GARCH turns yesterday’s shocks and volatility estimate into a forecast of today’s conditional variance. That is useful for describing risk that changes over time; it is not a forecast of whether price will rise or fall.
What a GARCH model estimates
GARCH, short for generalized autoregressive conditional heteroskedasticity, models a return series whose conditional variance changes with information from earlier periods. In the common GARCH(1,1) form, the new variance estimate combines a baseline, the previous squared return shock, and the previous variance estimate. A time-series lecture from Peking University sets out this equation and its assumptions; a separate study applies GARCH-family models to corn-futures return volatility (lecture notes, Texas Journal of Agriculture and Natural Resources study).
Why past shocks enter the estimate
A large return shock can raise the model’s next conditional variance. The lagged variance term carries some of that estimate forward, so the model can represent volatility persistence without treating variance as constant. That mechanism is explicit in the GARCH equation described in the Peking University notes and is the basis for the return-volatility modelling compared in the Texas corn-futures paper (Peking University, Texas Journal study).
A basic specification treats positive and negative shocks of the same size alike because it uses squared shocks. That symmetry can be a poor description when downside and upside moves have different volatility effects. The Texas study compares asymmetric variants, including EGARCH and TGARCH, for corn returns; the lecture notes also explain the symmetry limitation of the basic model (study, lecture notes).
Forecasts are not guarantees
A model can fit one series and still forecast another poorly. A study of energy-market volatility compared GARCH-family specifications with machine-learning models and reported that its machine-learning models outperformed traditional GARCH models out of sample in that dataset. Its result is specific to the assets, inputs and evaluation in that study—not a universal ranking of methods (arXiv paper record, Texas corn-futures study).
There are other limits. The standard form depends on the chosen return series, distributional assumptions and sample. Its symmetric response may miss asymmetry; a changing market regime can also make past relationships less useful. A volatility forecast is not automatically a calibrated probability interval, and it says nothing by itself about expected return.
How you would test a volatility forecast
Treat the model as a forecast, not as a strategy result. Specify the return series and forecast horizon first. Fit parameters only on the training window, then generate forecasts for dates the fit did not use. Compare each forecast with a clearly defined realised-volatility measure over the same horizon, and keep a simple benchmark such as a rolling historical estimate.
Check forecast errors across calm and turbulent periods, and inspect whether errors systematically miss large moves or respond differently to positive and negative shocks. If you compare GARCH with an asymmetric version or another model, keep the test dates and evaluation measure identical. Record every attempted specification; selecting the best result after many trials can make the winner look more convincing than it is. The same discipline applies to any trading backtest: keep the evaluation genuinely unseen, as explained in our guide to out-of-sample testing.
The cited corn and energy studies illustrate why that comparison matters: their reported preferred model depends on the data and competing specifications actually tested (Texas Journal study, arXiv energy-volatility study). Those papers are examples, not proof that their winning specification transfers to a different instrument or period.
Takeaway
GARCH gives volatility a memory. Whether that memory helps is an empirical question, answered only by forecasts checked on data the model did not see.