Forecasting the S&P 500 index using time series analysis and simulation methods

Abstract

The S&P 500 represents a diverse pool of securities in addition to Large Caps. A range of audiences are interested in the S&P 500 forecasts including investors, speculators, economists, government and researchers. The primary objective is to attempt to provide an accurate 3 month and 12 month forecast using the recent credit crisis data, specifically during the time range of 10/2008 - 09/2009. Several methods were used for prediction fit including: Linear Regression, Time Series Models: Autoregressive Integrated Moving Averages (ARIMA), Double Exponential Smoothing, Neural Networks, GARCH, and Bootstrapping Simulations. The criteria to evaluate forecasts were the following metrics for the evaluation range: Root Mean Square Error (RMSE), Absolute Error (MAE), Akaike information criterion (AIC) and Schwartz Bayesian criterion (SBC). But most importantly, the primary forecasting measure includes MAE and Mean Absolute Percentage Error (MAPE), which uses the forecasted value and the actual S&P 500 level as input parameters. S&P 500 empirical results indicate that the Hybrid Linear Regression outperformed all other models for 3 month forecasts with the explanatory variables: GDP, credit default rates, and VIX volatility conditioned on credit crisis data ranges, but performed poorly during speculation periods such as the Tech Bubble. The Average of Averages Bootstrapping Simulation had the most consistent historical forecasts forl2 month levels, and by using log returns from the Great Depression, Tech Bubble, and Oil Crisis the simulation indicates an expected value -2%, valid up to 12 months.

(cont.) ARIMA and Double Exponential smoothing models underperformed in comparison. ARIMA model does not adjust well in the "beginning" of a downward/upward pattern, and should be used when a clear trend is shown. However, the Double Exponential Smoothing is a good model if a steep incline/decline is expected. ARMAX + ARCH/EGARCH performed below average and is best used for volatility forecasts instead of mean returns. Lastly, Neural Network residual models indicate mixed results, but on average outperformed traditional time series models (ARIMA/Double Exponential Smoothing). Additional research includes forecasting the S&P 500 with other nontraditional time series methods such as VARFIMA (vector autoregressive fractionally integrated moving averages) and ARFIMA models. Other Neural Network techniques include Higher Order Neural Networks (HONN), Psi Sigma network (PSN), and a Recurrent Neural Network (RNN) for additional forecasting comparisons.