Improved IAMB with Expanded Markov Blanket for High-Dimensional Time Series Prediction

The classic regression model for multivariate time series prediction suffers from the curse of dimensionality because the least squares estimates become unreliable when the predictors of the time series are large and the number of samples is limited. The classic methods such as ridge regression, lasso regression, principal component regression are researched to solve the problem above. The ridge regression and principal component regression can not give the clear interpretation features for prediction, and lasso regression does not work well under collinearity, also the selections given by lasso regression are unstable and very sensitive to minor perturbations of the data. A practical method based on improved Incremental association Markov blanket (IAMB) with Expanded Markov blanket (EMB) was proposed for high-dimensional time series prediction. The EMB was constructed with simultaneous predictors and past predictors for time series. Since the faithfulness condition and reliable conditional independence test are not satisfied for high-dimensional time series with limited samples in practical applications. The symmetry of Markov blanket (MB) and the partial correlation coefficient criterion for conditional independent test were employed to learn the EMB, on which the regression was used for prediction. Empirical results show that our method based on EMB for macroeconomic prediction has less mean-square forecast error than other classic methods, especially when predicting the value with sharp fluctuation.