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Title: Spectral Analysis of a Symmetrized Auto-cross Covariance Matrix
Authors: WANG CHEN
Keywords: Spectral Analysis, Random Matrix Theory
Issue Date: 30-Dec-2013
Source: WANG CHEN (2013-12-30). Spectral Analysis of a Symmetrized Auto-cross Covariance Matrix. ScholarBank@NUS Repository.
Abstract: This thesis investigated some spectral properties of a symmetrized auto-cross covariance matrix M_n (t) where t is an integer referring to the number of lags. The first part derived an explicit expression of the limiting spectral distribution (LSD) of M_n (t) using Stieltjes transform. It is interesting to note that the LSD does not depend on the lag t. The second part established the strong limit of extreme eigenvalues of M_n (t) under the finiteness of the fourth moment of the underlying variables by showing that in any closed interval outside the support of the LSD, with probability 1 there would be no eigenvalues for all n sufficiently large. The results in this thesis can be applied in the estimation of the number of factors and lags in the framework of a large dynamic factor model, and will facilitate model selection of large dimensional models with a lagged time series structure.
Appears in Collections:Ph.D Theses (Open)

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