Generalized Correlation Measures of Causality and Forecasts of the VIX Using Non-Linear Models

This paper features an analysis of causal relations between the daily VIX, S&P500 and the daily realised volatility (RV) of the S&P500 sampled at 5 min intervals, plus the application of an Artificial Neural Network (ANN) model to forecast the future daily value of the VIX. Causal relations are analysed using the recently developed concept of general correlation Zheng et al. and Vinod. The neural network analysis is performed using the Group Method of Data Handling (GMDH) approach. The results suggest that causality runs from lagged daily RV and lagged continuously compounded daily return on the S&P500 index to the VIX. Sample tests suggest that an ANN model can successfully predict the daily VIX using lagged daily RV and lagged daily S&P500 Index continuously compounded returns as inputs.