Supplemental Appendix to 'Semiparametrically Point-Optimal Hybrid Rank Tests for Unit Roots'

21 Pages Posted: 12 Jul 2018 Last revised: 27 Nov 2018

See all articles by Bo Zhou

Bo Zhou

Durham University Business School

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Date Written: June 6, 2018

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.

Suggested Citation

Zhou, Bo and Van den Akker, Ramon and Werker, Bas J.M., Supplemental Appendix to 'Semiparametrically Point-Optimal Hybrid Rank Tests for Unit Roots' (June 6, 2018). Available at SSRN: https://ssrn.com/abstract=3197859 or http://dx.doi.org/10.2139/ssrn.3197859

Bo Zhou (Contact Author)

Durham University Business School ( email )

Mill Hill Lane
Durham, DH1 3LB
United Kingdom

HOME PAGE: http://https://sites.google.com/view/bo-zhou

Ramon Van den Akker

Tilburg University - CentER and department of Econometrics & OR ( email )

K-623
PO Box 90153
Tilburg, 5000 LE
Netherlands

HOME PAGE: http://sites.google.com/site/rvdnakker/

Bas J.M. Werker

Tilburg University - Center for Economic Research (CentER) ( email )

Econometrics and Finance Group
5000 LE Tilburg
Netherlands

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