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Nonparametric Approach for Non-Gaussian Vector Stationary Processes

Author

Listed:
  • Taniguchi, Masanobu
  • Puri, Madan L.
  • Kondo, Masao

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.

Suggested Citation

  • Taniguchi, Masanobu & Puri, Madan L. & Kondo, Masao, 1996. "Nonparametric Approach for Non-Gaussian Vector Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 56(2), pages 259-283, February.
    • Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:259-283
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    Citations

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    Cited by:

    1. Zhang, Xinyu & Tong, Howell, 2022. "Asymptotic theory of principal component analysis for time series data with cautionary comments," LSE Research Online Documents on Economics 113566, London School of Economics and Political Science, LSE Library.
    2. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    3. Holger Dette & Efstathios Paparoditis, 2009. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(4), pages 831-857, September.
    4. Hiroshi Shiraishi & Masanobu Taniguchi, 2008. "Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 193-215.
    5. Dimitrios Tsitsis & George Karavasilis & Alexandros Rigas, 2012. "Measuring the association of stationary point processes using spectral analysis techniques," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 21(1), pages 23-47, March.
    6. Michael Eichler, 2007. "A Frequency-domain Based Test for Non-correlation between Stationary Time Series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 133-157, February.
    7. Akashi, Fumiya & Taniguchi, Masanobu & Monti, Anna Clara, 2020. "Robust causality test of infinite variance processes," Journal of Econometrics, Elsevier, vol. 216(1), pages 235-245.
    8. 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.
    9. 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.
    10. 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.

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