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.

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    $\begingroup$ 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
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    $\begingroup$ 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
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    $\begingroup$ 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

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.

  • $\begingroup$ 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

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