On the Empirical Spectral Distribution of Lag-Covariance Matrix in Singular Spectrum Analysis

Rahmatan, Hormoz; Kalantari, Mahdi

doi:10.22080/cjms.2021.18838.1507

On the Empirical Spectral Distribution of Lag-Covariance Matrix in Singular Spectrum Analysis

Document Type : Research Articles

Authors

Hormoz Rahmatan ¹
Mahdi Kalantari ²

¹ Department of Mathematics, Faculty of Science, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

² Department of Statistics,, Faculty of Science, Payame Noor University, P.O.Box 19395-4697, Tehran, Iran

10.22080/cjms.2021.18838.1507

Abstract

Singular Spectrum Analysis (SSA) is a non-parametric and rapidly developing method of time series analysis. Recently, this technique receives much attention in a variety of fields. In SSA, a special matrix that is called lag-covariance matrix plays a pivotal role in analyzing stationary time series. The objective of this paper is to examine whether the Empirical Spectral Distribution (ESD) of lag-covariance matrix converges to Marˇcenko{Pastur distribution or not. Such limiting distribution can help us to provide more reliable statistical inference when encountering with high-dimensional data. Moreover, a simulation study is performed and some tools of Random Matrix Theory (RMT) are used.

Keywords