Jarque–Bera Test and its Competitors for Testing Normality – A Power Comparison

Abstract

For testing normality we investigate the power of several tests, first of all, the well known test of Jarque and Bera (1980) and furthermore the tests of Kuiper (1960) and Shapiro and Wilk (1965) as well as tests of Kolmogorov-Smirnov and Cramér-von Mises type. The tests on normality are based, first, on independent random variables (model I) and, second, on the residuals in the classical linear regression (model II). We investigate the exact critical values of the Jarque-Bera test and the Kolmogorov-Smirnov and Cramér-von Mises tests, in the latter case for the original and standardized observations where the unknown parameters µ and σ have to be estimated. The power comparison is carried out via Monte Carlo simulation assuming the model of contaminated normal distributions with varying parameters µ and σ and different proportions of contamination. It turns out that for the JarqueBera test the approximation of critical values by the chi-square distribution does not work very well. The test is superior in power to its competitors for symmetric distributions with medium up to long tails and for slightly skewed distributions with long tails. The power of the Jarque-Bera test is poor for distributions with short tails, especially if the shape is bimodal, sometimes the test is even biased. In this case a modification of the Cramér-von Mises test or the Shapiro-Wilk test may be recommended.

Desempenho de Empresas Diversificadas: Evidências da Indústria de Transporte Aéreo dos Estados Unidos

“…De acordo com o teste Jarque-Bera, existem indícios de que a normalidade dos erros não seja válida (p<0,01). Porém, o tamanho da amostra confere robustez aos resultados mesmo sem a validade da distribuição Normal para os erros (Thadewald & Büning, 2007). A estatística de Durbin-Watson serve para verificar a existência de correlação serial nos erros dos modelos e, conforme apresentado nos resultados da regressão original (Tabela 3), esta estatística assume valores próximos de 2, especialmente após o controle do tempo defasado, o que indica que a estrutura de correlação entre os tempos foi devidamente modelada (Wooldridge, 2010).…”

Designing and Applying a Nonparametric Option Valuation Model

“…Table 1 The measures demonstrate major deviations from normality (Thadewald and Büning, 2007). Kernel-smoothed return distributions (in percentage returns) for 1-and 99-day holding periods are charted under Figure 1 and illustrate considerable differences in their characteristics.…”

Statistical power of goodness-of-fit tests based on the empirical distribution function for type-I right-censored data

“…the number of uncensored observations). weight in the tails of the underlying distribution [10]. This statistic is defined as…”