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Testing nonparametric and semiparametric hypotheses in vector stationary processes

  • Eichler, Michael

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.

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

Volume (Year): 99 (2008)
Issue (Month): 5 (May)
Pages: 968-1009

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Handle: RePEc:eee:jmvana:v:99:y:2008:i:5:p:968-1009
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  1. Duchesne, Pierre & Roy, Roch, 2004. "On consistent testing for serial correlation of unknown form in vector time series models," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 148-180, April.
  2. Marc Hallin & Abdessamad Saidi, 2005. "Testing Non-Correlation and Non-Causality between Multivariate ARMA Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(1), pages 83-105, 01.
  3. Yasumasa Matsuda & Yoshihiro Yajima, 2004. "On testing for separable correlations of multivariate time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(4), pages 501-528, 07.
  4. Chafik Bouhaddioui & Roch Roy, 2006. "A Generalized Portmanteau Test For Independence Of Two Infinite-Order Vector Autoregressive Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(4), pages 505-544, 07.
  5. Eichler, Michael, 2007. "Granger causality and path diagrams for multivariate time series," Journal of Econometrics, Elsevier, vol. 137(2), pages 334-353, April.
  6. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-63, September.
  7. 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.
  8. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
  9. repec:cep:stiecm:/2005/482 is not listed on IDEAS
  10. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
  11. Roland Fried, 2003. "Decomposability and selection of graphical models for multivariate time series," Biometrika, Biometrika Trust, vol. 90(2), pages 251-267, June.
  12. Efstathios Paparoditis, 2000. "Spectral Density Based Goodness-of-Fit Tests for Time Series Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(1), pages 143-176.
  13. Pierre Duchesne, 2005. "Testing for serial correlation of unknown form in cointegrated time series models," Annals of the Institute of Statistical Mathematics, Springer, vol. 57(3), pages 575-595, September.
  14. Efstathios Paparoditis, 2005. "Testing the Fit of a Vector Autoregressive Moving Average Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 543-568, 07.
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