A Residuals-Based Nonparametric Variance Ratio Test for Cointegration

TL;DR

This paper introduces a nonparametric variance ratio test for cointegration that is easy to implement, robust to size distortions, and effective in finite samples, demonstrated through cryptocurrency price data.

Contribution

It develops the asymptotic theory for a residuals-based variance ratio test that requires no tuning parameters or correlation structure specification.

Findings

The test has smaller size distortions compared to other residuals-based tests.

It maintains good size-corrected power without power reversal issues.

Application to cryptocurrency prices shows practical usefulness.

Abstract

This paper derives asymptotic theory for Breitung's (2002, Journal of Econometrics 108, 343-363) nonparameteric variance ratio unit root test when applied to regression residuals. The test requires neither the specification of the correlation structure in the data nor the choice of tuning parameters. Compared with popular residuals-based no-cointegration tests, the variance ratio test is less prone to size distortions but has smaller local asymptotic power. However, this paper shows that local asymptotic power properties do not serve as a useful indicator for the power of residuals-based no-cointegration tests in finite samples. In terms of size-corrected power, the variance ratio test performs relatively well and, in particular, does not suffer from power reversal problems detected for, e.g., the frequently used augmented Dickey-Fuller type no-cointegration test. An application to daily prices of cryptocurrencies illustrates the usefulness of the variance ratio test in practice.