Dependence measures for model selection in singular spectrum analysis

Abstract

Selection of optimal dimension of trajectory matrix in singular spectrum analysis plays an important role in signal reconstruction from noisy time series. A noisy time series is embedded into a Hankel matrix and the dimension of this matrix depends on the window length considered for a time series. The window length requirement of a time series depends on its underlying data generating mechanism. Since the number of columns in a Hankel structured trajectory matrix is a function of number of rows (window length), dimension dependency occurs naturally in the trajectory matrix and this dependency is characterized by the statistical properties of a time series. In this paper, we develop an entropy based dimension dependency measure that accounts for changes in information content in the matrix in response to changes in window length for a time series. We examine the performance of this measure by using simulation experiments and analyzing real data sets. Results obtained from simulation experiments show that the dimension dependency measure finds reasonably meaningful dimension of the trajectory matrix and provides better forecasting outcome when applied to some popular climatic time series and production indices.