GARCH modelling and forecasting

pd811

New Member
#1
Hi,

I have a few questions regarding GARCH modelling and forecasting and it would be great if someone could help me. I am modelling oil spot prices log-return using various GARCH models: GARCH, APARCH, EGARCH... and I am trying to forecast the prices. I found using ACF and PACF plots that the best model for the series is ARMA(0,1) and then the best model for the error term follows GARCH(1,1) or APARCH(1,1) etc

Here are my questions:

1) I have a doubt whether I am forecasting the volatility of the prices or the actual values of return?

garch1<-garchFit(~arma(0,1)+garch(1,1),data=brentlog,trace=FALSE,include.mean=TRUE) predict(garch1,n.ahead=25)

2) Since I am not looking at options, is there a point forecasting the volatility? because it won't tell me whether prices will go up or down

3) Since I have an ARMA(0,1) for my model, my forecasts will always be constant and if I don't include a mean in the model then the forecasts are the same using egarch, garch, aparch or any model: it is 0. So is there a point of using those different models in this case?

thanks a lot!
 

JesperHP

TS Contributor
#2
1) I have a doubt whether I am forecasting the volatility of the prices or the actual values of return?
If you have price data P(t) often you model return - continuously compounded - where r(t) := ln P(t) - ln P(t-1). If we assume you
are applying the modelfitter to data of continuously compounded return r(t), t=1,..,T then:

The arma(0,1) is modelling the conditional mean of the returns E[r(t) | t-1] ..... sometimes called the mean model
The garch(1,1) or aparch(1,1) models the conditional variance in the ... the variance of the error term e(t) in the mean model defined as what some call the excess return e(t) := r(t) - E[r(t) | t-1].

2) Since I am not looking at options, is there a point forecasting the volatility? because it won't tell me whether prices will go up or down
The volatility tells you how fast prices change. When things change quickly they can change alot in short amounts of time. Variance of returns are traditionally interpreted as a measure of risk, reflecting the idea that theres a higher probability that you will loose a lot when investing in high variance assets, but hopefully there also a higher probability of making a large gain.

Im more than a little rusty on moving average but why should the forecast of MA(1) be 0? The one period ahead forecast should as I see it not be zero - even in a model without a constant - if you base the forecast on the conditional expectation E[r(t+1) | t]

the forecasts are the same using egarch, garch, aparch
certainly not ... these models are used for modelling the variance and they are very different models. But offcourse if you leave out modelling the mean then you implicitly assume it is ok to model returns as a mean zero uncorrelated proces .....