Jarque-Bera Test

Introduction: Jarque-Bera Test

The Jarque-Bera Test is a statistical method used to check whether a dataset follows a normal distribution. It focuses on the skewness (symmetry) and kurtosis (peakedness) of the data, which are two key characteristics of a normal curve.

Background

The test was introduced in 1980 by economists Carlos Jarque and Anil K. Bera. It is widely used in fields like econometrics, finance, and research, where the assumption of normality underpins many statistical models. Unlike tests such as Shapiro-Wilk, the Jarque-Bera Test is particularly useful for larger datasets.

Key Elements / Features

• Skewness: Measures whether data are symmetrically distributed. Normal data should have skewness close to zero.
• Kurtosis: Measures the “tailedness” of the distribution. Normal data should have kurtosis close to 3.
• Test statistic: The Jarque-Bera statistic combines deviations in skewness and kurtosis into a single measure.
• p-Value: A low p-value (e.g., <0.05) suggests the data deviate significantly from normality.

Applications / Examples

• Finance: Testing whether stock returns follow a normal distribution before risk modelling.
• Economics: Checking if error terms in regression models meet the assumption of normality.
• Quality control: Verifying whether production data show the expected normal variation.

For example, if a dataset of daily stock returns has high skewness and kurtosis, the Jarque-Bera Test may confirm that returns do not follow a normal distribution, prompting analysts to use models better suited for “fat-tailed” data.

Relevance / Impact

The Jarque-Bera Test is simple, fast, and effective for large samples. It highlights deviations from normality in skewness and kurtosis, helping researchers choose appropriate statistical tools. However, it is less reliable for very small datasets, where other tests like Shapiro-Wilk may be more suitable.

See also

• Shapiro-Wilk Test
• Anderson-Darling Normality Test
• Kolmogorov-Smirnov Test
• Lilliefors Test