Prediction of periodically correlated processes by wavelet transform and multivariate methods with applications to climatological data

Abstract

This article studies the prediction of periodically correlated process using wavelet transform and multivariate methods with applications to climatological data. Periodically correlated processes can be reformulated as multivariate stationary processes. Considering this fact, two new prediction methods are proposed. In the first method, we use stepwise regression between the principal components of the multivariate stationary process and past wavelet coefficients of the process to get a prediction. In the second method, we propose its multivariate version without principal component analysis a priori. Also, we study a generalization of the prediction methods dealing with a deterministic trend using exponential smoothing. Finally, we illustrate the performance of the proposed methods on simulated and real climatological data (ozone amounts, flows of a river, solar radiation, and sea levels) compared with the multivariate autoregressive model. The proposed methods give good results as we expected.