Time-Series Validation Approaches for GARCH Models

Summary

The document raises a validation problem for comparing GARCH volatility models on sequential time-series data. Its proposed setup leaves out one time window at a time while fitting on the remaining windows. When a held-out window lies between training windows, the model's latent volatility state must be initialized across the gap, making the resulting forecast evaluation sensitive to how that state is estimated.

The response suggests rolling regressions as a common approach and describes forming rows of lookback observations with a corresponding squared return, then subsampling those observations. It does not explain how this procedure handles GARCH state initialization, specify a complete validation protocol, or provide empirical comparisons. The material therefore highlights the tension between ordinary cross-validation and time-dependent volatility models but gives only a brief, incomplete recommendation; the validity of results depends on the forecast design and treatment of temporal dependence.

Key ideas

• Leaving out an interior time window creates a gap in the observed history used to initialize volatility.
• A GARCH validation design must account for the model's evolving latent volatility state.
• The response mentions rolling regressions and a lookback matrix paired with squared returns.
• The document does not establish that its brief suggestion resolves state initialization or temporal-dependence concerns.

Tags

# Cross validation of a garch model


# Cross validation of a garch model












Suppose I divide a time series into 10 sequential time windows, where each window contains 1000 data points.

I want to do test 5 different garch models using cross validation.

So for each model, I will fit it on 9 out of 10 time windows, and test it on data in the left-out window. This will be done for 10 different "left out" windows.

However, for each optimised garch model, the latent volatility variable will be a problem when I step over the "gap" created by the left-out window. The only time this won't be a problem is when the left-out window is either the first or last window. In the 8 other cases, I will have to take a guess at the initial volatility to use, using something such as the sample variance, or rolling volatility.

So 8 of the tests will have two starting points. And 2 of the models will have 1 starting point. And I will need to guess the volatility at each starting point.

So my question is, with all the guessing of these starting points... What is the recommended best practice? And how valid will be cross validation results be?

## Answer by Michael WS (score 2)

https://quant.stackexchange.com/a/9802

My guess would be most people approach this using rolling regressions.

My approach would be to generate a matrix using all the lookbacks that you want to predict the present on each row and a corresponding squared return, then subsample the two.

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