Orthogonal samples for estimators in time series

TL;DR

This paper introduces orthogonal samples for time series statistics, providing a simple, fast method to estimate nuisance parameters and sampling distributions, improving inference accuracy in stationary time series analysis.

Contribution

It proposes a novel orthogonal sample technique that simplifies estimation of nuisance parameters and sampling distributions for a broad class of time series statistics.

Findings

Orthogonal samples effectively estimate nuisance parameters.

The method accurately approximates sampling distributions.

Simulations demonstrate computational efficiency and reliability.

Abstract

Inference for statistics of a stationary time series often involve nuisance parameters and sampling distributions that are difficult to estimate. In this paper, we propose the method of orthogonal samples, which can be used to address some of these issues. For a broad class of statistics, an orthogonal sample is constructed through a slight modification of the original statistic, such that it shares similar distributional properties as the centralised statistic of interest. We use the orthogonal sample to estimate nuisance parameters of weighted average periodogram estimators and $L_{2}$-type spectral statistics. Further, the orthogonal sample is utilized to estimate the finite sampling distribution of various test statistics under the null hypothesis. The proposed method is simple and computationally fast to implement. The viability of the method is illustrated with various simulations.