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ARMA(1,1)-GARCH(1,1) rolling estimation

Should "AA.day.forecast.data" contain the series oh one step ahead 
forecasts? If yes, you need to index it also!

AA.day.forecast.data[i-start+1] <- garch.pred[,1]

Btw, if you are doing it with a loop, you might have a look on package 
foreach, which is likely to make your loop contruction easier, and 
especially can run it easily on parallel cores...

Mat

PS: try when posting to give a code fully reproducible!

mam3xs a ?crit :