Choosing GARCH Data Windows for Volatility Forecasts

Summary

The document considers how much daily return history to use when fitting a GARCH model to forecast a stock’s volatility several months ahead. It frames the choice as a balance between statistical uncertainty and model error: a short sample can make estimates noisy, while an overly long sample may include market regimes that no longer describe current conditions. It cautions that a large historical dataset does not necessarily make distributional assumptions meaningful for a forecast.

For a long forecast horizon, the response notes that GARCH forecasts tend toward unconditional variance at a rate linked to the persistence parameters, expressed as the persistence term raised to the horizon. It recommends choosing a meaningful forecast horizon, matching the estimation window to that horizon, and applying change-point tests to detect distribution shifts; if a shift is found, the sample window may need shortening. The discussion gives no universal data-length prescription or specific test method, and its advice is framed around trade-offs rather than a fixed sample-size rule.

Key ideas

• A short estimation window raises statistical uncertainty, while a long window can include obsolete market behavior.
• GARCH forecasts tend toward unconditional variance as the forecast horizon extends.
• The estimation window should be chosen in relation to a meaningful forecast horizon.
• Change-point tests can help identify distribution shifts that may justify shortening the sample.

Tags

# Evaluation volatility with Garch model


# Evaluation volatility with Garch model












I want to forecast the volatility (with Garch) of a canadian stock in 5 months with daily returns. How many data do I have to collect ?

Thanks.

## Answer by Drmanifold (score 4)

https://quant.stackexchange.com/a/9718

Fitting a time series on a given stock is really trade off between statistical risk and model error. If your time series is too short then your statistical error will be high. If your time series is too long, then the distribution of the market will probably have changed, and the your model error will be high.

5000 days is about 20 trading years. There is no way your choice of distribution will be meaningful a garch forecast. To add insult to injury, your forecast, tends to the unconditional variance very quickly $(\alpha +\beta)^n$ where $n$ is the number of days ahead. So if you are forecasting 105 days ahead, even if $\alpha + \beta$ quite high,$(\alpha +\beta)^{105}$ will be close to zero.

- Choose a proper and meaningful forecast horizon

- Depending on your forecast horizon choose reasonable time frame.

- Do several change of point test to see if your distribution has changed. If it did, try to reduce the time frame.

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