Multiscale Forecasting Models Based on Singular Values for Nonstationary Time Series

Abstract

Time series are valuable sources of information for supporting planning activities. Transport, fishery, economy and finances are predominant sectors concerned into obtaining information in advance to improve their productivity and efficiency. During the last decades diverse linear and nonlinear forecasting models have been developed for attending this demand. However the achievement of accuracy follows being a challenge due to the high variability of the most observed phenomena. In this research are proposed two decomposition methods based on Singular Value Decomposition of a Hankel matrix (HSVD) in order to extract components of low and high frequency from a nonstationary time series. The proposed decomposition is used to improve the accuracy of linear and nonlinear autoregressive models. The evaluation of the proposed forecasters is performed through data coming from transport sector and fishery sector. Series of injured persons in traffic accidents of Santiago and Valparaíso and stock of sardine and anchovy of central-south Chilean coast are used. Further, for comparison purposes, it is evaluated the forecast accuracy reached by two decomposition techniques conventionally used, Singular Spectrum Analysis (SSA) and decomposition based on Stationary Wavelet Transform (SWT), both joint with linear and nonlinear autoregressive models. The experiments shown that the proposed methods based on Singular Value Decomposition of a Hankel matrix in conjunction with linear or nonlinear models reach the best accuracy for one-step and multi-step ahead forecasting of the studied time series.