Hi list,

 

I’m still struggling with garch models. My first approach was doing a
fourier analysis on the series and then try to explain the residuals with an
ARIMA/GARCH model, but it turns out that this approach doesn’t work well
since the garch model doesn’t add many information to the arima model.

I’ve found that the differenced series of the DAX, corrected for mean and
slope has nearly the same residuals as the residuals from the fourier
residuals, hence I’ve littered the fourier approach… but now I’ve got a
question concerning pure garch models. 

 

How can I use them to predict the series? I hope you have some pointers to
literature, or examples for that. To make my actual approach clear, please
check the following code snippet:

 

library(quantmod)

from.dat <- as.Date("01/01/91", format="%m/%d/%y")

to.dat <- as.Date(Sys.Date(), format="%m/%d/%y")

getSymbols("^GDAXI", src="yahoo", from = from.dat, to = to.dat)

 

daxTs <- ts(Ad(GDAXI))

time <- c(1:length(daxTs))

tsData <- daxTs - lm(daxTs ~ time)$fitted.values

diffData <- diff(tsData)

 

garch.resids <- garch(diffData, order=c(1,1), trace=F)$residuals

garch.resids[which(is.na(garch.resids))] <- 0

plot.ts(garch.resids)

 

as you can see in the plot, there is only white noise in the standardized
residual series, but actually I’ve no idea how this information could help
me to predict the series. So it seems to me that the model works quite well,
but I’ve no clue how this information could help me with the prediction.

 

all the best

Konrad


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