Generalized Portmanteau Tests Based on Subspace Methods

Tests de Portmanteau generalizados basados en métodos de subespacios

The problem of diagnostic checking is tackled from the perspective of the subspace methods. Two statistics are presented and their asymptotic distributions are derived under the null hypothesis. The procedures are devised to deal with univariate and multivariate processes, are flexible and able to separately check regular and seasonal correlations. The performance in finite samples of the proposals is illustrated via Monte Carlo simulations and two examples with real data.

Este artículo trata el problema de la diagnosis residual desde la perspectiva de los métodos de subespacios. Se presentan dos estadísticos y sus distribuciones asintóticas bajo la hipótesis nula. Ambos estadísticos pueden usarse con procesos univariantes o multivariantes, son flexibles y permiten contrastar separadamente las correlaciones regulares y estacionales. El comportamiento en muestras finitas de las dos propuestas se ilustra mediante simulaciones de Monte Carlo y dos ejemplos con datos reales.

Generalized Portmanteau Tests Based on Subspace Methods Tests de Portmanteau generalizados basados en métodos de subespacios ALFREDO GARCÍA-HIERNAUX¹

¹Universidad Complutense de Madrid, Quantitative Economics Department, Spain. Professor. Email: agarciah@ucm.es

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Abstract

The problem of diagnostic checking is tackled from the perspective of the subspace methods. Two statistics are presented and their asymptotic distributions are derived under the null hypothesis. The procedures are devised to deal with univariate and multivariate processes, are flexible and able to separately check regular and seasonal correlations. The performance in finite samples of the proposals is illustrated via Monte Carlo simulations and two examples with real data.

Key words: Diagnostic checking, Portmanteau test, Residual autocorrelation, Residuals.

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Resumen

Palabras clave: autocorrelación residual, diagnosis de residuos, test de Portmanteau, residuos.

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Texto completo disponible en PDF

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References

1. Aoki, M. (1990), State Space Modelling of Time Series, Springer Verlag, New York.

2. Box, G. E. P. & Pierce, D. A. (1970), 'Distribution of residuals autocorrelations in autoregressive-integrated moving average time series models', Journal of the American Statistical Association 65(332), 1509-1526.

3. Casals, J., García-Hiernaux, A. & Jerez, M. (2012), 'From general State-Space to VARMAX models', Mathematics and Computers in Simulation 80(5), 924-936.

4. Casals, J., Sotoca, S. & Jerez, M. (1999), 'A fast and stable method to compute the likelihood of time invariant state space models', Economics Letters 65(3), 329-337.

5. García-Hiernaux, A., Jerez, M. & Casals, J. (2010), 'Unit roots and cointegration modeling through a family of flexible information criteria', Journal of Statistical Computation and Simulation 80(2), 173-189.

6. Grubb, H. (1992), 'A multivariate time series analysis of some flour price data', Applied Statistics 41, 95-107.

7. Hosking, J. R. M. (1980), 'The multivariate Pormanteau statistic', Journal of the American Statistical Association 75(371), 602-608.

8. Katayama, T. (2005), Subspace Methods for System Identification, Springer Verlag, London.

9. Li, W. K. (2004), Diagnostic Checks in Time Series, Chapman and Hall/CRC, Florida.

10. Liu, L. M. (2006), Time Series Analysis and Forecasting, 2 edn, Scientific Computing Associates Corporation, Illinois.

11. Ljung, G. M. & Box, G. E. P. (1978), 'On a measure of lack of fit in time series models', Biometrika 65, 297-303.

12. Lütkepohl, H. & Poskitt, D. S. (1996), 'Specification of echelon form VARMA models', Journal of Business and Economic Statistics 14(1), 69-79.

13. Mauricio, J. A. (2007), 'Computing and using residuals in time series models', Computational Statistics and Data Analysis 52(3), 1746-1763.

14. McLeod, A. I. (1978), 'On the distribution of residual autocorrelations in Box-Jenkins model', Journal of the Royal Statistics Society B 40, 296-302.

15. Monti, A. C. (1994), 'A proposal for residual autocorrelation test in linear models', Biometrika 81, 776-780.

16. Rousseeuw, P. J. & Leroy, A. M. (1987), Robust Regression and Outlier Detection, John Wiley, New York.

17. Tsay, R. S. (1988), 'Outliers, Level shifts, and variance changes in time series', Journal of Forecasting 7, 1-20.

18. Ursu, E. & Duchesne, P. (2009), 'On multiplicative seasonal modelling for vector time series', Statistics and Probability Letters 79(19), 2045-2052.

19. White, H. (2001), Asymptotic Theory for Econometricians, Academic Press.

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[Recibido en noviembre de 2012. Aceptado en mayo de 2013]

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Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv36n2a03,
    AUTHOR  = {García-Hiernaux, Alfredo},
    TITLE   = {{Generalized Portmanteau Tests Based on Subspace Methods}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2013},
    volume  = {36},
    number  = {2},
    pages   = {221-235}
}

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