On Random Matrix Theory and Autoregressive Modeling

Random matrix theory has attracted growing interest in signal processing and communications over the last one or two decades. It has gained further impetus due to the upsurge in the occurrence of 'big data'. However so far little of this interest has seeped into system identification. Random matrix theory refers to a regime where the number of variables or parameters of interest is of the same order as the number of observations. This is by far the most common situation with big data. However in this case, traditional asymptotic analysis of estimator performance, which assumes the number of parameters is of much smaller order than the number of observations, breaks down. Much of the use of random matrix theory in signal processing has been to study the asymptotics of sample covariance matrices. However there has been little application to modelling. We begin the process of changing that by analysing some aspects of autoregressive modelling in the random matrix theory regime.