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SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS

Published online by Cambridge University Press:  12 September 2017

Jungbin Hwang  and
Yixiao Sun
Jungbin Hwang
Affiliation:
University of Connecticut
Yixiao Sun*
Affiliation:
University of California, San Diego
*
*Address correspondence to Yixiao Sun, Department of Economics, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0508, USA; e-mail: yisun@ucsd.edu.
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Abstract

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This paper proposes new, simple, and more accurate statistical tests in a cointegrated system that allows for endogenous regressors and serially dependent errors. The approach involves first transforming the time series using orthonormal basis functions in L2[0, 1], which have energy concentrated at low frequencies, and then running an augmented regression based on the transformed data and constructing the test statistics in the usual way. The approach is essentially the same as the trend instrumental variable approach of Phillips (2014), but the number of orthonormal basis functions is held fixed for the development of the standard F and t asymptotic theory. The tests are extremely simple to implement, as they can be carried out in exactly the same way as if the transformed regression is a classical linear normal regression. In particular, critical values are from the standard F or t distribution. The proposed F and t tests are robust in that they are asymptotically valid regardless of whether the number of basis functions is held fixed or allowed to grow with the sample size. The F and t tests have more accurate size in finite samples than existing tests such as the asymptotic chi-squared and normal tests based on the fully modified OLS estimator of Phillips and Hansen (1990) and can be made as powerful as the latter test.

Type
ARTICLES
Information
Econometric Theory , Volume 34 , Issue 5 , October 2018 , pp. 949 - 984
Copyright
Copyright © Cambridge University Press 2017 

Footnotes

We thank Michael Jansson and two anonymous referees for constructive comments. We are particularly grateful to Peter C.B. Phillips, the editor, for his detailed comments, constructive suggestions, and considerable input. We acknowledge partial research support from NSF under Grant No. SES-1530592.

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