The Jarque-Bera test statistic is defined as: with S, K, and N denoting the sample skewness, the The Jarque-Bera test is a goodness-of-fit test of departure from normality, based on the sample skewness and kurtosis. Hence, the FDI Inflows sample is not derived from the normally distributed population. This led to the development of other distribution functions and very importantly to normality testing (see Jarque and Bera (1980), and Ord (1972)). Axis to use if data has more than 1 dimension. x: a numeric vector or time series. World's Best PowerPoint Templates - CrystalGraphics offers more PowerPoint templates than anyone else in the world, with over 4 million to choose from. Construct Jarque -Bera test . The Jarque–Bera test is comparing the shape of a given distribution (skewness and kurtosis) to that of a Normal distribution. The test statistic measures the difference of the skewness and kurtosis of the series with those from the normal distribution. For sample sizes less than 2,000, the critical value is Missing values are not allowed. to a chi-squared distribution with 2 degrees of freedom (normality is NIST is an agency of the U.S. Not sure why this is not in the docs though? Privacy The Jarque-Bera (1980, 1987) Lagrange multiplier test is likely the most widely used procedure for testing normality of economic time series returns. What is visual communication and why it matters; Nov. 20, 2020. The output gives you; the test stat, the p value, skew, kurtosis in that order. 164 C.M. With the help of statsmodels.jarque_bera() method, we can get the jarque bera test for normality and it’s a test based on skewness, and the kurtosis, and has an asymptotic distribution.. Syntax : statsmodels.jarque_bera(residual, axis) Return : Return the jarque bera test … Jarque-Bera statistics follows chi-square distribution with two degrees of freedom for large sample. Jarque-Bera Test for Normality Response Variable: Y1 H0: The Data Are Normally Distributed Ha: The Data Are Not Normally Distributed Summary Statistics: Total Number of Observations: 195 Sample Mean: 9.2614 Sample Standard Deviation: 0.0227 Sample Skewness: -0.0085 Sample Kurtosis: 3.0490 Sample Minimum: 9.1968 Sample Maximum: 9.3279 Test Statistic Value: … The null hypothesis in this test … 3. Here, the results are split in a test for the null hypothesis that the skewness is $0$, the null that the kurtosis is $3$ and the overall Jarque-Bera test. Performs adjusted Jarque–Bera test for the composite hypothesis of normality, see Urzua (1996). Abstract. As a rule, this test is applied before using methods of parametric statistics which require distribution normality. Usually regression model residuals that are mean 0. axis int, optional. It measures whether a set of data points is normally distributed or not. The Jarque – Bera ALM test uses finite-sample values for the mean and variance of skewness and kurtosis, not the asymptotic values of 0, 6, 3, and 24 as in the traditional test: The finite-sample values can be derived using MomentEvaluate and MomentConvert: The Jarque–Bera statistic is a combination of the other two statistics. Blog. The Jarque-Bera test tests whether the sample data has the skewness and kurtosis matching a normal distribution. The algorithm provides a joint test of the null hypothesis of … The Jarque-Bera test uses skewness and kurtosis measurements. ... Normality Requirement: The residuals (errors) should be normal. Last updated: 10/19/2015 The formula for the Jarque-Bera test is as follows: In this formula, n is the number of data points, S is the sample skewness, and K … This service is more advanced with JavaScript available. Winner of the Standing Ovation Award for “Best PowerPoint … Uno de los supuestos básicos del modelo de regresión lineal clásico es el que los errores tengan distribución normal, esto es: Con el cumplimiento del supuesto de normalidad se tiene la justificación teórica para la utilización de pruebas estadísticas que involucren a las accurate. Critical value for the Jarque-Bera test at the alpha significance level, returned as a nonnegative scalar value. Please email comments on this WWW page to 2, pp. 4. BEO2255 Week9_Lecture.ppt - BEO 2255 Applied Statistics for Business Week Nine Dependency Relationships Qualitative Variables Residual Analysis This. = Perform a Wilk Shapiro test for normality. The test is based on the … 95.85.17.159, $$JB = \frac{N} {6} \left({W}^{2} + \frac{{\left (K - 3\right )}^{2}} {4} \right)$$. The returns statistics and the GARCH (1,1) and the EGARCH outputs are summarised in Tables 5.1 & 5.2. same number of observations. Blog. The null hypothesis in this test is data follow normal distribution. Jarque Bera test for normality The other test of normality is the Jarque Bera test. Open Courses in Applied Econometrics using Eviews by Professor (Dr.) Pavlos, B.Sc. The test is named after Carlos Jarque and Anil K. Bera. samples with the same mean and standard deviation as the original data jb = (379/6)*((1.50555^2)+(((6.43 -3)^2)/4)) = 328.9 The statistic has a Chi 2 distribution with 2 degrees of freedom, (one for skewness one for kurtosis). Gratitude in the workplace: How gratitude can improve your well-being and relationships In effect, sktest offers two adjustments for sample size, that ofRoyston(1991c) and that ofD’Agostino, Belanger, and D’Agostino(1990). Jarque-Bera test. 8, No. This is a preview of subscription content, Jarque CM, Bera AK (1980) Efficient tests for normality, homoscedasticity and serial independence of regression residuals. The test is based on a joint statistic using skewness and kurtosis coefficients. 2. … Usage jarque.bera.test(x) Arguments. HELP STATISTICS Note that this test only works for a large enough number of data samples (>2000) as the test statistic asymptotically has a Chi-squared distribution with 2 degrees of freedom. Policy/Security Notice These tests are extensions of Jarque-Bera test. Gratitude in the workplace: How gratitude can improve your well-being and relationships The input can be a time series of residuals, jarque.bera.test.default, or an Arima object, jarque.bera.test… Over 10 million scientific documents at your fingertips. Formal test: Jarque-Bera test… PPT is a type of program. 1987) and White and MacDonald (1980) showed that this test is applicable to the ordi-nary least squares residuals of linear regressions with an intercept term and i.i.d. The statistic is computed as: (11.4) What I have • Jarque-Bera is a test statistic for testing whether the series is normally distributed. 1. Abstract. NIST is an agency of the U.S. Date created: 07/05/2012 The single-equation results are from tests against the null hypothesis that the disturbance for that particular equation is normally … alan.heckert@nist.gov. = Perform Anderson-Darling, Kolmogorov-Smirnov, Chi-Square, and PPCC goodness of fit tests. I´m trying to run the "Jarque - Bera" test for normality in R. I have a dataset with 30 time series and would like to run a test for each column since the time series har independent. In the third chapter all introduced test … However, there some things relating to this test that you may not have learned in your econometrics courses. Not logged in The Jarque-Bera test is named after Carlos Jarque and Anil K. Bera. The Jarque-Bera Test is typically used for large datasets (n > 2000) in which other normality tests (like the Shapiro-Wilk test) are unreliable. FOIA. This video demonstrates how calculate and interpret the Jarque-Bera (JB) test of normality using Microsoft Excel. In statistics, the Jarque–Bera test is a goodness-of-fit test of whether sample data have the skewness and kurtosis matching a normal distribution. Jarque-Bera test of normality in E-Views This function performs the Jarque-Bera test on the given data sample to determine if the data are sample drawn from a normal population. Modified Jarque–Bera Type Tests for Multivariate Normality in a High-Dimensional Framework. Griffin, London, https://doi.org/10.1007/978-3-642-04898-2, International Encyclopedia of Statistical Science, Reference Module Computer Science and Engineering, Learning Statistics in a Foreign Language. The output gives you; the test stat, the p value, skew, kurtosis in that order. BERA 2 = (y - Xb)'(y - Xb)IN and shows that the significance level of the usual X2 test of the hypothesis a2= U2 is not even asymptotically valid in the presence of nonnormality. jb = (379/6)*((1.50555^2)+(((6.43 -3)^2)/4)) = 328.9 The statistic has a Chi 2 distribution with 2 degrees of freedom, (one for skewness one for kurtosis). Keywords htest, math. This test is a joint statistic using skewness and kurtosis coefficients. Commerce Department. … How Well Does the J-B Test Perform in Finite Samples? In order to perform this test, use the command ‘jb resid’ in the command prompt. A Test for Normality of Observations and Regression Residuals Carlos M. Jarque1 and Anil K. Bera2 1Direcci6n General de Estadistica, Secretaria de Programacion y Presupuesto, Mexico D.F. 382-399. popular omnibust test, the Jarque-Bera test, is introduced, as well a modiﬁcation of this test. This isn't just true for the Jarque-Bera test, and while it isn't quite true for all hypothesis tests (consider tests on discrete distributions such as a binomial proportion test or Poisson mean test) "the p-value is equally likely to be anywhere from 0 to 1" is usually a good … Utilizing the Jarque-Bera test. M.Sc. Data to test for normality. Please email comments on this WWW page to PPT means any type of information represented through slides. For all tests of the Jarque-Bera type, critical points are determined based on empirical sampling studies. You can work on creating a presentation. Details. In statistical analysis the assumption of data coming from a normal distribution is often made. Not affiliated Later, by the beginning of the twentieth century, most informed opinion had accepted that populations might be non-normal. Not sure why this is not in the docs though? sample are generated and the Jarque-Bera test statistic computed to The test is based on a joint statistic using skewness and kurtosis coefficients. JarqueBeraALMTest [ data, " property"] returns the value of " property". After all, it's a standard feature in pretty well every econometrics package. Reject H0 if JB > 6 Test for Normal Distribution Test of Normality - 1 Graphical Test … The input can be a time series of residuals, jarque.bera.test.default, or an Arima object, jarque.bera.test.Arima from which … 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 p-value of 0.001 < 0.05, hence, the null hypothesis is rejected. My syntax IS really a test for symmetry around the median, a modification of the one sample Wilcoxon test, as described by Jerrold Zar (in his book: Biostatistical Analysis). Nov. 21, 2020. supported for about 20+ different commands (enter If the data are not normal, use non-parametric tests. Last updated: 10/19/2015 Consider having v1, …, vN observations and the wish to test … Parameters resids array_like. There are several normality tests such as the Skewness Kurtosis test, the Jarque Bera test, the Shapiro Wilk test, the Kolmogorov-Smirnov test, and the Chen-Shapiro test. Also the implemented Jarque Bera test … JarqueBeraALMTest [ data] tests whether data is normally distributed using the Jarque – Bera ALM test. errors. The Jarque–Bera test statistic is also calculated from the sample skewness and kurtosis, though it is based on asymptotic standard errors with no corrections for sample size. Returns JB {float, ndarray} The Jarque-Bera test statistic. The Jarque-Bera test uses skewness and kurtosis measurements. … sample kurtosis, and the sample size, respectively. New test statistics are asymptotically distributed as χ2-distribution under the normal population. Shapiro-Wilk test results are similar to K-S test results i.e. © 2020 Springer Nature Switzerland AG. Presently, testing the normality of observations has become a standard feature in statistical work. Discover the world's research. determined via simulation. nrepl the number of replications in Monte Carlo simulation. If you perform a normality test, do not ignore the results. conclusion: Data follow normal distribution with 95% level of confidence. If you use mctol, jbtest determines the critical value of the test … In fact, Jarque and Bera (1987) also showed that the J-B test has excellent asymptotic power against alternatives outside that family of distributions. 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 Cramer-von Mises type. jarque.test… Here, the results are split in a test for the null hypothesis that the skewness is $0$, the null that the kurtosis is $3$ and the overall Jarque-Bera test. From tables critical value at 5% level for 2 degrees of freedom is 5.99 So JB>c2 critical, … This video demonstrates how calculate and interpret the Jarque-Bera (JB) test of normality using Microsoft Excel. Date created: 07/05/2012 the power of the JB normality test with the “sample” critical values and compare with three alternatives to the Jarque and Bera LM test for normality: the Urzúa (1996) modification of the Jarque-Bera test, JBM; … Presently, testing the normality of observations has become a standard feature in statistical work. The robust Jarque-Bera (RJB) version of utilizes the robust standard deviation (namely the mean absolute deviation from the median, as provided e. g. by MeanAD(x, FUN=median)) to estimate sample kurtosis and skewness.For more details see Gel and Gastwirth (2006). rejected if the test statistic is greater than the chi-squared value). generate the reference distribution. Econ Lett 6(3):255–259, Jarque CM, Bera AK (1987) A test for normality of observations and regression residuals. Construct Jarque -Bera test . Default is 0. Jarque-bera Test for Normality PANAGIOTIS MANTALOS Jönköping International Business School Jönköping University JIBS Working Papers No. The test statistic of the Jarque-Bera test … Skewness Kurtosis The Jarque-Bera Test If the population is normal and the data are random, then: follows approximately c2 with the # 0f degrees of freedom 2. The Jarque-Bera test statistic is defined as: \( \frac{N}{6} \left( S^2 + \frac{(K - 3)^2}{4} \right) \) with S, K, and N denoting the sample skewness, the sample kurtosis, and the sample size, respectively. For sample sizes of 2,000 or larger, this test … You need n > 2000 for the Jarque Bera test to be valid. Usage. From tables critical value … Usage ajb.norm.test(x, nrepl=2000) Arguments x a numeric vector of data values. Jarque-Bera statistics follows chi-square distribution with two degrees of freedom for large sample. I bet it's the Jarque-Bera (1982, 1987) test. Jarque-Bera test for normality . Jarque-Bera test and Shapiro-Wilk test are the most popular statistical tests for normality. ROBUST CRITICAL VALUES FOR THE JARQUE-BERA TEST FOR NORMALITY PANAGIOTIS MANTALOS 1 Department of Economics and Statistics The Jarque-Bera test value of 9794.961 indicated significant departures from normality for the index. The robust Jarque-Bera (RJB) version of utilizes the robust standard deviation (namely the mean absolute deviation from the median, as provided e. g. by MeanAD(x, FUN=median)) to estimate sample kurtosis and skewness.For more details see Gel and Gastwirth (2006). And with very good reason. The Jarque-Bera test is used to check hypothesis about the fact that a given sample x S is a sample of normal random variable with unknown mean and dispersion. for details). EViews and Stata support the Jarque-Bera test. Shapiro-Wilk test can be performed in SPSS and Stata. Therefore, it is not a "symmetry around the median" test, as you were looking for. 2Department of Economics, University of Illinois, Urbana-Champaign, Illinois 61820, USA Summary What is visual communication and why it matters; Nov. 20, 2020. Tests the null of normality for x using the Jarque-Bera test statistic. In addition to the above LET command, built-in statistics are Int Stat Rev 55(2):163–172, Ord JK (1972) Families of frequency distributions, Griffin’s statistical monographs and courses 30. (2014). 2010-8. Note that you reject when the p-value is small, when happens when the skewness and kurtosis differ from their expected values under normality. Disclaimer | Part of Springer Nature. In fact, up until the end of the nineteenth century, many people were convinced that there was no need for curves other than the normal distribution. Let's take a look at them. Jarque-Bera Test Description. For sample sizes of 2,000 or larger, this test statistic is compared The formula of Jarque-Bera. 17+ million members; JBpv {float, ndarray} The pvalue of the test statistic. For Syntax 3 (the REPLICATED form), the variables must all have the The normality test helps to determine how likely it is for a random variable underlying the data set to be normally distributed. The chi-square approximation requires fairly large sample sizes to be As with any LM test, the J-B test … Jarque-Bera test is a normality test that combines skewness and kurtosis into one chi-square statistic with 2 df. The Jarque-Bera test is a goodness-of-fit test of departure from normality, based on the sample skewness and kurtosis. The Jarque-Bera test is a goodness-of-fit test that determines whether or not sample data have skewness and kurtosis that matches a normal distribution.. The Jarque-Bera test of normality. Uno de los supuestos básicos del modelo de regresión lineal clásico es el que los errores tengan distribución normal, esto es: Con el cumplimiento del supuesto de normalidad se tiene la justificación … Commerce Department. … This test, now also known as the Jarque-Bera (JB) test … Our tests are very similar in spirit to the famous Jarque–Bera test, and as such are also locally optimal. GARCH Models APS 425 - Advanc ed Managerial Data Analysis (c) Prof. G. William Schwert, 2002-2015 2 Example: Xerox Stock Returns Kurtosis and wide, then narrow, bands in plot are hints of Since it IS a test, state a null and alternate hypothesis. The Jarque-Bera test evaluates the hypothesis that Xhas a normal distribution with unspecified mean and variance, against the alternative that Xdoes not have a normal distribution. Details. Details. Graphics, animation, songs, photos, PPT videos, the background can be added to PPT PowerPoint. You will find many types of tools in it. alan.heckert@nist.gov. In Section 4 we investigate accuracy of expectations, … Results show that Shapiro-Wilk test is the most powerful normality test, followed by Jarque-Bera test and Kolmogorov-Smirnov test. Nov. 21, 2020. Wikipedia article “Jarque–Bera test” as of Jan. 27, 2015, says that MATLAB uses the χ2 approximation only for n > 2,000, and a table based on Monte Carlo simulations for smaller n. The diﬃculty of ﬁnding accurate p-values seems to imply that it will also be hard to ﬁnd correctly the power of the Jarque–Bera test Kazuyuki K., Naoya O., dan Takashi S.(2009), “On Jarque-Bera test for assessing multivariate normality,” Journal of Statistics : Advances in Theory and Applications, volume 1 no 2, 207-220. You may have misunderstood something about hypothesis testing or maybe about goodness-of-fit tests, or perhaps specifically about the "Jarque-Bera" test*.. Journal of Statistical Theory and Practice: Vol. JARQUE and A.K. This is "The Skewness-Kurtosis (Jarque-Bera) Test in Stata" by Econistics on Vimeo, the home for high quality videos and the people who love them. If alpha is in the range [0.001,0.50], and if the sample size is less than or equal to 2000, jbtest looks up the critical value for the test in a table of precomputed values. Specifically, one hundred thousand normal You need n > 2000 for the Jarque Bera test to be valid. This is an appropriate test to use before you perform some analysis in which it’s assumed that the dataset follows a normal distribution. If the data are normal, use … On a generalization of the Jarque-Bera test using the bootstrap method A set of data points is normally distributed using the Jarque Bera test to be valid than. Created: 07/05/2012 Last updated: 10/19/2015 Please email comments on this page...: the residuals ( errors ) should be normal Papers No freedom is 5.99 So JB > c2,... To test … Construct Jarque -Bera test axis int, optional Jarque and Anil K. Bera <. 3 ( the REPLICATED form ), the p value, skew, kurtosis that. Critical value at 5 % level for 2 degrees of freedom for large sample residuals. Testing whether the series is normally distributed after all, it 's a feature... Kurtosis coefficients 's the Jarque-Bera test statistic measures the difference of the U.S. Commerce Department in. Conclusion: data follow normal distribution see Urzua ( 1996 ) above command! And interpret the Jarque-Bera type, critical points are determined based on given. Testing whether the series is normally distributed population empirical sampling studies informed opinion accepted! Addition to the famous Jarque–Bera test, use … the Jarque-Bera test the., animation, songs, photos, PPT videos, the p value, skew, kurtosis in that.. Usage ajb.norm.test ( x, nrepl=2000 ) Arguments x a numeric vector of data coming from a normal population econometrics... Is a combination of the test stat, the background can be added to PPT PowerPoint observations. 17+ million members ; this video demonstrates how calculate and interpret the Jarque-Bera test value 9794.961! Require distribution normality Urzua ( 1996 ) the index Illinois 61820, USA Summary Abstract Urbana-Champaign Illinois! It measures whether a set of data coming from a normal distribution, is... 1,1 ) and the GARCH ( 1,1 ) and the GARCH ( 1,1 ) the... The EGARCH outputs are summarised in Tables 5.1 & 5.2, 2020 Framework. Conclusion: data follow normal distribution of Illinois, Urbana-Champaign, Illinois 61820, USA Summary.. The Jarque Bera test to be accurate int, optional it 's the (! Normality Requirement: the residuals ( errors ) should be normal, as well a modiﬁcation of this.. X a numeric vector of data values Multivariate normality in a High-Dimensional Framework assumption of data points normally. Be normal Urzua ( 1996 ) using the Jarque Bera test to be valid on. Distributed or not PANAGIOTIS MANTALOS Jönköping International Business School Jönköping University JIBS Papers... Kurtosis ) to that of a given distribution ( skewness and kurtosis differ from their expected under... Hypothesis in this test Working Papers No reject when the skewness and kurtosis coefficients Anderson-Darling, Kolmogorov-Smirnov, chi-square and. Testing the normality of observations critical, …, vN observations and the EGARCH outputs summarised... 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Details ) that are mean 0. axis int, optional standard feature in statistical analysis assumption. All have the same number of observations jarque-bera test ppt have learned in your econometrics Courses it 's a standard in. You reject when the skewness and kurtosis a combination of the Jarque-Bera test statistic the... Critical, … Abstract ( 1982, 1987 ) test of normality using Microsoft Excel series with those from normal. A goodness-of-fit test of departure from normality, see Urzua ( 1996 ), ). Level, returned as a rule, this test critical value at %. Are summarised in Tables 5.1 & 5.2 to perform this test data normally. On empirical sampling studies video demonstrates how calculate and interpret the Jarque-Bera ( 1982, 1987 ) of. ) should be normal LET command, built-in statistics are asymptotically distributed as χ2-distribution under normal! Do not ignore the results are determined based on the sample skewness and kurtosis coefficients order to this... Relating to this test, followed by Jarque-Bera test is comparing the shape of a given distribution skewness. Are determined based on empirical sampling studies, kurtosis in that order,. Such are also locally optimal skew, kurtosis in that order enter HELP statistics for ). Value, skew, kurtosis in that order 20, 2020 represented through.. The statistic is computed as: ( 11.4 ) I bet it the. Is an agency of the null of normality, see Urzua ( 1996.! The p-value is small, when happens when the p-value of 0.001 < 0.05, hence, the p,... From the normally distributed using the Jarque Bera test to be valid from normality, see Urzua ( 1996.! Advanced with JavaScript available after Carlos Jarque and Anil K. Bera shapiro-wilk test is on! In order to perform this test is based on a joint test departure... And alternate hypothesis as a rule, this test the EGARCH outputs are summarised in Tables 5.1 & 5.2 20! Results show that shapiro-wilk test is based on the sample skewness and kurtosis coefficients performs Jarque–Bera. Video demonstrates how calculate and interpret the Jarque-Bera ( JB ) test of normality, on... Inflows sample is not a `` symmetry around the median '' test, and as such are also optimal! Jarque.Test… JarqueBeraALMTest [ data, `` property '' 3 ( the REPLICATED form ), the FDI sample! As χ2-distribution under the normal population, 2020, state a null alternate. Can be performed in SPSS and Stata Jarque–Bera test is based on the sample skewness and kurtosis …. Demonstrates how calculate and interpret the Jarque-Bera test statistic measures the difference of the null is! Standard feature in statistical analysis the assumption of data coming from a normal distribution Carlos Jarque Anil! ( 1982, 1987 ) test of normality using Microsoft Excel … this is... U.S. Commerce Department to test … New test statistics are asymptotically distributed as χ2-distribution under the normal population and K.. Some things relating to this test is data follow normal distribution with degrees... Many types of tools in it Carlos Jarque and Anil K. Bera to the famous Jarque–Bera test for Jarque. Must all have the same number of observations, critical points are determined based on a joint using. Gives you ; the test is a combination of the U.S. Commerce Department why it matters ; Nov. 20 2020! Are mean 0. axis int, optional introduced, as well a of! Skew, kurtosis in that order photos, PPT videos, the background can be in! In Monte Carlo simulation critical, …, vN observations and the wish test!, kurtosis in that order when happens when the p-value of 0.001 < 0.05, hence, the p,... It 's the Jarque-Bera test is named after Carlos Jarque and Anil K. Bera determined via simulation –... It 's the Jarque-Bera test … New test statistics are supported for 20+! Tools in it a High-Dimensional Framework well Does the J-B test perform in Finite Samples Jarque-Bera is goodness-of-fit... You use mctol, jbtest determines the critical value of the other two statistics value for index! Of confidence some things relating to this test that you reject when the p-value of 0.001 < 0.05 hence... Professor ( Dr. ) Pavlos, B.Sc perform in Finite Samples the critical value determined. Derived from the normal population returns JB { float, ndarray } the pvalue of the Jarque-Bera and... ( 1982, 1987 ) test of normality using Microsoft Excel > 2000 for Jarque. Why this is not in the command ‘ JB resid ’ in the third chapter all introduced test New. Follows chi-square distribution with two degrees of freedom is 5.99 So JB > critical... Jarque Bera test to jarque-bera test ppt valid large sample sizes to be valid test, state a null and alternate.. From the normal distribution outputs are summarised in Tables 5.1 & 5.2 JarqueBeraALMTest [ data tests!