使用 rugarch 包在 R 中进行 GARCH 参数估计和预测

Question

I have a problem with parameter estimation and forecast for a GARCH model. I have a time series of volatilities, starting in 1996 and ending in 2009. I tried to estimate the parameters with the ugarchspec and ugarchfit function:

garch1.1 <- ugarchspec(variance.model=list(model="sGARCH", garchOrder=c(1,1)),mean.model=list(armaOrder=c(0,0)),distribution="std")
garch1.1fit <- ugarchfit(spec=garch1.1,data=RV)

The results seemed to be okay, so I went on with the forecast. I wanted to use the ugarchforecast or ugarchroll function. But when I tried to do it, I recognized that they work with the wrong date. For example, If I try to do a simple forecast like

forecast <- ugarchforecast(garch1.1fit,n.ahead=2)

I get the following results:

0-roll forecast [T0=1979-04-05 01:00:00]:
    Series     Sigma
T+1  5.373e-05 3.733e-05
T+2  5.373e-05 3.762e-05

So my problem is: why does R say that T0=1979? This cant be correct as my data starts in 1996 and ends in 2009. When I had a look at the residuals from garch1.1fit, the date is also wrong. What's the problem here?

Answer 1

I am not sure what object do you use as RV , but I assume it is a numeric vector. Package rugarch works better with xts objects supported by xts package.

Following code should do the job:

require(xts)

time <- #put here time vector from your data
RV.xts <- na.omit(xts(x = RV, order.by = time))

and then your code with changed object RV for new one RV.xts :

garch1.1 <- ugarchspec(variance.model=list(model="sGARCH", garchOrder=c(1,1)),
                       mean.model=list(armaOrder=c(0,0)),
                       distribution="std")
garch1.1fit <- ugarchfit(spec=garch1.1,data=RV.xts)
forecast <- ugarchforecast(garch1.1fit,n.ahead=2)

The code i provided does two things: first it makes an xts object using time . This object will tell your ugarchfit() function what is the time of this model. Second, it omits possible NA data, which function ugarchfit() do not handle.

Make sure if object xts connected dates correctly by checking:

head(RV.xts)
tail(RV.xts)

Answer 2

I think you did not specify date for your ugarch model. Note that R "Date" class is coded in the number of days from the day 1970-01-01 .

Following code may help to understand the concept:

as.Date("1970-01-01")
as.numeric(as.Date("1970-01-01"))

as.Date("1970-01-10")
as.numeric(as.Date("1970-01-10"))

As the date is not specified for ugarch model, your data seems to have the number of observations to fill the 1970-1979 years (probably weekends are excluded), and the prediction starts after that period.