Adaptive Rate-Optimal Detection of Small Autocorrelation Coefficients

Alain Guay, Emmanuel Guerre and Stepana Lazarova

Cahiers de recherche from CIRPEE

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 test; 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
New Economics Papers: this item is included in nep-ecm
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http://www.cirpee.org/fileadmin/documents/Cahiers_2009/CIRPEE09-25.pdf (application/pdf)

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Working Paper: Adaptive Rate-optimal Detection of Small Autocorrelation Coefficients (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:lvl:lacicr:0925

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