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I'm using financial data - logarithmic rates of return of WIG-Banks index, 2000 observations. I'm supposed to find ARMA-GARCH type of model, the most fitting one. Relying on ACF and PACF i estimated AR(7) process, and few parameters turned out relevant. I did Jung-Box test and it said that there could be autocorrelation between observations. I also did Dickey-Fuller test and it said that procces is stationary. I don't know whether that were good decisions. How shoudl I know what ARMA-GARCH model choose? What to do next?

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So try fitting AR(7) and MA(7) and see if serial correlation in residuals is removed. Once it has been removed, fit GARCH(p,q) to the residuals, with (p,q) largely dictated by stability issues and AIC / BIC. Much depends on how many observations you have got. Typically, GARCH(1,1) or GARCH(2,1) is a good place to start.

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  • $\begingroup$ For financial returns, anything beyond AR(1) or at most ARMA(1,1) is unlikely to be helpful regardless of what the ACF/PACF graphs are showing. This is due to market efficiency which usually holds at least approximately. $\endgroup$ Jan 21, 2021 at 6:49

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