JarqueBeraBacktest function

Jarque-Bera backtest for normality.

Jarque-Bera (JB) is a backtest to test whether the skewness and kurtosis of a given sample matches that of normal distribution. JB test statistic is defined as [REMOVE_ME]$JB=\frac{n}{6}\left(s^2+\frac{(k-3)^2}{4}\right) [REMOVE_ME_2]$ where $n$ is sample size, $s$ and $k$ are coefficients of sample skewness and kurtosis.

JarqueBeraBacktest(sample.skewness, sample.kurtosis, n)

Arguments

• sample.skewness: Coefficient of Skewness of the sample
• sample.kurtosis: Coefficient of Kurtosis of the sample
• n: Number of observations

Returns

Probability of null hypothesis H0

Description

Jarque-Bera (JB) is a backtest to test whether the skewness and kurtosis of a given sample matches that of normal distribution. JB test statistic is defined as

where $n$ is sample size, $s$ and $k$ are coefficients of sample skewness and kurtosis.

Examples

# JB test statistic for sample with 500 observations with sample
   # skewness and kurtosis of -0.075 and 2.888
   JarqueBeraBacktest(-0.075,2.888,500)

Author(s)

Dinesh Acharya

References

Dowd, Kevin. Measuring Market Risk, Wiley, 2007.

Jarque, C. M. and Bera, A. K. A test for normality of observations and regression residuals, International Statistical Review, 55(2): 163-172.