I am trying to create one-step ahead forecasts for the S&P500 using a GARCH(1,1) model. I am using the rugarch package in R.
As you can see, the forecasted points are consistently higher than the volatility suggested by Parkinson's HL volatility formula. I have also checked Realized Volatility measures using 5-min intraday data, and I found that it is very close to the Parkinson HL.
I found that if I adjust the Parkinson's HL vol by 0.0025, it fits very close to the volatility suggested by the GARCH(1,1) model.
What could be the issue that makes the GARCH model volatility forecasts higher?
library(quantmod)
library(xts)
library(forecast)
library(rugarch)
library(fGarch)
library(tseries)
library(ggplot2)
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df <- getSymbols("^GSPC",auto.assign = FALSE, from = "2004-12-31", to= "2019-03-31")
price = coredata(df$GSPC.Adjusted)
df$logret <- diff(log(df$GSPC.Adjusted))
logreturns = df$logret[-1,]
df2<-df[2:3585]
T <- nrow(logreturns)
T_train <- round(2/3*T)
T_test <- T - T_train
dates_out_of_sample <- tail(index(logreturns), T_test)
dates_all <- index(logreturns)
dates_in_sample <- dates_all[1:T_train]
model1=ugarchspec(
variance.model = list(model = "sGARCH", garchOrder = c(1, 1)),
mean.model = list(armaOrder = c(0, 0), include.mean = TRUE),
distribution.model = "norm")
garch1.fit <- ugarchfit(spec=model1,data=logreturns, out.sample = T_test)
garch1.forecast <- ugarchforecast(garch1.fit, n.ahead = 1, n.roll = T_test - 1 )
garch1.volforecast <- t(garch1.forecast@forecast[["sigmaFor"]])
HLVol <- (log(df$GSPC.High[2:3585]) - log(df$GSPC.Low[2:3585]))/(4*log(2))
garch1.forecast
do we see in the plot? Moreover, why do you think it is GARCH rather than Parkinson that is biased? (I am not necessarily challending this, just asking for clarification.) $\endgroup$garch1.volforecast <- t(garch1.forecast@forecast[["sigmaFor"]])
This is the code for extracting the sigma from the forecast. I am suspicious of the GARCH rather than Parkinson because I calculated Realised Volatility using intra-day data as well rather than the Parkinson, and it is very close to the Parkinson estimate. Also I know the library calls are redundant here but I copied only the relevant section of the code for clarity. $\endgroup$