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Testing nonparametric and semiparametric hypotheses in vector stationary processes

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  • Eichler, Michael

Abstract

We propose a general nonparametric approach for testing hypotheses about the spectral density matrix of multivariate stationary time series based on estimating the integrated deviation from the null hypothesis. This approach covers many important examples from interrelation analysis such as tests for noncorrelation or partial noncorrelation. Based on a central limit theorem for integrated quadratic functionals of the spectral matrix, we derive asymptotic normality of a suitably standardized version of the test statistic under the null hypothesis and under fixed as well as under sequences of local alternatives. The results are extended to cover also parametric and semiparametric hypotheses about spectral density matrices, which includes as examples goodness-of-fit tests and tests for separability.

Suggested Citation

  • Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    • Handle: RePEc:eee:jmvana:v:99:y:2008:i:5:p:968-1009
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    2. 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.
    3. 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.
    4. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
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    6. Sundararajan, Raanju R., 2021. "Principal component analysis using frequency components of multivariate time series," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    7. Jentsch, Carsten & Pauly, Markus, 2012. "A note on using periodogram-based distances for comparing spectral densities," Statistics & Probability Letters, Elsevier, vol. 82(1), pages 158-164.
    8. Loubaton, Philippe & Rosuel, Alexis & Vallet, Pascal, 2023. "On the asymptotic distribution of the maximum sample spectral coherence of Gaussian time series in the high dimensional regime," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    9. 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.
    10. Preuß, Philip & Hildebrandt, Thimo, 2013. "Comparing spectral densities of stationary time series with unequal sample sizes," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1174-1183.
    11. Mahmoudi, Mohammad Reza, 2021. "A computational technique to classify several fractional Brownian motion processes," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    12. Dilip Nachane & Aditi Chaubal, 2022. "A Comparative Evaluation of Some DSP Filters vis-à-vis Commonly Used Economic Filters," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 20(1), pages 161-190, September.
    13. Shibin Zhang & Xin M. Tu, 2022. "Tests for comparing time‐invariant and time‐varying spectra based on the Anderson–Darling statistic," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(3), pages 254-282, August.
    14. Leucht, Anne & Paparoditis, Efstathios & Rademacher, Daniel & Sapatinas, Theofanis, 2022. "Testing equality of spectral density operators for functional processes," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    15. Sourav Das & Suhasini Subba Rao & Junho Yang, 2021. "Spectral methods for small sample time series: A complete periodogram approach," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(5-6), pages 597-621, September.
    16. Dette, Holger & Paparoditis, Efstathios, 2008. "Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities," Technical Reports 2008,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    17. Philip Preuss & Mathias Vetter & Holger Dette, 2013. "Testing Semiparametric Hypotheses in Locally Stationary Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 417-437, September.
    18. Ruprecht Puchstein & Philip Preuß, 2016. "Testing for Stationarity in Multivariate Locally Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(1), pages 3-29, January.

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