2013-07-18_GARCH_example

5 2025564 1880231 if you used raw residuals upper

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Unformatted text preview: rom bootstrap distribution. Some conditions apply. > B <- 100000 #significantly large number > res0 <- res-mean(res) #demean residuals > res.boot <- sample(res0, B, replace=TRUE) > quantile(res.boot, probs=c(0.025, 0.975)) 2.5% 97.5% -2.025564 1.880231 If you used raw residuals, upper value of 95% prediction interval: lower value: Xt +h + 1.880231 Xt +h − 2.025564 If you used standardized residuals (our case), upper value of 95% prediction interval: Xt +h + 1.880231 · s.e.(Rt ) lower value: Xt +h − 2.025564 · s.e.(Rt ) GARCH model for DAX time series Predicting using fGarch objects −0.02 x 0.02 0.04 > library(fGarch) > G <- garchFit(formula = ˜ garch(1, 1), data = dlDAXout) > predict(G, n.ahead=30, crit_val=qt(alpha/2,df=5), plot=T) Prediction with confidence intervals −0.06 ^ Xt+h ^ Xt+h − 2.571 MSE ^ Xt+h + 2.571 MSE 0 100 200 300 Index 400 500 Remark Note, that we re-estimated model in another package. Results will be different from the previous ones. Therefore, the model diagnostics should be repeated. The output of garchFit is a S4 object of class “fGARCH”. For a list of its slots see > ?garchFit For example, residuals (non-standardized, comparing to garch output) can be obtained by > residuals(G) GARCH model for DAX time series...
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This note was uploaded on 08/04/2013 for the course ECON 201 taught by Professor Vandewaal during the Spring '09 term at Waterloo.

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