Testing for unit roots based on sample autocovariances

TL;DR

This paper introduces a nonparametric unit-root test based on sample autocovariances that effectively distinguishes stationary processes from those with unit roots, with strong theoretical backing and practical implementation in R.

Contribution

It proposes a novel, nonparametric test for unit roots using sample autocovariances, addressing the divergence issue and providing an asymptotically powerful, user-friendly R implementation.

Findings

Test effectively distinguishes I(0) from I(1) processes

Sample autocovariance diverges under unit-root alternative

Test has asymptotic power of one

Abstract

We propose a new unit-root test for a stationary null hypothesis $H_0$ against a unit-root alternative $H_1$. Our approach is nonparametric as $H_0$ only assumes that the process concerned is $I(0)$ without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function (ACVF) converges to the finite population ACVF for an $I(0)$ process while it diverges to infinity for a process with unit-roots. Therefore the new test rejects $H_0$ for the large values of the sample ACVF. To address the technical challenge `how large is large', we split the sample and establish an appropriate normal approximation for the null-distribution of the test statistic. The substantial discriminative power of the new test statistic is rooted from the fact that it takes finite value under $H_0$ and diverges to infinity under $H_1$. This allows us to truncate the critical values of the test to make it with the asymptotic power one. It also alleviates the loss of power due to the sample-splitting. The test is implemented in a user-friendly R-function.