[R-SIG-Finance] RUGARCH multi-period ahead forecasting

[stoyan.stoyanov]

Hi all,

I am trying to produce multi period ahead volatility forecasts using the
rugarch package and specifically the ugarchboot function, and using daily
returns. I would like to be able to report my forecasts in units of
annualized volatility.

My initial intuition to create a forecast for the period covering the next 5
trading days was to use the ugarchboot function in the following way:
boot.pred=ugarchboot(fit, data=NULL, method="partial", n.ahead=5,
n.bootfit=100, n.bootpred=500, out.sample=0,     solver="solnp")
sigma=as.data.frame(boot.pred, which="sigma",
type="summary")[3,5]*sqrt(252)*100

However, after thinking about it more carefully, I am starting to convince
myself that this will only report the annualized volatility predicted for
one single period (t+5) and not over the 5-day period I am interested in.
Thus, I am now computing the 5-day volatility forecast in the following way:

sigma=sqrt(sum(as.data.frame(boot.pred, which="sigma",
type="summary")[3,1:5]^2))*sqrt(252/5)*100

This essentially sums the 5 daily variance forecasts, takes the square root
of the sum,  and annualizes it.

Although I feel somewhat confident that this approach is correct, I am
confused by a couple of issues:
1. My annualized measure for the multi-period volatility, should be at least
as big as any of the single-day annualized volatility forecasts. Either this
statement is incorrect or I am not annualizing correctly. In cases when
single-period volatility forecasts are decreasing (unconditional variance <
conditional variance), I see my multi-period annualized forecast being lower
than my 1-period annualized forecast. The fact that I forecast volatility
over the next one day to be higher than volatility over the next five days
makes me uneasy.

2. The forecast numbers produced by the two methods above are strikingly
close (across a variaty of datasets and different forecast horizons). I am
really not sure how to make sense of this, so any explanations would be
greatly appreciated.

3. Finally, am I correct to think that ugarchboot creates 1-period ahead
forecasts and does not aggregate them?

Thanks in advance.

Best,
Stoyan



-----
Stoyan Stoyanov
The University of Chicago Booth School of Business
MBA Class of 2013
(312) 532-0120 | stoyanov at chicagobooth.edu
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