2
$\begingroup$

I am using a GARCH(1, 1) model to try model volatility for a certain stock.

I have a GARCH function in matlab that returns the three parameters, omega, alpha & beta.

I then use this parameters in the formula below to see the forecast volatility. The numbers seems reasonable however the parameters do not.

Sigma t = omega + alpha * Return Squared t-1 + beta * Sigma t-1

The omega is very high half the time above 0.8. My alpha + beta are tend to be very low suggesting low persistance. What would cause this low persistance? I have read that you would expect alpha + beta typically to be close to 1.

$\endgroup$
  • 1
    $\begingroup$ How long is your data sample? If it is too short then there is no room for volatility to fluctuate. $\endgroup$ – Kiwiakos Mar 22 '15 at 0:26
  • $\begingroup$ I am using 90 observations - is this too short then? $\endgroup$ – mHelpMe Mar 22 '15 at 15:09
  • 1
    $\begingroup$ If you mean 90 days then yes, I would say estimating parameters is meaningless. Volatility models are there to capture fluctuations that take place over months and years. $\endgroup$ – Kiwiakos Mar 22 '15 at 22:34
  • $\begingroup$ Ok. To give more insight I'm trying to create a model to forecast volatility to be used for trading costs. Ideally I understand you would use intraday data but that is not possible. I thought by using 90 days that would be ok. Is there a minimum number of observations you would suggest? $\endgroup$ – mHelpMe Mar 22 '15 at 22:52
  • 1
    $\begingroup$ I would not attempt to estimate parameters for individual stocks. Instead I would just set the recursion parameters to something reasonable based on the literature or long estimation. For instance, one can take the RiskMetrics parameters omega=0, alpha=0.06, beta=0.94 in your notation as fixed. Simple, in works, and you are not exposed to estimation noise, risk of failure and computational overheads. Volatility is unobserved anyway. $\endgroup$ – Kiwiakos Mar 23 '15 at 7:33
1
$\begingroup$

alpha + beta < 1 is the stationary condition for GARCH. If alpha and beta are low that means volatility of the stock does not have clustering behaviors. I think you can have a look at ADF and PACF of Return^2 time series first. If the first order autocorrelation is very significant but alpha is not, then perhaps you can check on the parameter calibration.

$\endgroup$
  • $\begingroup$ Sorry what do you mean by ADF & PACF? Will check the squared returns & the autocorrelation $\endgroup$ – mHelpMe Mar 22 '15 at 15:11
  • $\begingroup$ I have checked the autocorrelation on the returns & from lags 1 to 5 there is no significant values. $\endgroup$ – mHelpMe Mar 23 '15 at 11:05
  • $\begingroup$ Adf - autocorrelation function. pacf - partial autocorrelation function. And try the autocorrelation of return squared instead of returns. If there is no volatility clustering observed, then perhaps the question is why Garch? $\endgroup$ – hotsource Mar 29 '15 at 17:23

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.