Using GARCH(1,1) as a Baseline for Variance Forecasts

Summary

The question asks whether an instrument’s historical variance can help predict its future variance and whether variance is stable over time. The response recommends a basic GARCH(1,1) model as a starting point: it uses past information about volatility to forecast the next period’s variance. It also points to a survey by Hansen and Lunde (2005), which the answer describes as finding that few models outperform this simple specification.

The discussion is brief and does not explain GARCH estimation, compare forecasting horizons, or address why different instruments have different volatility. It also does not provide the survey’s data, evaluation criteria, or conditions under which the result holds. Treat the recommendation as a baseline to investigate, rather than a universal claim that historical variance is stable or that GARCH(1,1) is always best.

Key ideas

• GARCH(1,1) is presented as a simple baseline for forecasting variance from past volatility information.
• The answer cites a survey that reportedly found few models outperforming this specification.
• The discussion does not explain instrument-specific volatility or the causes of sudden variance increases.
• The recommendation is a starting point, and its applicability depends on the data and forecasting context.

Tags

# Are Variances generally stable for any given instrument?


# Are Variances generally stable for any given instrument?












My hesitation, as I look at getting into forecasting based on observed variances, is the nagging question - if variances are not constant per-instrument, is it any good to use the last month or year's variance to predict this year's ?

If variances are constant(ish), then my follow-up is - what is the causal model that predicts why this is so? I'm uncomfortable without a mental model of why one stock should have variance distinct from another one, and I want to have some sense of how to know the likeliness of a sudden increase of variance, which would be very bad news indeed!

Thanks in advance.

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/23002

I am not sure what you are exactly asking. But usually even a simple Garch(1,1) would be the naive approach of forecasting variance using last period's variance. A very good survey of volatility modelling on the Arch/garch family is the Hansen and Lunde 2005.

They show that hardly one can beat a garch(1,1), so that is a good first guess.

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