Why GARCH Is Used Despite Correlated Volatility Forecast Errors

# Why are GARCH models used to forecast volatility if residuals are often correlated?


# Why are GARCH models used to forecast volatility if residuals are often correlated?












The answers to this question on forecast assessment suggest that if the sequence of residuals from the forecast are not properly independent, then the model is missing something and further changes should be made to remove the correlation.

That does make sense to me and it suggests that we should be able to do better than a simple GARCH(1,1) model.

However, in almost all the literature on the subject, this issue is never discussed, and the fact that forecasts produced residuals that are serially correlated is taken as a fact of life. Indeed, people have produced methods for accounting for both serial and contemporaneous correlations when comparing different forecast models.

So, why is this the case? If the GARCH(1,1) model does have such problems, why is it still considered a standard approach for modeling volatility?

## Answer by Richard Herron (score 15, accepted)

https://quant.stackexchange.com/a/611

One of the reasons the ARCH family of models is used is that you only need price data to generate the model. These data exist back to the 1800s, so ARCH is great for looking at volatility over very long periods. I don't know that I'd say that the ARCH model has a lot of problems -- it solved the problem of not allowing volatility in time or in the level of the underlying process. It allowed Robert Engle to put to rest Milton Friedman's idea that inflation uncertainty varied with inflation level and won Engle the Nobel Prize.

However, I agree with Brian that there are probably better volatility forecasts. ARCH models are necessarily based in the past, not in expectations. I think I would look first at implied volatility from options. Using implied volatility from options will also allow to forecast higher moments like skew and kurtosis.

## Answer by Brian B (score 11)

https://quant.stackexchange.com/a/610

GARCH(1,1) is a "standard approach for modeling volatility" mainly in academic literature. Most of us in the real world don't use it. Volatility forecasting tends to come more from looking at more-liquid comparables for future market volatility than from fitting fancy retrospective models.

As for ignoring the dependence of residuals, well, folks are probably considering the problem to be less nettlesome than problems introduced by trying to fit complex models with too many parameters.

## Answer by Quant Trader (score 2)

https://quant.stackexchange.com/a/3194

If you calculate a var swap using SPX term structure implied vol versus a GARCH(1,1) estimated on 2yrs of past prices, you may see the first 4-5 (non-weekly) expiries offer roughly constant premiums over realised (negative varswap value) which would suggest at least someone is pricing using GARCH in the market.

## Answer by Richard Hardy (score 2)

https://quant.stackexchange.com/a/30738

You might be conflating two different things:

- autocorrelation in model residuals in a fixed sample (window) and

- autocorrelation in forecast errors across samples (rolling or expanding windows).

(1) is undesirable as it indicates the model misses a pattern which it should ideally capture. This can be remedied, for example, by changing the model. One may add an ARMA structure to the model's error term (to get ARMA-GARCH from pure GARCH, for example), change the model's autoregressive order, or do some other changes.

(2) can happen by construction and need not indicate any problem with the forecasts or the modelling scheme that is generating them. Indeed, forecast errors of $h$ steps ahead will necessarily be MA($h-1$) processes; see e.g. Diebold "Forecasting in Economics, Business, Finance and Beyond" Chapter 10 "Point Forecast Evaluation", section 10.1 "Absolute Standards for Point Forecasts" (version of 14 December 2015; the linked version might change over time).

## Answer by Ram Ahluwalia (score 1)

https://quant.stackexchange.com/a/2613

GARCH models were developed by Robert Engle precisely to deal with the problem of auto-correlated residuals (which occurs when you have volatility clustering for example) in time-series regression. To ask "Why are GARCH models used to forecast volatility if residuals are often correlated?" misses this point.