Bera Test Research Articles

Three different measures of sample skewness and kurtosis and their effects on the Jarque Bera test for normality

Monte Carlo methods are used to study the size and the power of three versions of the Jarque and Bera Lagrangian multiplier test for normality, JB(g1, g2), JB(b1, b2) and, finally, JB(k1, k2). The difference between these tests comes from the different definitions (estimates) of sample skewness and kurtosis. The Jarque and Bera test has rather poor small sample properties: the slow convergence of the test statistic to its limiting distribution makes the test oversized for small nominal level and undersized for larger than 3% levels even in a reasonably large sample. However, the JB(k1, k2) for a 5% nominal level shows good properties for all samples. The power of the tests shows the same erratic form.

Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE

In this paper, we study the Jarque–Bera test for a class of univariate parametric stochastic differential equations (SDE) dX t = b(X t , α)dt + dZ t , constructed based on the sample observed at discrete time points $${t^{n}_{i}=ih_{n}}$$ , i = 1, 2, . . . , n, where Z is a nondegenerate Levy process with finite moments and h is a sequence of positive real numbers with nh n → ∞ and $${nh_{n}^{2} \to 0}$$ as n → ∞. It is shown that under proper conditions, the Jarque–Bera test statistic based on the Euler residuals can be used to test for the normality of the unobserved Z and the proposed test is consistent against the presence of any nontrivial jump components. Our result indicates that the Jarque–Bera test is easy to implement and asymptotically distribution-free with no fine-tuning parameters. Simulation results to validate the test are given for illustration.

Behaviour of skewness, kurtosis and normality tests in long memory data

We establish the limiting distributions for empirical estimators of the coefficient of skewness, kurtosis, and the Jarque–Bera normality test statistic for long memory linear processes. We show that these estimators, contrary to the case of short memory, are neither \({\sqrt{n}}\)-consistent nor asymptotically normal. The normalizations needed to obtain the limiting distributions depend on the long memory parameter d. A direct consequence is that if data are long memory then testing normality with the Jarque–Bera test by using the chi-squared critical values is not valid. Therefore, statistical inference based on skewness, kurtosis, and the Jarque–Bera normality test, needs a rescaling of the corresponding statistics and computing new critical values of their nonstandard limiting distributions.

OC037: Volume calculation of intracranial structures using 3‐D ultrasound in normal and growth restricted fetuses

24 pregnancies that evaluated by both U/S and MRI, 5 underwent TOP: in 1 both U/S and MRI were normal, in 2 pregnancies the U/S was normal and MR abnormal, and in 2 both U/S and MR considered abnormal. 19 women delivered at term. Normal U/S and MRI findings diagnosed during pregnancy in 14 pregnancies: 13 of them are developing normal and deafness was diagnosed in one. Normal U/S and abnormal MRI found in 4 pregnancies: 3 of them are developing normal and 1 with pathologic Bera test. In one pregnancy abnormal findings diagnosed in both U/S (echogenic bowel and IUGR) and MRI (hyperintense signals in the white matter in the temporal and parietal areas). The child is developing normal at 2 years of age. The time of maternal infection in the 19 women that delivered was: 5 cases in the first trimester, 9 cases in the second, and 5 cases in the third trimester of pregnancy. Conclusions: Primary CMV infection with normal U/S and MRI follow-up have favorable outcome for the infant. If the U/S followup alone is considered normal the risk for severe neurologic sequlae is minimal.

A distribution-free test for symmetry with an application to S&P index returns

We propose a distribution-free test of symmetry. Monte Carlo results show the new test usually outperforms the nonnormality robust version of the Jarque–Bera test. Empirical results indicate that the tail of the distribution is too heavy to apply the latter test, while the former is always valid.

Goodness-of-fit tests based on a robust measure of skewness

In this paper we propose several goodness-of-fit tests based on robust measures of skewness and tail weight. They can be seen as generalisations of the Jarque---Bera test (Bera and Jarque in Econ Lett 7:313---318, 1981) based on the classical skewness and kurtosis, and as an alternative to the approach of Moors et al. (Stat Neerl 50:417---430, 1996) using quantiles. The power values and the robustness properties of the different tests are investigated by means of simulations and applications on real data. We conclude that MC-LR, one of our proposed tests, shows the best overall power and that it is moderately influenced by outlying values.

A robust modification of the Jarque–Bera test of normality

We propose a new robust Jarque–Bera (RJB) test utilizing a robust measure of variance. The RJB statistic is asymptotically χ 2 2-distributed and has equal or higher power than the JB test for several common alternatives to normality.

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

For testing normality we investigate the power of several tests, first of all, the well-known test of Jarque & Bera (1980) and furthermore the tests of Kuiper (1960) and Shapiro & 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 Jarque–Bera 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.

Robust directed tests of normality against heavy-tailed alternatives

Many statistical procedures rely on the assumption that the observed data are normally distributed. Consequently, there exists a vast literature on tests of normality and their statistical properties. Today the most commonly used omnibus test for general use is the Shapiro–Wilk method while the Jarque–Bera test is the most popular omnibus test in economics and related applications. In a recent securities law case concerning an allegation of profit sharing, an inference is drawn on a relationship between the hypothetical profits, which customers made on days with special stock offerings, and the ratio of their commission business to those profits became an issue. Two common statistical tests are based on the Pearson or Spearman correlation coefficients. The results provided by the two tests are dramatically different with contradictory implications for the existence of a “profit sharing arrangement”. In particular, the Pearson correlation coefficient is of - 0.13 with a p -value of 0.35 while the Spearman coefficient is of - 0.68 with a p -value less than 0.0001 . However, if the data do not come from a bivariate normal distribution, the usual sampling theory for the Pearson correlation would not be applicable. As stock market data are typically heavy-tailed, a simple test of normality directed against heavy-tailed alternatives complemented by a graphical method is desired for presentation in a courtroom. In this paper we utilize the idea of the Shapiro–Wilk test whose test statistic W is the ratio of the classical standard deviation s n to the optimal L-estimator of the population spread. In particular, we replace the mean and standard deviation by the median and a robust estimator of spread in the Shapiro–Wilk statistic W . This eventually leads to a new more powerful directed test and a clearer QQ plot for assessing departures from normality in the tails. Somewhat surprisingly, the robust estimator of spread that yields the more powerful test of normality utilizes the average absolute deviation from the median (MAAD) while the statistic based on the median absolute deviation from the median (MAD) usually provides a clearer graphical display. The asymptotic distribution of the proposed test statistic is derived, and the use of the new test is illustrated by simulations and by application to data sets from the securities law, finance and meteorology.

Shipping finance: time to follow a new track?

In this paper we introduce, for the first time, a methodology from the most recent literature of finance to reveal the duration of shipping cycles and then show the benefit of the use of this information to make more successful shipping loans. This is so as banks are willing to finance, during boom periods, shipping loans for new buildings but by this way ‘create’ oversupply and thus depress the freight market by their own actions. The information about cycles, especially their forecasting, is mostly important as shipping loans are based on project financing/cash flow financing, which means that ship revenue is of utmost importance. The Rescaled Range Analysis is applied here to 379 monthly freight trips—made stationary—between 1971 and 2002 (July), due to Hurst 1 and elaborated and popularized by Mandelbrot 2. The most important effect, however, is that shipping freight series exhibit non-normality and long-run dependence rendering the use of random walk models such as GARCH (Generalized Autoregressive Conditional Heteroscedasticity) problematic. Thus an adequate literature review is carried out with criticism against the models used. The cycles have been calculated as equal to 4.5 years and 2.25 years. This is almost compatible with the most recent paper of Stopford 3. The Hurst exponent was found equal to 0.93, alternating over the periods examined (0.65, 0.73, 0.62, 0.59 and 0.55) and indicating long-term persistence but seriously away from normal/random walk domain. Most studies have said the same using the Jarque--Bera test for normality but provided no alternative.

More on the correct use of omnibus tests for normality

This Monte Carlo study compares the small sample properties of some commonly used omnibus and directional tests, based on the standardized third and fourth moments, for assessing the normality of random variables: the omnibus D'Agostino K 2 test and the directional components, and three versions of the Jarque–Bera test.

Testing the information matrix equality with robust estimators

The information matrix (IM) equality can be used to test for misspecification of a parametric model. We study the behavior of the IM test when the maximum-likelihood (ML) estimators used in the construction of this test are replaced with robust estimators. The latter do not suffer from the masking effect in the presence of outliers and can improve the power of the IM test. At the normal location-scale model, the IM test using the ML estimators is known as the Jarque–Bera test, and uses skewness and kurtosis to detect deviations from normality. When robust estimators are employed to test the IM equality, a robust version of the Jarque–Bera test emerges. We investigate in detail the local asymptotic power of the IM test, for various estimators and under a variety of local alternatives. For the normal regression model, it is shown by simulations under fixed alternatives that in many cases the use of robust estimators substantially increases the power of the IM test.

Impulsive noise suppression from images with Jarque-Bera test based median filter

A novel impulsive noise (IN) eliminator filter, entitled Jarque–Bera test based Median Filter (JM), which shows a high performance at the restoration of images distorted by IN is proposed in this paper. The JM uses statistical methods in order to find out the corrupted pixels more accurately. The JM replaces only those corrupted pixels with the values obtained from standard median filter as explained in the paper. The simulation results reveal that the proposed filter shows better performance than the other filters mentioned in this paper in the cases of being effective in noise suppression and detail preservation, especially when the noise ratio is very high.

Information-Theoretic Distribution Tests with Application to Symmetry and Normality

We derive distribution free tests based on the Maximum Entropy densities to test the null hypotheses of symmetry and normality. The proposed tests are derived from maximizing the difierential entropy subject to moment constraints. By exploiting the equivalence between Maximum Entropy and Maximum Likelihood estimates of the exponential families, we can use the conventional Likelihood Ratio, Wald and Lagrange Multiplier testing principles in the maximum entropy framework. Monte Carlo evidence suggests that they have desirable small sample properties, when compared with the standard parametric tests used in the literature, such as the standardized skewness coe‐cient test for symmetry or the Jarque and Bera (1980) test for normality. We apply the proposed symmetry tests to test the nominal wage rigidity hypothesis of wage determination process.

On the validity of the Jarque–Bera normality test in conditionally heteroskedastic dynamic regression models

We show that the Jarque–Bera (JB) test, originally devised for constant conditional variance models with no functional dependence between conditional mean and variance parameters, can be safely applied to a broad class of GARCH-M models, but not to all.

Neural Tests for Conditional Heteroskedasticity in ARCH-M Models

Abstract This paper deals with tests for detecting conditional heteroskedasticity in ARCH-M models using three kinds of methods: neural networks techniques, bootstrap methods and both combined.As regards the ARCH models, Péguin-Feissolle (2000) developed tests based on the modelling techniques with neural network. However, as regards the ARCH-M models, a nuisance parameter is not identified and the tests are not applicable. To solve this problem, we propose to adapt these neural tests to Davies procedure (1987) leading to new tests. The performance of these latter tests are compared with those of Bera and Ra test (1995).However, Bera and Ra test has not really satisfactory performance and suffer from serious size distortion. Our neural test will have the same problem. To solve this second problem, without loss of power, we apply parametric and nonparametric bootstrap methods on the underlying test statistics.Lastly, to examine the size and the power properties of the tests in small samples, Monte Carlo simulations are carried out with various standard and non-standard models for conditional heteroskedasticity as to illustrate a variety of situations. In addition, the graphical presentation of Davidson and MacKinnon (1998a) is used to show the "true" power of the tests and not only the (nominal) power, as it is often the case, that can be meaningless.

Realized volatility in the futures markets

Using intraday returns on four futures contracts over a 5-year period, we calculate and analyze model-free measures of futures return volatility. We focus on the temporal characteristics and distributional properties of daily returns, return volatilities, (log of) standard deviations, standardized returns and pairwise correlations. The behavior of a number of tests for Gaussianity under long memory is explored via a simulation study. The simulation results indicate that tests of the “goodness-of-fit” variety are appropriate to use while the commonly employed Jarque–Bera test is severely oversized and its use is not recommended. We find that the standard deviations and the pairwise correlations exhibit long memory while the standardized returns are serially uncorrelated. We also find that the (unconditional) distributions of daily returns' volatility are leptokurtic and highly skewed to the right while the distributions of the standardized returns, the standard deviations and the pairwise correlations are statistically indistinguishable from the Gaussian distribution. Our results are consistent with that of Andersen et al. [Journal of the American Statistical Association 96 (2001a) 42; Journal of Financial Economics 61 (2001c) 43] on the time-series properties of realized volatility. The dynamic characteristics of the volatility series are modelled using fractionally integrated ARMA models.

PROPRIEDADES ESTATÍSTICAS DAS SÉRIES DE RETORNOS DAS PRINCIPAIS AÇÕES BRASILEIRAS

O artigo analisa seis séries de retornos, escolhidas entre as mais líquidas do mercado e de setores diferentes da economia. São estudadas a estacionariedade, a distribuição incondicional e a independência; de maneira geral as séries podem ser consideradas estacionárias, com distribuição não normal (leptocúrtica) e dependentes no tempo. A estacionariedade é analisada através do teste ADF, através dos coeficientes de modelos GARCH ajustados aos dados, pelos coeficientes de bicorrelação e com o uso de regressão localmente ponderada. A normalidade é rejeitada pelo teste de Jarque e Bera. A dependência (linear e não linear) é constatada pelas autocorrelações dos retornos e dos seus quadrados: tenta-se modelar a dependência com modelos ARMA, de amortecimento exponencial e GARCH mas os resíduos dos modelos, testados pelo teste BDS, mostram que nenhum deles representa bem o processo gerador dos dados

Assessment of diagnostic parameters in meniere’s disease

Meniere's disease has been ever served as one of the most debatable issue amongst the otologist. Various proposals for it's accurate diagnosis have arised in medical forefronts. The randomized study over here, of various diagnostic criteria in 52 nos are critically analysed in view of confirmation of clinically suspected Meniere's disease.Conclusions are drawn on basis of the autcomes of BERA,EcochG and caloric tests in form of individual as well cobined sensitivity in favour to attempt to standardize the deciding parameters in relation to the stage of the disease.

Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence

Existing results for the asymptotic validity of the Jarque–Bera test in vector autoregressive (VAR) models assume stationarity. In applied work, however, researchers often work with possibly integrated and cointegrated process. We prove the asymptotic validity of the Jarque–Bera test for vector error-correction (VEC) models and for unrestricted VAR models with possibly integrated or cointegrated variables. We also propose the use of bootstrap critical values in stationary VAR models and in VEC models. We show that the bootstrap version of the Jarque–Bera test is considerably more accurate in small samples than the asymptotic test, even for processes with roots close to unity.