Jarque–Bera test
In
The test statistic JB is defined as
where n is the number of observations (or degrees of freedom in general); S is the sample skewness, K is the sample kurtosis :
where and are the estimates of third and fourth central moments, respectively, is the sample mean, and is the estimate of the second central moment, the variance.
If the data comes from a normal distribution, the JB statistic
For small samples the chi-squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. Furthermore, the distribution of
Calculated p-values equivalents to true alpha levels at given sample sizes True α level 20 30 50 70 100 0.1 0.307 0.252 0.201 0.183 0.1560 0.05 0.1461 0.109 0.079 0.067 0.062 0.025 0.051 0.0303 0.020 0.016 0.0168 0.01 0.0064 0.0033 0.0015 0.0012 0.002
(These values have been approximated using
In
History
The statistic was derived by Carlos M. Jarque and Anil K. Bera while working on their Ph.D. Thesis at the Australian National University.
Jarque–Bera test in regression analysis
According to Robert Hall, David Lilien, et al. (1995) when using this test along with multiple regression analysis the right estimate is:
where n is the number of observations and k is the number of regressors when examining residuals to an equation.
Implementations
- ALGLIB includes an implementation of the Jarque–Bera test in C++, C#, Delphi, Visual Basic, etc.
- gretl includes an implementation of the Jarque–Bera test
- Julia includes an implementation of the Jarque-Bera test JarqueBeraTest in the HypothesisTests package.[2]
- MATLABincludes an implementation of the Jarque–Bera test, the function "jbtest".
- Python statsmodels includes an implementation of the Jarque–Bera test, "statsmodels.stats.stattools.py".
- R includes implementations of the Jarque–Bera test: jarque.bera.test in the package tseries,[3] for example, and jarque.test in the package moments.[4]
- Wolfram includes a built in function called, JarqueBeraALMTest[5] and is not limited to testing against a Gaussian distribution.
See also
- D'Agostino's K-squared test, another test based on kurtosis and skewness.
References
- ^ "Analysis of the JB-Test in MATLAB". MathWorks. Retrieved May 24, 2009.
- ^ "Time series tests". juliastats.org. Retrieved 2020-02-04.
- ^ "tseries: Time Series Analysis and Computational Finance". R Project.
- ^ "moments: Moments, cumulants, skewness, kurtosis and related tests". R Project.
- ^ "JarqueBeraALMTest—Wolfram Language Documentation". reference.wolfram.com. Retrieved 2017-10-26.
Further reading
- .
- .
- JSTOR 1403192.
- Judge; et al. (1988). Introduction and the theory and practice of econometrics (3rd ed.). pp. 890–892.
- Hall, Robert E.; Lilien, David M.; et al. (1995). EViews User Guide. p. 141.