A0878
Title: Asymptotic of large autocovariance matrices
Authors: Monika Bhattacharjee - IIT Bombay (India) [presenting]
Abstract: The high dimensional moving average process is considered, and the asymptotics for eigenvalues of its sample autocovariance matrices are explored. It is proved that under quite weak conditions, in a unified way, the limiting spectral distribution (LSD) of any symmetric polynomial in the sample autocovariance matrices, after suitable centring and scaling, exists and is non-degenerate. Methods from free probability in conjunction with the method of moments to establish our results are used. In addition, a general description of the limits in terms of some freely independent variables is provided. Asymptotic normality results are shown for the traces of these matrices. Statistical uses of these results in problems such as order determination of high dimensional MA and AR processes and testing hypotheses for such processes' coefficient matrices are suggested.
