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Multivariate Normality Tests for Serially Correlated Data
Pruebas de normalidad multivariadas para datos correlacionados en serie
DOI:
https://doi.org/10.15446/rce.v47n2.111979Keywords:
Macroeconomic Data, Monte Carlo, Multivariate normality, Orthogonalization, Time series, χ2-distribution. (en)Datos macroeconómicos, Monte Carlo, Normalidad multivariada, Ortogonalización, χ2-distribución, Series de tiempo. (es)
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We extend univariate normality tests for time-dependent observations to their multivariate versions using orthogonalization or empirical standardization of the data. This extension allows us to assess the multivariate normality of serially correlated data. The proposed test statistics asymptotically follow the χ2 distribution, which allows for readily applicable tests. A comprehensive Monte Carlo study indicates that the proposed tests exhibit good size control and high empirical power. Furthermore, we provide empirical illustrations of all the extended tests using West German macroeconomic data (Lütkepohl, 2005).
Extendemos las pruebas de normalidad univariadas para observaciones dependientes del tiempo a sus versiones multivariadas usando ortogonalización o estandarización empírica de los datos. Esta extensión nos permite evaluar la normalidad multivariada. de datos correlacionados en serie. Las estadísticas de prueba propuestas siguen asintóticamente la distribución χ2, que permite pruebas fácilmente aplicables. Un comprensivo Estudio de Montecarlo indica que las pruebas propuestas presentan buen tamaño control y alto poder empírico. Además, proporcionamos ilustraciones empíricas. De todas las pruebas ampliadas utilizando datos macroeconómicos de Alemania Occidental (Lütkepohl, 2005).
References
Andreassen, T. W., Lorentzen, B. G. & Olsson, U. H. (2006), 'The impact of nonnormality and estimation methods in sem on satisfaction research in marketing', Quality and Quantity 40(1), 39_58.
Bai, J. & Ng, S. (2005), 'Tests for skewness, kurtosis, and normality for time series data', Journal of Business & Economic Statistics 23(1), 49_60. https://doi.org/10.1198/073500104000000271
Chen, W. & Genton, M. G. (2023), 'Are you all normal? it depends!', International Statistical Review 91(1), 114_139.
D'Agostino, R. B. & Stephens, M. A. (1986), Goodness-of-Fit Techniques, Statistics: A Series of Textbooks and Monographs, CRC Press.
Elbouch, S., Michel, O. J. & Comon, P. (2022), Joint normality test via two-dimensional projection, in 'ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)', IEEE, pp. 5802_5806.
Horváth, L., Kokoszka, P. & Wang, S. (2020), 'Testing normality of data on a multivariate grid', Journal of Multivariate Analysis 179, 104640. http://www.sciencedirect.com/science/article/pii/S0047259X20302219
Jarque, C. M. & Bera, A. K. (1987), 'A test for normality of observations and regression residuals', International Statistical Review / Revue Internationale de Statistique 55(2), 163_172. http://www.jstor.org/stable/1403192
Khan, A. & Rayner, G. D. (2003), 'Robustness to non-normality of common tests for the many-sample location problem', Advances in Decision Sciences 7(4), 187_206.
Kilian, L. & Demiroglu, U. (2000), 'Residual-based tests for normality in autoregressions: Asymptotic theory and simulation evidence', Journal of Business & Economic Statistics 18(1), 40_50.
https://www.tandfonline.com/doi/abs/10.1080/07350015.2000.10524846
Kim, N. (2016), 'A robustified jarque-bera test for multivariate normality', Economics Letters 140, 48_52.
Koizumi, K., Okamoto, N. & Seo, T. (2009), 'On jarque-bera tests for assessing multivariate normality', Journal of Statistics: Advances in Theory and Applications 1(2), 207_220.
Lobato, I. N. & Velasco, C. (2004), 'A simple test of normality for time series', Econometric Theory 20(4), 671_689.
Loy, A., Follett, L. & Hofmann, H. (2016), 'Variations of q-q plots: The power of our eyes!', The American Statistician 70(2), 202_214.
Lütkepohl, H. (2005), New introduction to multiple time series analysis, Springer Science & Business Media.
Mardia, K. V. (1970), 'Measures of multivariate skewness and kurtosis with applications', Biometrika 57(3), 519_530.
Newey, W. K. & West, K. D. (1987), 'A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix', Econometrica 55(3), 703_708. http://www.jstor.org/stable/1913610
Newey, W. K. & West, K. D. (1994), 'Automatic lag selection in covariance matrix estimation', The Review of Economic Studies 61(4), 631_653.
Olivier, M. J., Pierre, C. et al. (2022), Multivariate normality test for colored data, in '2022 30th European Signal Processing Conference (EUSIPCO)', IEEE, pp. 2096_2100.
Psaradakis, Z. & Vávra, M. (2018), 'Normality tests for dependent data: large sample and bootstrap approaches', Communications in Statistics-Simulation and Computation pp. 1_22.
Thode, H. C. (2002), Testing For Normality, Statistics: A Series of Textbooks and Monographs, CRC Press.
Villasenor Alva, J. A. & Estrada, E. G. (2009), 'A generalization of shapirowilk's test for multivariate normality', Communications in Statistics-Theory and Methods 38(11), 1870_1883.
Yuan, K.-H., Bentler, P. M. & Zhang, W. (2005), 'The effect of skewness and kurtosis on mean and covariance structure analysis: The univariate case and its multivariate implication', Sociological Methods & Research 34(2), 240_258.
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