In practice, when modeling volatility do people tend to use expanding or sliding windows to fit GARCH models?
For example see rolling forecast generation vs recursive forecast generation in the Python arch package here: Arch Documentation
In short, is it only useful to fit GARCH parameters on more recent data, or better to use the whole history of returns data to fit GARCH model to predict one/n step forward volatility?
If you are just modelling volatility and not stochastic volatility of volatility then it should be better to use a sliding window. The reason is that volatility itself is time-varying and therefore an expanding window does not take into account regime shifts in volatility.
The fact that volatility is time-varying is a stylized fact, two prominent references are:
Either the above you will see either regime shifts in volatility or time-varying volatility of volatility. This means that the unconditional mean for volatility that you get with an expanding window might severely impact negatively your estimates specially in bad times such as the financial crisis. In either case whether it is better to use an expanding window or a rolling window is an empirical question. I suggest you estimate both ways and check empirically what works better.
This other question guides on how to empirically test the performance or Arch-type models.
I tend to use an expanding window.
The reason is that the GARCH model aims to capture time-varying volatility effects so if the average level has changed overtime, then hopefully the model will take this into account. By contrast, if you estimated a constant variance, then the prior history may be less relevant than the more recent history.
In addition, GARCH can also be thought of as a model similar to exponential smoothing, though exponential smoothing does not have the mean-reversion effect that GARCH does. Exponential smoothing tends to be used with an expanding window rather than a sliding window.
