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

Generalized correlation and kernel causality with applications in development economics

<p>New generalized correlation measures of 2012, GMC(<i>Y</i>|<i>X</i>), use Kernel regressions to overcome the linearity of Pearson's correlation coefficients. A new matrix of generalized correlation coefficients is such that when |<i>r</i>*_<i>ij</i>| > |<i>r</i>*_<i>ji</i>|, it is more likely that the column variable <i>X_j</i> is what Granger called the “instantaneous cause” or what we call “kernel cause” of the row variable <i>X_i</i>. New partial correlations ameliorate confounding. Various examples and simulations support robustness of new causality. We include bootstrap inference, robustness checks based on the dependence between regressor and error, and on the out-of-sample forecasts. Data for 198 countries on nine development variables support growth policy over redistribution and Deaton's criticism of foreign aid. Potential applications include Big Data, since our R code is available in the online supplementary material.</p