Semiparametric Testing With Highly Persistent Predictors

57 Pages Posted: 2 Aug 2018 Last revised: 17 Sep 2020

See all articles by Bas J. M. Werker

Bas J. M. Werker

Tilburg University - Center for Economic Research (CentER)

Bo Zhou

Durham University Business School

Date Written: July 13, 2018


We address the issue of semiparametric efficiency in the bivariate regression problem with a highly persistent predictor, where the joint distribution of the innovations is regarded an infinite-dimensional nuisance parameter. Using a structural representation of the limit experiment and exploiting invariance relationships therein, we construct invariant point-optimal tests for the regression coefficient of interest. This approach naturally leads to a family of feasible tests based on the component-wise ranks of the innovations that can gain considerable power relative to existing tests under non-Gaussian innovation distributions, while behaving equivalently under Gaussianity. When an i.i.d.\ assumption on the innovations is appropriate for the data at hand, our tests exploit the efficiency gains possible. Moreover, we show by simulation that our test remains well behaved under some forms of conditional heteroskedasticity.

Keywords: Predictive Regression, Limit Experiment, LABF, Maximal Invariant, Rank Statistics

JEL Classification: C12, C14

Suggested Citation

Werker, Bas J.M. and Zhou, Bo, Semiparametric Testing With Highly Persistent Predictors (July 13, 2018). Available at SSRN: or

Bas J.M. Werker

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

Econometrics and Finance Group
5000 LE Tilburg

Bo Zhou (Contact Author)

Durham University Business School ( email )

Mill Hill Lane
Durham, DH1 3LB
United Kingdom

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