Finite sample inference for generic autoregressive models

TL;DR

This paper introduces a data splitting method for finite sample inference in autoregressive models, providing valid confidence sets and hypothesis tests without relying on complex asymptotic arguments.

Contribution

It offers a simple, data-driven approach for finite sample inference in autoregressive models, improving practical applicability over traditional asymptotic methods.

Findings

Valid finite sample confidence sets and tests are constructed.

Method demonstrated effective through simulation studies.

Sequential inference tools are also validated.

Abstract

Autoregressive models are a class of time series models that are important in both applied and theoretical statistics. Typically, inferential devices such as confidence sets and hypothesis tests for time series models require nuanced asymptotic arguments and constructions. We present a simple alternative to such arguments that allow for the construction of finite sample valid inferential devices, using a data splitting approach. We prove the validity of our constructions, as well as the validity of related sequential inference tools. A set of simulation studies are presented to demonstrate the applicability of our methodology.