Approximate Normality of T-Ratios Based on M-Estimators for the Unit Root

11 Pages Posted: 6 Jan 1998 Last revised: 15 Jan 2012

See all articles by Karim M. Abadir

Karim M. Abadir

Imperial College Business School

Andre Lucas

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute

Date Written: January 15, 2012

Abstract

We derive formulae for the asymptotic density and distribution functions of the t-statistic for autoregressive unit roots based on M-estimators. The distribution depends upon a nuisance parameter. Consequently, new critical values for this test have to be generated for each new estimator that is used. We therefore also derive simple yet accurate normal approximations to the asymptotic distribution of these unit root M-tests. Using these asymptotic approximations, critical values of the tests can easily be obtained without resorting to extensive simulation experiments. The approximation requires no new tabulation, and the resulting distribution function has a maximum absolute error of 0.002 for typical quantiles.

JEL Classification: C12, C22

Suggested Citation

Abadir, Karim M. and Lucas, Andre, Approximate Normality of T-Ratios Based on M-Estimators for the Unit Root (January 15, 2012). Economics Letters, Forthcoming. Available at SSRN: https://ssrn.com/abstract=51021

Karim M. Abadir

Imperial College Business School ( email )

South Kensington Campus
Exhibition Road
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/portal/page?_pageid=61,629646&_dad=portallive&_schema=PORTALLIVE

Andre Lucas (Contact Author)

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.tinbergen.nl

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