A Critical Value Function Approach, with an Application to Persistent Time-Series

TL;DR

This paper introduces a new numerical method for critical value functions in hypothesis testing, especially effective with highly persistent regressors, improving size control and test performance over existing methods.

Contribution

It proposes a novel critical value function approach that outperforms existing simulation-based methods in controlling size for persistent time-series models.

Findings

The new method effectively controls size in persistent regressors.

It outperforms existing similar tests in power and size accuracy.

The approach is applicable to models with highly persistent data.

Abstract

Researchers often rely on the t-statistic to make inference on parameters in statistical models. It is common practice to obtain critical values by simulation techniques. This paper proposes a novel numerical method to obtain an approximately similar test. This test rejects the null hypothesis when the test statistic is larger than a critical value function (CVF) of the data. We illustrate this procedure when regressors are highly persistent, a case in which commonly-used simulation methods encounter difficulties controlling size uniformly. Our approach works satisfactorily, controls size, and yields a test which outperforms the two other known similar tests.