COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1844 Lag Length Selection for Unit Root Tests in the Presence Giuseppe Cavaliere, Peter C.B. Phillips, Stephan Smeekes, and A.M. Robert Taylor January 2012 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. |
