Skip to content
All library documents

Evaluate ARIMA and GARCH with Out-of-Sample Forecasts

Article Quant Q&A · Author: Prgmr
Read the original

Summary

The document asks whether adding GARCH to an ARIMA model can improve forecasts, with the stated interest in forecasting returns and obtaining longer forecast horizons. Its answer cautions that results cannot be known in advance and raises a key distinction: GARCH is generally used to model conditional volatility, so it may not directly improve forecasts of return levels. The model comparison should match the quantity being forecast.

The response cites a study that found little that outperformed a GARCH(1,1) model for volatility in a stock and an exchange rate, while emphasizing that this finding may not carry over to other assets. It recommends evaluating alternatives out of sample. The cited result is not a universal ranking, and the short exchange does not specify forecast horizons, assets beyond those examples, evaluation metrics, or implementation details. It therefore supports empirical model comparison rather than a blanket claim that GARCH extends useful return forecasts.

Key ideas

  • GARCH models conditional volatility, which differs from forecasting return levels.
  • Whether adding GARCH improves forecasts depends on the target, asset, and evaluation setup.
  • A cited study found GARCH(1,1) difficult to beat for volatility on a stock and an exchange rate.
  • Compare candidate models out of sample instead of assuming performance from convergence or model form.

Tags

StatisticsVolatilityBacktesting
Full text
# ARIMA vs ARIMA + GARCH


# ARIMA vs ARIMA + GARCH












If an ARIMA model converges quickly, would using GARCH improve the forecast performance? By improve I mean provide longer time periods for forecasts. Basically trying to forecast returns.

## Answer by phdstudent (score 1)

https://quant.stackexchange.com/a/38805

Without testing it is hard to know. I am assuming you are trying to predict volatility and not returns. Hansen and Lunde (2005) concluded that hardly anything beats a Garch(1,1) for a stock and an exchange rate. But this conclusion could be re markedly different for another assets. There is know way to tell a priori. You need to run the models out-of-sample and see what performs better.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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