Adaptive Rate-optimal Detection of Small Autocorrelation Coefficients

Alain Guay, Emmanuel Guerre and Štěpána Lazarová
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Emmanuel Guerre: Queen Mary, University of London
Štěpána Lazarová: Queen Mary, University of London

No 645, Working Papers from Queen Mary University of London, School of Economics and Finance

Abstract: A new test is proposed for the null of absence of serial correlation. The test uses a data-driven smoothing parameter. The resulting test statistic has a standard limit distribution under the null. The smoothing parameter is calibrated to achieve rate-optimality against several classes of alternatives. The test can detect alternatives with many small correlation coefficients that can go to zero with an optimal adaptive rate which is faster than the parametric rate. The adaptive rate-optimality against smooth alternatives of the new test is established as well. The test can also detect ARMA and local Pitman alternatives converging to the null with a rate close or equal to the parametric one. A simulation experiment and an application to monthly financial square returns illustrate the usefulness of the proposed approach

Keywords: Absence of serial correlation; Data-driven nonparametric tests; Adaptive rate-optimality; Small alternatives; Time series (search for similar items in EconPapers)
JEL-codes: C12 C32 (search for similar items in EconPapers)
Date: 2009-06-01
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Working Paper: Adaptive Rate-Optimal Detection of Small Autocorrelation Coefficients (2009)
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