Confidence intervals with higher accuracy for short and long memory linear processes

Abstract

In this paper an easy to implement method of stochastically weighing short and long memory linear processes is introduced. The method renders asymptotically exact size confidence intervals for the population mean which are significantly more accurate than their classical counterparts for each fixed sample size $n$. It is illustrated both theoretically and numerically that the randomization framework of this paper produces randomized (asymptotic) pivotal quantities, for the mean, which admit central limit theorems with smaller magnitudes of error as compared to those of their leading classical counterparts. An Edgeworth expansion result for randomly weighted linear processes whose innovations do not necessarily satisfy the Cramer condition, is also established.