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Testing the Fit of a Vector Autoregressive Moving Average Model

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  • Efstathios Paparoditis

Abstract

. A new procedure for testing the fit of multivariate time series model is proposed. The method evaluates in a certain way the closeness of the sample spectral density matrix of the observed process to the spectral density matrix of the parametric model postulated under the null and uses for this purpose nonparametric estimation techniques. The asymptotic distribution of the test statistic is established and an alternative, bootstrap‐based method is developed in order to estimate more accurately this distribution under the null hypothesis. Goodness‐of‐fit diagnostics useful in understanding the test results and identifying sources of model inadequacy are introduced. The applicability of the testing procedure and its capability to detect lacks of fit is demonstrated by means of some real data examples.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:26:y:2005:i:4:p:543-568
    DOI: 10.1111/j.1467-9892.2005.00419.x
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    References listed on IDEAS

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    1. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    2. Jens‐Peter Kreiss & Jürgen Franke, 1992. "Bootstrapping Stationary Autoregressive Moving‐Average Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 297-317, July.
    3. Hong, Yongmiao, 1996. "Consistent Testing for Serial Correlation of Unknown Form," Econometrica, Econometric Society, vol. 64(4), pages 837-864, July.
    4. 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, March.
    5. Fan, Yanqin & Li, Qi, 2000. "Consistent Model Specification Tests," Econometric Theory, Cambridge University Press, vol. 16(6), pages 1016-1041, December.
    6. Kohn, R, 1979. "Asymptotic Estimation and Hypothesis Testing Results for Vector Linear Time Series Models," Econometrica, Econometric Society, vol. 47(4), pages 1005-1030, July.
    7. Kaizô I. BeltraTo & Peter Bloomfield, 1987. "Determining The Bandwidth Of A Kernel Spectrum Estimate," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 21-38, January.
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    Cited by:

    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. Jentsch, Carsten & Kreiss, Jens-Peter, 2010. "The multiple hybrid bootstrap -- Resampling multivariate linear processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2320-2345, November.
    4. 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.
    5. Marie-Christine Duker & David S. Matteson & Ruey S. Tsay & Ines Wilms, 2024. "Vector AutoRegressive Moving Average Models: A Review," Papers 2406.19702, arXiv.org.
    6. 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.
    7. Simos G. Meintanis & Joseph Ngatchou-Wandji & James Allison, 2018. "Testing for serial independence in vector autoregressive models," Statistical Papers, Springer, vol. 59(4), pages 1379-1410, December.
    8. 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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