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Nonparametric Approach for Non-Gaussian Vector Stationary Processes

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  • Taniguchi, Masanobu
  • Puri, Madan L.
  • Kondo, Masao
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    Abstract

    Suppose that {z(t)} is a non-Gaussian vector stationary process with spectral density matrixf([lambda]). In this paper we consider the testing problemH: [integral operator][pi]-[pi] K{f([lambda])} d[lambda]=cagainstA: [integral operator][pi]-[pi] K{f([lambda])} d[lambda][not equal to]c, whereK{·} is an appropriate function andcis a given constant. For this problem we propose a testTnbased on [integral operator][pi]-[pi] K{f([lambda])} d[lambda]=c, wheref([lambda]) is a nonparametric spectral estimator off([lambda]), and we define an efficacy ofTnunder a sequence of nonparametric contiguous alternatives. The efficacy usually depnds on the fourth-order cumulant spectraf4Zofz(t). If it does not depend onf4Z, we say thatTnis non-Gaussian robust. We will give sufficient conditions forTnto be non-Gaussian robust. Since our test setting is very wide we can apply the result to many problems in time series. We discuss interrelation analysis of the components of {z(t)} and eigenvalue analysis off([lambda]). The essential point of our approach is that we do not assume the parametric form off([lambda]). Also some numerical studies are given and they confirm the theoretical results.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 56 (1996)
    Issue (Month): 2 (February)
    Pages: 259-283

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    Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:259-283

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    Related research

    Keywords: non-Gaussian vector stationary process nonparametric hypothesis testing spectral density matrix fourth-order cumulant spectral density non-Gaussian robustness efficacy measure of linear dependence principal components analysis of time series nonparametric spectral estimator asymptotic theory;

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    Cited by:
    1. Dette, Holger & Hildebrandt, Thimo, 2012. "A note on testing hypotheses for stationary processes in the frequency domain," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 101-114, February.
    2. McElroy, Tucker & Holan, Scott, 2009. "A local spectral approach for assessing time series model misspecification," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 604-621, April.
    3. Michael Eichler, 2007. "A Frequency-domain Based Test for Non-correlation between Stationary Time Series," Metrika, Springer, vol. 65(2), pages 133-157, February.
    4. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    5. Tamaki, Kenichiro, 2007. "Second order optimality for estimators in time series regression models," Journal of Multivariate Analysis, Elsevier, vol. 98(3), pages 638-659, March.
    6. Dimitrios Tsitsis & George Karavasilis & Alexandros Rigas, 2012. "Measuring the association of stationary point processes using spectral analysis techniques," Statistical Methods and Applications, Springer, vol. 21(1), pages 23-47, March.

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