On Functionals of Linear Processes with Estimated Parameters

Abstract

For a stationary linear process with independent and identically distributed innovations, the paper addresses asymptotic properties of partial sums of nonlinear functional applied to the process when an unknown parameter is estimated. General representations are established under the condition that the innovation coefficients are either summable or regularly varying with index in (-1, -1/2). The usefulness of the representations is demonstrated through the derivation of limiting distributions for several common examples such as kurtosis, the sign test, and the absolute deviation from the mean.