I used SPY data to fit GARCH(1,1) in my model. My data starts from Jan, 2000 until Dec, 2013. I compared the volatility using runSD on the 21 rolling window and GARCH(1,1). It looks a pretty good fit so far.
My question would be how can I forecast the future volatility going forward from Dec, 2013? Should I just use the coefficient to calculate the next day's volatility? But what about if I want to simulate 10 days ahead? Is there a simple way to do this in R? I looked at ugarchroll and I don't really understand that function. Hope you guys can shed some lights!
Here are the coeffs and summary of GARCH using tseries package:
Call: garch(x = dailyreturn[, 1], order = c(1, 1)) Coefficient(s): a0 a1 b1 1.637e-06 8.857e-02 9.001e-01 Call: garch(x = dailyreturn[, 1], order = c(1, 1)) Model: GARCH(1,1) Residuals: Min 1Q Median 3Q Max -7.1755 -0.5418 0.0716 0.6266 4.0432 Coefficient(s): Estimate Std. Error t value Pr(>|t|) a0 1.637e-06 2.266e-07 7.223 5.1e-13 *** a1 8.857e-02 7.074e-03 12.520 < 2e-16 *** b1 9.001e-01 7.916e-03 113.703 < 2e-16 *** --- Signif. codes: 0 ?**?0.001 ?*?0.01 ??0.05 ??0.1 ??1 Diagnostic Tests: Jarque Bera Test data: Residuals X-squared = 358.7767, df = 2, p-value < 2.2e-16 Box-Ljung test data: Squared.Residuals X-squared = 7.8313, df = 1, p-value = 0.005135