Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility

36 Pages Posted: 9 Jan 2012

See all articles by Giuseppe Cavaliere

Giuseppe Cavaliere

University of Bologna - Department of Economics

Peter C. B. Phillips

University of Auckland Business School; Yale University - Cowles Foundation; Singapore Management University - School of Economics

Stephan Smeekes

affiliation not provided to SSRN

A. M. Robert Taylor

University of Nottingham - School of Economics

Date Written: January 9, 2012

Abstract

A number of recently published papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, assumed that the lag length in the unit root test regression is a deterministic function of the sample size, rather than data-determined, the latter being standard empirical practice. In this paper we investigate the finite sample impact of unconditional heteroskedasticity on conventional data-dependent methods of lag selection in augmented Dickey-Fuller type unit root test regressions and propose new lag selection criteria which allow for the presence of heteroskedasticity in the shocks. We show that standard lag selection methods show a tendency to over-fit the lag order under heteroskedasticity, which results in significant power losses in the (wild bootstrap implementation of the) augmented Dickey-Fuller tests under the alternative. The new lag selection criteria we propose are shown to avoid this problem yet deliver unit roots with almost identical finite sample size and power properties as the corresponding tests based on conventional lag selection methods when the shocks are homoskedastic.

Keywords: Unit root test, Lag selection, Information criteria, Wild bootstrap, Nonstationary volatility

JEL Classification: C22, C15

Suggested Citation

Cavaliere, Giuseppe and Phillips, Peter C. B. and Smeekes, Stephan and Taylor, A. M. Robert, Lag Length Selection for Unit Root Tests in the Presence of Nonstationary Volatility (January 9, 2012). Cowles Foundation Discussion Paper No. 1844, Available at SSRN: https://ssrn.com/abstract=1981983 or http://dx.doi.org/10.2139/ssrn.1981983

Giuseppe Cavaliere

University of Bologna - Department of Economics ( email )

Bologna
Italy
+390512098489 (Phone)

Peter C. B. Phillips (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

Stephan Smeekes

affiliation not provided to SSRN

A. M. Robert Taylor

University of Nottingham - School of Economics ( email )

University Park
Nottingham, NG7 2RD
United Kingdom

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