Semiparametrically Point-Optimal Hybrid Rank Tests for Unit Roots

TL;DR

This paper introduces a new semiparametric rank-based unit root test that is point-optimal with correct size and performs well across various innovation distributions, including non-Gaussian ones.

Contribution

It develops a novel class of invariant, rank-based unit root tests that are semiparametric, point-optimal under correct reference density, and robust to different innovation distributions.

Findings

Test is asymptotically valid regardless of true innovation density.

Achieves near efficiency and point-optimality with correct reference density.

Demonstrates improved power over traditional tests in simulations with non-Gaussian innovations.

Abstract

We propose a new class of unit root tests that exploits invariance properties in the Locally Asymptotically Brownian Functional limit experiment associated to the unit root model. The invariance structures naturally suggest tests that are based on the ranks of the increments of the observations, their average, and an assumed reference density for the innovations. The tests are semiparametric in the sense that they are valid, i.e., have the correct (asymptotic) size, irrespective of the true innovation density. For a correctly specified reference density, our test is point-optimal and nearly efficient. For arbitrary reference densities, we establish a Chernoff-Savage type result, i.e., our test performs as well as commonly used tests under Gaussian innovations but has improved power under other, e.g., fat-tailed or skewed, innovation distributions. To avoid nonparametric estimation, we propose a simplified version of our test that exhibits the same asymptotic properties, except for the Chernoff-Savage result that we are only able to demonstrate by means of simulations.