Consistency Tests Based on Moments

Czesław Kazimierz Domański, Alina Jędrzejczak

Abstract


In the paper we are going to present the results of the research on selected statistical tests based on moments. In particular, the well-known Jarque-Bera test properties have been compared and contrasted with its modification proposed by White (1987). According to the outcomes of the simulation studies, the modified Jarque-Bera statistic is recommended as the normality test because the standard Jarque-Bera test is based on skewness and kurtosis and their distributions are derived under normality assumption.

Keywords


consistency tests

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References


Bera A., John S., Tests for Multivariate Normality with Pearson Alternatives, “Comm Statist.-Theory Methods” 1983, No. 12.

Bera A., Premaratne G., Adjusting the Tests for Symmetry on Application to S&P Index Returs, 2001, http://office.soka.ac.jp/faculty/economics/DP/004.pdf [data dostępu: 10.04.2016].

D’Agostino R.B., Pearson E.S., Tests for Departure from Normality. Empirical Results for the Distributions of b2 and √(b_1 ), “Biometrika” 1973, Vol. 60, DOI: https://doi.org/10.2307/2335012,

https://doi.org/10.1093/biomet/60.3.613.

Domański C., Testy statystyczne, PWE, Warszawa 1990.

Domański C., Uwagi o testach Jarque’a-Bera, „Przegląd Statystyczny” 2010, z. 4.

Domański C., Baszczyńska A., Pekasiewicz D., Witaszczyk A., Testy statystyczne w procesie podejmowania decyzji, Wydawnictwo UŁ, Łódź 2014.

Godfrey L.G., Orme C.D., Testing for Skewness of Regression Disturbances, “Economics Letters” 1991, Vol. 37, Issue 1.

Jarque C.M., Bera A.K., A Tests of Observations and Regression Residuals, “International Statistical Review” 1987, Vol. 55, DOI: https://doi.org/10.2307/1403192.

Mulholland H.P., On the Null Distribution of √(b_1 ) for Samples of Size at Most 25, with Tables, “Biometrika” 1977, Vol. 64, DOI: https://doi.org/10.1093/biomet/64.2.401,

https://doi.org/10.2307/2335708.

Oliveria A., Oliveria T., Seijas-Macias A., Skewness into the Product of Two Normally Distributed Variables and the Risk Consequences, “REVSTAT – Statistical Journal” 2016, Vol. 14, No. 4.

Pearson E.S., Hartley H.O., Biometrika Tables for Statisticians, Vol. I, 3. ed., University Press, Cambridge 1966.

Pearson E.S., Hartley H.O., Biometrika Tables for Statisticians, Vol. 2, Cambridge University Press, London 1972.

Stephens M.A., Tests for Normality, “Stanford University Department of Statistics Technical Reports” 1969, No. 152.

White H., Specification Testing in Dynamic Models, Advanced in Econometrics, Fifth World Congress, 1, 1–58, Cambridge University Press, New York 1987, DOI: https://doi.org/10.1017/CCOL0521344301.001.




DOI: http://dx.doi.org/10.17951/h.2016.50.4.89
Date of publication: 2017-02-20 17:31:15
Date of submission: 2016-07-14 14:50:21


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