GARCH Stationarity and Time-Varying Conditional Volatility

Summary

The document addresses an apparent tension between the stationarity assumptions used in GARCH models and their purpose of modeling changing volatility. Its answer distinguishes unconditional stationarity from conditional volatility: a stationary process can have volatility that depends on past observations, allowing periods of high and low volatility to cluster even when the process has stable long-run behavior.

It also notes practical reasons for using GARCH, including tractable forecasts of expected volatility and a relatively simple model structure that can be fitted to historical data. These advantages do not remove the assumptions: the model relies on a stationary mean and volatility behavior, and those properties may not hold in changing markets or may be difficult to assess empirically. The explanation is qualitative and gives no equations, estimation details, diagnostics, or guidance for selecting a GARCH specification, so it is an overview rather than a modeling procedure.

Key ideas

• Stationarity does not require conditional volatility to remain constant through time.
• GARCH models represent volatility clustering through dependence on past information.
• The model structure can support tractable forecasts of expected volatility.
• Model usefulness depends on assumptions about stable mean and volatility behavior, which can be difficult to verify.

Tags

# Garch models and assumption of stationarity ?


# Garch models and assumption of stationarity ?












I found big inconsistency in the GARCH models and their underlying assumption of stationarity. GARCH models require that data must be stationary, where stationary means both mean and variance are time invariant. If variance is time invariant i.e. constant then what is logic behind using GARCH models.

## Answer by meh (score 3, accepted)

https://quant.stackexchange.com/a/19110

GARCH models are essentially white noise models with some time dependency. The reason GARCH models are used is because they have a lot of nice properties. The main being that the Conditional Volatility is time-dependent. This means that volatility can cluster.

It's true that conditional vol will regress towards "normality" as a random walk process with drift.

The second nice property is the closed-form solution allows you to calculate expected vol with ease.

A third nice property is that the model is simple and very easy to fit to historical data.

As with all models you need to understand it's underlying assumptions so you can assess it's downfalls. In this case your big assumption is the stationary mean and volatility. One of which may not be true and the other nigh impossible to measure.

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