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

## TL;DR

This paper introduces a simple stochastic weighting method for linear processes with short and long memory, providing more accurate confidence intervals for the mean than traditional methods, supported by theoretical and numerical evidence.

## Contribution

It presents a novel stochastic weighting approach that yields asymptotically exact and more precise confidence intervals for the mean in linear processes.

## Key findings

- Produces asymptotically exact confidence intervals with improved accuracy.
- Offers a new Edgeworth expansion for weighted processes without Cramér condition.
- Demonstrates theoretical and numerical superiority over classical methods.

## 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.