TEST_XKURT - Excess Kurtosis Test

1. The data sample may include missing values (e.g. #N/A).
2. The test hypothesis for the population excess kurtosis:
   $$H_{o}: K=0$$
   $$H_{1}: K\neq 0$$
   Where:
   
   • $H_{o}$ is the null hypothesis.
   • $H_{1}$ is the alternate hypothesis.
3. For the case in which the underlying population distribution is normal, the sample excess kurtosis also has a normal sampling distribution:
   $$\hat K \sim N(0,\frac{24}{T}) $$
   Where:
   
   • $\hat k$ is the sample excess kurtosis (i.e. 4th moment).
   • $T$ is the number of non-missing values in the data sample.
   • $N(.)$ is the normal (i.e. gaussian) probability distribution function.
4. Using a given data sample, the sample excess kurtosis is calculated as:
   $$\hat K (x)= \frac{\sum_{t=1}^T(x_t-\bar x)^4}{(T-1)\hat \sigma^4}-3$$
   Where:
   
   • $\hat K(x) $ is the sample excess kurtosis.
   • $x_i $ is the i-th non-missing value in the data sample.
   • $T$ is the number of non-missing values in the data sample.
   • $\hat \sigma$ is the sample standard deviation.
5. The underlying population distribution is assumed normal (gaussian).
6. This is a two-sides (i.e. two-tails) test, so the computed p-value should be compared with half of the significance level ($\frac{\alpha}{2}$).

Example 1:

Files Examples

Related Links

• Financial Dictionary - Excess kurtosis
• Wikipedia - Excess kurtosis
• Wikipedia - Statistical hypothesis testing