Powerful Self-Normalizing Tests for Stationarity Against the Alternative of a Unit Root

Abstract

The authors propose a family of tests for stationarity against a local unit root. It builds on the Karhunen–Loève (KL) expansions of the limiting CUSUM process under the null hypothesis and a local alternative. The variance ratio type statistic VRq is a ratio of quadratic forms of q weighted Gaussian sums such that the nuisance long-run variance cancels asymptotically without having to be estimated. Asymptotic critical values and local power functions can be calculated by standard numerical means, and power grows with q. However, Monte Carlo experiments show that q may not be too large in finite samples to obtain tests with correct size under the null. Balancing size and power results in a superior performance compared to the classic KPSS test.

Citation

Hassler, U. and Hosseinkouchack, M. (2023), "Powerful Self-Normalizing Tests for Stationarity Against the Alternative of a Unit Root", Chang, Y., Lee, S. and Miller, J.I. (Ed.) Essays in Honor of Joon Y. Park: Econometric Theory (Advances in Econometrics, Vol. 45A), Emerald Publishing Limited, Leeds, pp. 97-114. https://doi.org/10.1108/S0731-90532023000045A003