Effect of Dimension Reduction on Prediction Performance of Multivariate Nonlinear Time Series

The dynamic system approach in time series has been used in many real problems. Based on Taken's embedding theorem, we can build the predictive function where input is the time delay coordinates vector which consists of the lagged values of the observed series and output is the future values of the observed series. Although the time delay coordinates vector from multivariate time series brings more information than the one from univariate time series, it can exhibit statistical redundancy which disturbs the performance of the prediction function. We apply dimension reduction techniques to solve this problem and analyze the effect of this approach for prediction. Our experiment uses delayed Lorenz series; least squares support vector regression approximates the predictive function. The result shows that linearly preserving projection improves the prediction performance.