Title: Asymptotics 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. Under quite weak conditions, we prove, in a unified way, that the limiting spectral distribution (LSD) of any symmetric polynomial in the sample autocovariance matrices, after suitable centering and scaling, exists and is nondegenerate. We use methods from free probability in conjunction with the method of moments to establish our results. In addition, we are able to provide a general description of the limits in terms of some freely independent variables. We also establish asymptotic normality results for the traces of these matrices. We suggest statistical uses of these results in problems such as order determination of high dimensional MA and AR processes and testing of hypotheses for coefficient matrices of such processes.