Deconvolution and Estimation of Transfer Function Phase and Coefficients for Nongaussian Linear Processes

Abstract

NonGaussian linear processes are considered. It is shown that the phase of the transfer function can be estimated under broad conditions. This is not true of Gaussian linear processes and in this sense Gaussian linear processes are atypical. The asymptotic behavior of a phase estimate is determined. The phase estimates make use of bispectral estimates. These ideas are applied to a problem of deconvolution which is effective even when the transfer function is not minimum phase. A number of computational illustrations are given. Introduction.Most of the literature on finite parameter time series models is either centered on Gaussian models or the results are motivated by what one can do in the case of Gaussian models. Here we deal with stationary nonGaussian linear processes and show that under broad conditions, aspects of the structure that are completely nonidentifiable in the Gaussian case can be resolved in the nonGaussian case. Assume that the random variables v t , t = • • • , -1,0,1, • • • are independent and identically distributed with mean zero, Ev t = 0, and variance one Evf = 1. Let {a,} be a sequence of real constants with