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You can use Matlab too, that, in my humble opinion, is simpler than R from a syntax point of view. The model you need for is run by the Matlab function arima that can be used with seasonality option to do what you have to do. Here you can find an example and a brief explanation of the model. Type ctrl + F and search for: "Specify a seasonal ARIMA model" ...

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Actually, neither of your two results are quite correct. As explained in the Details for the Return.calculate function, most of the PerformanceAnalytics functions use discrete returns, not log returns. To get the correct results, you will have to convert your data from log returns to simple returns. Compare the charts from the following: ...

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The mean equation specification for ARIMAX(8,0,0)(5,0,1)[7] (as in the R code above): $$(1 - \phi_1L^1 - \ldots - \phi_8L^8)(1-\Phi_1L^7 - \Phi_2L^{14} - \ldots - \Phi_5L^{35})y_t = \beta x_t + (1 + \Theta_1L^7)\varepsilon_t$$ where $x_t$ is the holiday dummy variable. Equivalent ARIMA fit in Matlab (+ GARCH and forecasting): % specify seasonal ...

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I have the same problem as you. Up to my knowledge, there is no package allowing to combine seasonal ARIMA process with GARCH effects.

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It is a classical misunderstanding, your model is right, you always have a acf equal to one at lag zero (and not one) since if there is no lag acf = covariance(x , x_lag 0) / variance x = variance x / variance x = 1. So you need to pay attention to the x axis , some software displays ACF starting at lag zero and some others from 1 (which make better ...

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