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Use the R package fgarch. Hope this is helpful to you.


1

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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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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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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You can pass in the parameters are you estimating with EWMA or GARCH using the mu (mean), sigma (co/variance) m3 (co/skewness) and m4(co/kurtosis) arguments. e.g. blahblah = EWMA(my_time_series) VaR(my_time_series,mu=blahblah)


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I would suggest you to forecast the series using different models and to determine which one is the best accordingly loss functions such as RMSE, MAPE.. or using the Mincer-Zarnowitz regression . You could also compare one-step forecast versus dynamic forecast. Another way is to compute VaR and observe the model having the lowest failure rate. AIC/BIC ...


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Did you try rmgarch package of R ? http://cran.r-project.org/web/packages/rmgarch/index.html http://unstarched.net/r-examples/rmgarch/mgarch-comparison-using-the-hong-li-misspecification-test/



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