The Bracketing Condition for Limit Theorems on Stationary Linear Processes

Abstract

This paper aims at improvement in regularity conditions on spectral densities for the limit theorems of the quasi maximum-likelihood estimator and the quasi likelihood-ratio statistic. The approach parallels the Daniels-Huber-Pollard proofs of central limit theorems under nonstandard conditions for i.i.d. situations. The results of the paper enable one to dispense with excessive regularity conditions on the spectral density.