Combining Rolling ARMA and GARCH Forecasts for S&P 500 Trading

Summary

This article describes a directional S&P 500 strategy that refits a return model on a rolling window, forecasts the next day, and takes a long or short position according to the forecast sign. For each window, it selects an ARMA specification by Akaike Information Criterion, then combines that mean model with a GARCH(1,1) volatility model using a skewed error distribution. The example uses 500 daily observations per fitting window and compares the resulting strategy with buy and hold.

The implementation is presented in R, with forecast directions shifted to align signals with the returns they could have predicted and avoid look-ahead bias. The article reports an equity-curve comparison through October 2015, but the supplied text does not give a precise performance estimate. It warns that fitting many models each day is computationally slow, and that the vectorised backtest omits realistic commissions and slippage, so live results may be weaker. The window length is also a choice that could be optimized, bringing a risk of overfitting.

Key ideas

• The strategy refits an ARMA mean model and GARCH volatility model on a rolling window of index returns.
• Akaike Information Criterion selects among candidate ARMA orders for each window.
• The next-day forecast sign determines whether the strategy is long or short the index.
• Forecast signals must be aligned with subsequent returns to prevent look-ahead bias.
• The reported backtest omits trading costs and slippage, and its window choice may be overfit.

Tags

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