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On the power transformation of kernel-based tests for serial correlation in vector time series: Some finite sample results and a comparison with the bootstrap

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  • Poulin, Jennifer
  • Duchesne, Pierre

Abstract

Portmanteau test statistics represent useful diagnostic tools for checking the adequacy of multivariate time series models. For stationary and partially non-stationary vector time series models, Duchesne and Roy [Duchesne, P., Roy, R., 2004. On consistent testing for serial correlation of unknown form in vector time series models. Journal of Multivariate Analysis 89, 148-180] and Duchesne [Duchesne, P., 2005a. Testing for serial correlation of unknown form in cointegrated time series models. Annals of the Institute of Statistical Mathematics 57, 575-595] have proposed kernel-based test statistics, obtained by comparing the spectral density of the errors under the null hypothesis of non-correlation with a kernel-based spectral density estimator; these test statistics are asymptotically standard normal under the null hypothesis of non-correlation in the error term of the model. Following the method of Chen and Deo [Chen, W.W., Deo, R.S., 2004a. Power transformations to induce normality and their applications. Journal of the Royal Statistical Society, Ser. B 66, 117-130], we determine an appropriate power transformation to improve the normal approximation in small samples. Additional corrections for the mean and variance of the distance measures intervening in these test statistics are obtained. An alternative procedure to estimate the finite distribution of the test statistics is to use the bootstrap method; we introduce bootstrap-based versions of the original spectral test statistics. In a Monte Carlo study, comparisons are made under various alternatives between: the original spectral test statistics, the new corrected test statistics, the bootstrap-based versions, and finally the classical Hosking portmanteau test statistic.

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Bibliographic Info

Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 52 (2008)
Issue (Month): 9 (May)
Pages: 4432-4457

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Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4432-4457

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References

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  1. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
  2. Kheoh, Thian S. & McLeod, A. Ian, 1992. "Comparison of two modified portmanteau tests for model adequacy," Computational Statistics & Data Analysis, Elsevier, vol. 14(1), pages 99-106, June.
  3. Willa W. Chen & Rohit S. Deo, 2004. "Power transformations to induce normality and their applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 117-130.
  4. 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.
  5. Hardle, W. & Mammen, E., 1990. "Comparing nonparametric versus parametric regression fits," CORE Discussion Papers 1990065, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Ralf BRUEGGEMANN & Helmut LUETKEPOHL & Pentti SAIKKONEN, 2004. "Residual Autocorrelation Testing for Vector Error Correction Models," Economics Working Papers ECO2004/08, European University Institute.
  7. Chen, Willa W. & Deo, Rohit S., 2004. "A Generalized Portmanteau Goodness-Of-Fit Test For Time Series Models," Econometric Theory, Cambridge University Press, vol. 20(02), pages 382-416, April.
  8. 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.
  9. Pierre Duchesne, 2005. "On the asymptotic distribution of residual autocovariances in VARX models with applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 14(2), pages 449-473, December.
  10. Kwan, Andy C.C. & Sim, Ah-Boon & Wu, Yangru, 2005. "A comparative study of the finite-sample performance of some portmanteau tests for randomness of a time series," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 391-413, February.
  11. 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.
  12. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-64, July.
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Cited by:
  1. Duchesne, Pierre & Li, Linyuan & Vandermeerschen, Jill, 2010. "On testing for serial correlation of unknown form using wavelet thresholding," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2512-2531, November.

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