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## Abstract for "Testing for the Number Of Factors And Lags in High Dimensional Factor" by Matthew Harding

In this paper, we develop novel nonparametric statistical procedures for estimating the number of factors and lags in high dimensional dynamic factor models. We employ a Random Matrix Theory based approach to characterize the eigenvalue distribution of the symmetric time-delayed covariance matrices (also called commutator matrices in the context of free probability) in order to test for the number of factors and time delay effects in the data. To this end, we will use the Stieltjes Transform to obtain closed form solutions of the moments of the eigenvalue distribution function of the commutator matrix in terms of the number of individuals, number of time periods , temporal lag and the parameters of the covariance matrix of the idiosyncratic noise. We then develop an algorithm using these theoretical moments and a generalized method of moments (GMM) methodology to uncover the underlying dynamic structure. In addition, we will use results from matrix pertrubation theory to help in the assessing the robustness of the identification algorithm. The resulting statistical procedure is applied to the estimation of two dynamic factor models.