Diagnosing Low Persistence in a GARCH(1,1) Volatility Model

Summary

The document asks why a stock’s fitted GARCH(1,1) model has a large omega and low alpha and beta, even though the resulting volatility forecasts appear reasonable. The answer explains that alpha plus beta below one is the stationarity condition, and suggests that low coefficients may indicate little volatility clustering in the stock’s returns.

For diagnosis, it recommends examining the autocorrelation structure of squared returns with the ADF and PACF. If first-order autocorrelation is significant while the fitted alpha remains low, the parameter calibration may need review. This is a short troubleshooting suggestion, not a full estimation guide. It does not address other causes of low persistence, the interpretation of omega’s scale, or how to validate forecasts; its conclusions depend on the data and calibration process.

Key ideas

• For GARCH(1,1), alpha plus beta below one is the stationarity condition.
• Low alpha and beta may indicate weak volatility clustering in the modeled stock.
• The response suggests examining squared returns with ADF and PACF diagnostics.
• Significant first-order autocorrelation alongside low alpha may warrant checking parameter calibration.

Tags

# using garch to forecast volatility but getting low persistence model


# using garch to forecast volatility but getting low persistence model












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.

## Answer by hotsource (score 1)

https://quant.stackexchange.com/a/17057

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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.