偏度、峰度与Jarque–Bera检验

R 中的定量风险管理

Alexander McNeil

Professor, University of York

偏度与峰度

$$ = {1 \over n}\sum_{t=1}^n(X_t-\hat{\mu})^3 \over \hat{\sigma}^3 $$

$$ = {1 \over n}\sum_{t=1}^n(X_t-\hat{\mu})^4 \over \hat{\sigma}^4 $$

library(moments)

skewness(ftse)

-0.01187921

kurtosis(ftse)

7.437121

$$ T = {1 \over 6}n\left(b^2 + \frac{1}{4}(k - 3)^2\right) $$

jarque.test(ftse)

    Jarque-Bera Normality Test
data: ftse
JB = 428.23, p-value < 2.2e-16
alternative hypothesis: greater

R 中的定量风险管理