Superiority of the Neural Network Models for Multivariate Price and Volatility Forecasting

Forecasting stock prices and volatility plays a crucial role in making better investment decisions. Recently, there has been a growing interest in studying the Forecast Linear Augmented Projection (FLAP) method for multivariate normally distributed time series to reduce the forecast error variance and mean squared error (MSE) of long-term forecasts. FLAP method consists of three steps: formation of principal components, forecasting original and component series (base forecasts), and then projecting those base forecasts. First, this paper shows that the non-linear prediction (conditional mean) has a smaller MSE than the linear prediction. Then, it demonstrates that for multivariate time series, forecasts using the neural network autoregressive (NNAR) model with FLAP outperform those obtained by the commonly used autoregressive integrated moving average (ARIMA) model forecasts with FLAP (resulting in lower out-of-sample root mean squared error (RMSE) in general). For simulated multivariate data with t-distributed errors, the combined forecast model with NNAR and FLAP outperforms the NNAR forecast model. In the empirical study, we forecast stock price and volatility for 55 most traded stocks and S&P500 index using the ARIMA model with FLAP and the NNAR model with FLAP. The results show that FLAP is more effective in reducing forecast error variance and RMSE for non-stationary multivariate price and volatility forecasts.