Testing normality in econometric models

Journal of Statistical Computation and …, 1986

This paper is concerned with testing normality of observations and regression disturbances when the alternative belongs to the stable f ami 1 y .

International Statistical Review/Revue Internationale …, 1987

Using the Lagrange multiplier procedure or score test on the Pearson family of distributions we obtain tests for normality of observations and regression disturbances. The tests suggested have optimum asymptotic power properties and good finite sample performance. Due to their simplicity they should prove to be useful tools in statistical analysis.

Economics Letters, 1996

A comprehensive empirical evaluation is presented of the sensitivity to non-normality of the main tests for individual effects in a one-way error components panel data model.

Methodology and Computing in Applied Probability, 2003

The present work introduces four families of tests of normality. The tests in two of them are of the Kolmogorov–Smirnov type, and the tests of the other two are of the Cramér–von Mises type. One family of each type is focused to detect alternatives of skewness and the other one is designed to be specially sensitive to changes in kurtosis.

2017

A well known result is that many of the tests used in econometrics such as the Rao score (RS) test, may not be robust to misspecified alternatives, that is, when the alternative model does not correspond to the underlying data generating process. Under this scenario, these tests spuriously reject the null hypothesis too often. We generalize this result to GMM based tests. We also extend the method proposed in Bera and Yoon (Econometric Theory 9, 1993) for constructing RS tests that are robust to local misspecification to GMM based tests. Finally, a further generalization for general estimating and testing functions is developed. This framework encompasses both the Bera-Yoon likelihood based results as well as its use in the GMM environment. JEL classification: C12; C52

CENTRAL EUROPEAN SYMPOSIUM ON THERMOPHYSICS 2019 (CEST)

The assumption of normal distribution of a random variable plays an important role in various fields of science. The Jarque-Bera test is the most widely adopted omnibus test of normality in econometrics, finance and related fields. As outliers in the data sets in the field of economics and finance are frequently present, the Jarque-Bera test is not sufficiently robust, since it is based on the classical characteristics of skewness and kurtosis and has a zero breakdown value. Thus, the Jarque-Bera test is very sensitive to small deviations from normality, e.g. presence of outliers. In this contribution, we introduce the general RT class of robust tests for normality which is less sensitive to small deviations from normality, particularly in the form of a few outliers. We also present and discuss the trade-off between power and robustness of selected classical and robust normality tests of random variables where outliers could be presented.

TEST, 2020

In thinking of possible authors to write a review of the area of L 2 goodness-of-fit tests for multivariate normality, it would be difficult to find authors who are better suited than Professors Ebner and Henze. The authors' joint experience in the area of goodness-offit testing has "spanned four decades, covered broad classes of distributions, pioneered numerous distinct approaches, were published across several continents, and motivated the research of many co-authors", to paraphrase Hadjicosta and Richards (2019). In the present review, the authors repeatedly rise to the occasion, providing a review that is detailed and comprehensive. In each and every section of the review article, I learnt new results. For instance, I was unaware of the results of Pudelko (2005), of the results of Manzotti and Quiroz (2001) that involve spherical harmonics, of the projection pursuit approach to tests for multivariate normality, and other many topics. Indeed, the review is so extensive that it is likely to become required reading for those intending to work in the area. In my view, the crowning feature of a good review article is its offerings of potential research questions. In this regard, the Ebner-Henze review is superb. In each and every section, a reader comes across questions and open problems that appeal for investigation. In providing below a partial list of such problems, I ask the reader to keep in mind that this choice of problems reflects my own research interests: Section 1: Here, the authors carefully delineate the limits of their review; in particular, tests that are based on incomplete data are outside their purview. This raises in my mind the hope for future investigations of L 2 tests for situations in which the data are incomplete. Of particular importance in the case of incomplete data will be situations in which the data are not monotone incomplete, and indeed it appears that little is known about this particular area.

Exacta

A análise de normalidade na distribuição dos resíduos é um critério determinante para verificar e validar um modelo. Na modelagem de séries temporais financeiras por regressão linear, por exemplo, os resíduos devem ser independentes uns dos outros, identicamente distribuídos, possuir uma distribuição normal e homocedásticos. Desta forma, este estudo tem como objetivo estudar o desempenho de alguns testes de normalidade aplicados em resíduos obtidos da modelagem por regressão linear da tendência de uma série temporal utilizando polinômios de diferentes graus. Foram utilizados os testes de Jarque-Bera, Anderson-Darling, Kolmogorov-Smirnov Lilliefors, Doornik-Hansen e Shapiro-Wilk, havendo concordância quase que na totalidade dos resultados dos testes, com exceção do teste Doornik-Hansen.

Sociological Methods & Research, 1992

A great deal of recent work in econometrics has focused on the development of tests to detect violations of the assumptions of ordinary least squares regression. These tests are referred to collectively as specification tests. This article evaluates some important and computationally convenient specification tests for the normal regression model as applied to cross-sectional data. Because these tests achieve their optimal properties in large samples, their size and power in finite samples are of great interest and are evaluated with Monte Carlo simulations. Although the authors' experiments showed a tendency toward overrejection in some tests, their results suggest that specific variations of the RESET and information matrix tests behave quite well even in small samples. They conclude by proposing a strategy for the sequential application of specification tests.

Review of Economics and Statistics, 2012