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CUMULATED SUM OF SQUARES STATISTICS FOR NONLINEAR AND NONSTATIONARY REGRESSIONS

Published online by Cambridge University Press:  22 February 2019

Vanessa Berenguer-Rico  and
Bent Nielsen
Vanessa Berenguer-Rico
Affiliation:
University of Oxford
Bent Nielsen*
Affiliation:
University of Oxford
*
*Address correspondence to Bent Nielsen, Nuffield College, Oxford, OX1 1NF, UK; e-mail: bent.nielsen@nuffield.ox.ac.uk.
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Abstract

We show that the cumulated sum of squares statistic has a standard Brownian bridge–type asymptotic distribution in nonlinear regression models with (possibly) nonstationary regressors. This contrasts with cumulated sum statistics which have been previously studied and whose asymptotic distribution has been shown to depend on the functional form and the stochastic properties, such as persistence and stationarity, of the regressors. A recursive version of the test is also considered. A local power analysis is provided, and through simulations, we show that the test has good size and power properties across a variety of situations.

Type
ARTICLES
Information
Econometric Theory , Volume 36 , Issue 1 , February 2020 , pp. 1 - 47
Copyright
Copyright © Cambridge University Press 2019 

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Footnotes

Comments from Giuseppe Cavaliere and the referees are gratefully acknowledged.

References

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