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ASYMPTOTIC BEHAVIOR OF THE CUSUM OF SQUARESTEST UNDER STOCHASTIC AND DETERMINISTIC TIMETRENDS

Published online by Cambridge University Press:  11 July 2011

Bent Nielsen  and
Jouni S. Sohkanen
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Abstract

We generalize the cumulative sum of squares (CUSQ) testto the case of nonstationary autoregressivedistributed lag models with deterministic timetrends. The test may be implemented with eitherordinary least squares residuals or standardizedforecast errors. In explosive cases the asymptotictheory applies more generally for the least squaresresiduals-based test. Preliminary simulations of thetests suggest a very modest difference between thetests and a very modest variation with nuisanceparameters. This supports the use of the tests inexplorative analysis.

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Type
Brief Report
Information
Econometric Theory , Volume 27 , Issue 4 , August 2011 , pp. 913 - 927
Copyright
Copyright © Cambridge University Press 2011

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Footnotes

The authors received support from the ESRC(RES-000-27-0179 and PTA-031-2006-00174), the OpenSociety Institute and the Oxford Martin School.Comments from Andrew Whitby are gratefullyacknowledged.

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