup$ @CowboyTrader, it depends on how the original variable is defined. You seem to define the original variable as a the cumulative sum of asset returns, while the OP defines it as asset returns. Statistically there is absolutely no problem in fitting ARFIMA to a return series. $\endgroup$ – Richard Hardy Nov 27 '18 at 19:54
  • $\begingroup$ @CowboyTrader .. its a time series of log returns .. ln(P2/P1).. I am not sure if my GARCH modeling attempt with an ARMA(0,0) is sound or not.. I went through several related questions suggested by stackexchange.. but could not find what I am looking for.. Any comments / pointers would be helpful.. Thanks $\endgroup$ – square_one Nov 28 '18 at 13:40

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