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A SIMPLE TEST OF NORMALITY FOR TIME SERIES

Published online by Cambridge University Press:  01 August 2004

Ignacio N. Lobato  and
Carlos Velasco
Ignacio N. Lobato
Affiliation:
Instituto Tecnológico Autónomo de México (ITAM)
Carlos Velasco
Affiliation:
Institució Catalana de Recerca i Estudis Avançats and Universitat Autònoma de Barcelona
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Abstract

This paper considers testing for normality for correlated data. The proposed test procedure employs the skewness-kurtosis test statistic, but studentized by standard error estimators that are consistent under serial dependence of the observations. The standard error estimators are sample versions of the asymptotic quantities that do not incorporate any downweighting, and, hence, no smoothing parameter is needed. Therefore, the main feature of our proposed test is its simplicity, because it does not require the selection of any user-chosen parameter such as a smoothing number or the order of an approximating model.We are very grateful to Don Andrews and two referees for useful comments and suggestions. We are especially thankful to a referee who provided a FORTRAN code. Lobato acknowledges financial support from Asociación Mexicana de Cultura and from Consejo Nacional de Ciencia y Tecnologìa (CONACYT) under project grant 41893-S. Velasco acknowledges financial support from Spanish Dirección General de Enseñanza Superior, BEC 2001-1270.

Type
Research Article
Information
Econometric Theory , Volume 20 , Issue 4 , August 2004 , pp. 671 - 689
Copyright
© 2004 Cambridge University Press

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References

REFERENCES

Bai, J. & S. Ng (2001) Tests for Skewness, Kurtosis, and Normality for Time Series Data. Preprint, Boston College.
Bontemps, C. & N. Meddahi (2002) Testing Normality: A GMM Approach. Preprint, Université de Montréal.
Bowman, K.O. & L.R. Shenton (1975) Omnibus test contours for departures from normality based on and b2. Biometrika 62, 243–250.Google Scholar
Brillinger, D.R. (1981) Time Series: Data Analysis and Theory. Holden Day.
Davison, A.C. & D.V. Hinkley (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Epps, T.W. (1987) Testing that a stationary time series is Gaussian. Annals of Statistics 15, 1683–1698.Google Scholar
Epps, T.W. (1999) Limiting behavior of the integrated characteristic function test for normality under Gram-Charlier alternatives. Statistics and Probability Letters 42, 175–184.Google Scholar
Epps, T.W. & L.B. Pulley (1983) A test for normality based on the empirical characteristic function. Biometrika 70, 723–726.Google Scholar
Gasser, T. (1975) Goodness-of-fit tests for correlated data. Biometrika 62, 563–570.Google Scholar
Gleser, L.J. & D.S. Moore (1983) The effect of dependence on chi-squared and empiric distribution tests of fit. Annals of Statistics 11, 1100–1108.Google Scholar
Henze, N. (1997) A new approach to the BEHP tests for multivariate normality. Journal of Multivariate Analysis 62, 1–23.Google Scholar
Jarque, C.M. & A.K. Bera (1987) A test for normality of observations and regression residuals. International Statistical Review 55, 163–172.Google Scholar
Kilian, L. & U. Demiroglu (2000) Residual-based tests for normality in autoregressions: Asymptotic theory and simulation evidence. Journal of Business and Economic Statistics 18, 40–50.Google Scholar
Lobato, I.N., J.C. Nankervis, & N.E. Savin (2002) Testing for zero autocorrelation in the presence of statistical dependence. Econometric Theory 18, 730–743.Google Scholar
Lomnicki, Z.A. (1961) Tests for departure from normality in the case of linear stochastic processes. Metrika 4, 37–62.Google Scholar
Lütkepohl, H. (1991) Introduction to Multiple Time Series Analysis. Springer Verlag.
Mardia, K.V. (1980) Tests of univariate and multivariate normality. In P.R. Krishnaiah (ed.), Handbook of Statistics: Robust Inference, vol. 1, pp. 279–320. North-Holland.
Robinson, P.M. (1998) Inference-without-smoothing in the presence of nonparametric autocorrelation. Econometrica 66, 1163–1182.Google Scholar
Robinson, P.M. & C. Velasco (1997) Autocorrelation robust inference. In G.S. Maddala & C.R. Rao (eds.), Handbook of Statistics: Robust Inference, vol. 15, pp. 267–298. North-Holland.
Rosenblatt, M. (1985) Stationary Sequences and Random Fields. Birkhäuser.
Shapiro, S.S. & M.B. Wilk, (1965) An analysis of variance test for normality (complete samples). Biometrika 52, 591–611.Google Scholar
Shapiro, S.S., M.B. Wilk, & H.J. Chen (1968) A comparative study of various tests for normality. Journal of the American Statistical Association 63, 1343–1372.Google Scholar
Zygmund, A. (1977) Trigonometric Series. Cambridge University Press.