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

Singular spectrum analysis (ssa) is a non-parametric and rapidly developing method of time series analysis. recently, this technique receives much attention in a wide variety of fields. in ssa, a special matrix, which 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 highdimensional data. moreover, a simulation study is performed and some tools of random matrix theory (rmt) are used.