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

Uwe Hassler and Mehdi Hosseinkouchack

A chapter in Essays in Honor of Joon Y. Park: Econometric Theory, 2023, vol. 45A, pp 97-114 from Emerald Group Publishing Limited

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 statisticVRqis 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.

Keywords: I(0); KPSS; variance ratio tests; Karhunen-Loève; scale invariance; local alternative; C12 (hypothesis testing); C22 (time series) (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eme:aecozz:s0731-90532023000045a003

DOI: 10.1108/S0731-90532023000045A003

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