I have a big question!!! Can someone please help... how to set up the code
for the instruction below?
" Monthly idiosyncratic volatility can also be estimated from monthly returns.
Bali and Cakici (2008) compare the estimates from different data frequency and find
that the realized monthly idiosyncratic volatility from daily data is subject to
market microstructure biases. Using the conditional idiosyncratic volatility
estimates from GARCH (1, 1) and EGARCH (1, 1) models as benchmarks, they show that the idiosyncratic volatility based on past monthly returns provides a
more accurate prediction of conditional idiosyncratic volatility both in sample
and out of sample.
In our study,we use an EGARCH model to estimate conditional idiosyncratic
volatility from monthly returns. Developed by Nelson (1991), this model is a
generalization of the ARCH model of Engel (1982) and the GARCH model
of Bollerslev (1986). These models estimate the mean and variance of returns
jointly and capture volatility persistence from residual variance and past
squared innovations. The EGARCH model accommodates the asymmetric property
of volatility, that is, the leverage effect, whereby negative surprises
increase volatility more than positive surprises. Foster and Nelson (1996) show that
the resulting conditional volatility estimate is a weighted average of the lagged
realized idiosyncratic volatilities from monthly returns. Following the approach in Fu (2009), we choose the best-fit EGARCH model among nine EGARCH (p, q) models (where p = 1, 2, 3, and q = 1, 2, 3) for each individual stock according to the Akaike Information Criterion. In each EGARCH model, we estimate mean returns using the Fama and French (1993) three-factor model.We then estimate conditional idiosyncratic volatility each month from the chosen model with a rolling window of the previous thirty months. The resulting forecast for the next month comprises our estimation for idiosyncratic volatility measure. Fu (2009) indicates that this estimate is a better measure of idiosyncratic risk when compared with realized monthly idiosyncratic volatility from daily returns. "
Actually, what does this instruction want me to do?? I typed out the code like this:
proc autoreg data = twostocks outest = EGARCH_twostocks;
model Return = GDP Inflation / garch=( p=1, q=1, mean = sqrt);
by stock year;
output out=EGARCHres Residual=res ;
Is this correct?
When do I use "sqrt" or "linear" or "log"?
How do I interpret the data?