IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i9p4432-4457.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • Poulin, Jennifer & Duchesne, Pierre, 2008. "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," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4432-4457, May.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4432-4457
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00149-7
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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(2), pages 382-416, April.
    3. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    4. Pierre Duchesne, 2005. "Testing for serial correlation of unknown form in cointegrated time series models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(3), pages 575-595, September.
    5. 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, February.
    6. Bruggemann, Ralf & Lutkepohl, Helmut & Saikkonen, Pentti, 2006. "Residual autocorrelation testing for vector error correction models," Journal of Econometrics, Elsevier, vol. 134(2), pages 579-604, October.
    7. 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, July.
    8. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
    9. 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.
    10. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    11. Enno Mammen, "undated". "Comparing nonparametric versus parametric regression fits," Statistic und Oekonometrie 9205, Humboldt Universitaet Berlin.
    12. 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.
    13. 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;Sociedad de Estadística e Investigación Operativa, vol. 14(2), pages 449-473, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.
    2. Catani, P.S. & Ahlgren, N.J.C., 2017. "Combined Lagrange multiplier test for ARCH in vector autoregressive models," Econometrics and Statistics, Elsevier, vol. 1(C), pages 62-84.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Eichler, Michael, 2008. "Testing nonparametric and semiparametric hypotheses in vector stationary processes," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 968-1009, May.
    2. Lütkepohl, Helmut, 2008. "Problems related to over-identifying restrictions for structural vector error correction models," Economics Letters, Elsevier, vol. 99(3), pages 512-515, June.
    3. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164, Edward Elgar Publishing.
    4. Proietti, Tommaso & Luati, Alessandra, 2015. "The generalised autocovariance function," Journal of Econometrics, Elsevier, vol. 186(1), pages 245-257.
    5. Helmut Luetkepohl, 2007. "Econometric Analysis with Vector Autoregressive Models," Economics Working Papers ECO2007/11, European University Institute.
    6. 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.
    7. Li, Meiyu & Gençay, Ramazan, 2017. "Tests for serial correlation of unknown form in dynamic least squares regression with wavelets," Economics Letters, Elsevier, vol. 155(C), pages 104-110.
    8. Patilea, V. & Raïssi, H., 2013. "Corrected portmanteau tests for VAR models with time-varying variance," Journal of Multivariate Analysis, Elsevier, vol. 116(C), pages 190-207.
    9. Karaman Örsal, Deniz Dilan & Droge, Bernd, 2014. "Panel cointegration testing in the presence of a time trend," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 377-390.
    10. repec:wyi:journl:002087 is not listed on IDEAS
    11. Baek, Jungho & Cho, Yongsung & Koo, Won W., 2009. "The environmental consequences of globalization: A country-specific time-series analysis," Ecological Economics, Elsevier, vol. 68(8-9), pages 2255-2264, June.
    12. Ralf Brüggemann & Helmut Lütkepohl, 2006. "A small monetary system for the euro area based on German data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 683-702, September.
    13. Raja Ben Hajria & Salah Khardani & Hamdi Raïssi, 2017. "Testing the lag length of vector autoregressive models: A power comparison between portmanteau and Lagrange multiplier tests," Working Papers 2017-03, Escuela de Negocios y Economía, Pontificia Universidad Católica de Valparaíso.
    14. Elena Argentesi & Helmut Lütkepohl & Massimo Motta, 2010. "Acquisition of Information and Share Prices: An Empirical Investigation of Cognitive Dissonance," German Economic Review, Verein für Socialpolitik, vol. 11(3), pages 381-396, August.
    15. Klaus Prettner & Robert Kunst, 2012. "The dynamic interrelations between unequal neighbors: an Austro-German case study," Empirical Economics, Springer, vol. 43(2), pages 741-761, October.
    16. Laura Mayoral, 2007. "Minimum distance estimation of stationary and non-stationary ARFIMA processes," Econometrics Journal, Royal Economic Society, vol. 10(1), pages 124-148, March.
    17. Nankervis, John C. & Savin, N. E., 2010. "Testing for Serial Correlation: Generalized Andrews–Ploberger Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 246-255.
    18. Elena Argentesi & Helmut Lütkepohl & Massimo Motta, 2010. "Acquisition of Information and Share Prices: An Empirical Investigation of Cognitive Dissonance," German Economic Review, Verein für Socialpolitik, vol. 11(3), pages 381-396, August.
    19. Ida Wolden Bache, 2008. "Assessing estimates of the exchange rate pass-through," Working Paper 2007/12, Norges Bank.
    20. Søren Johansen & Anders Rygh Swensen, 2009. "On a numerical and graphical technique for evaluating some models involving rational expectations," CREATES Research Papers 2009-19, Department of Economics and Business Economics, Aarhus University.
    21. Boubacar Mainassara, Y. & Francq, C., 2011. "Estimating structural VARMA models with uncorrelated but non-independent error terms," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 496-505, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:52:y:2008:i:9:p:4432-4457. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.