moment.test {OLCPM}

test whether the k-th moment exists

Description

This function tests the existence of k-th moment by randomized method in Trapani (2016).

Usage

moment.test(x, k = 16, R = 400)

Arguments

x

a numeric vector of data samples.

k

a number no smaller than 4, indicating that the procedure will test the existence of the k-th moment when k is even. Otherwise, the procedure will test the existence of the k'-th moment, with k'=round(k/2,0)\times 2.

R

the number of standard Gaussian variables generated in the randomized test; see more details in Trapani (2016).

Details

The procedure is adapted from Trapani (2016) with \psi=2, where \psi is a tuning parameter to scale the sample moments defined in Section 3.1 of Trapani (2016). For simplicity, we only test the 4th, 6th, ... 2c-th moments.

Value

a scalar in [0,1], indicating the p-value of the test. The null hypothese is that the k-th moment doesn't exist. Therefore, a small p-value indicates the existense of the k-th moment.

Author(s)

Yong He, Xinbing Kong, Lorenzo Trapani, Long Yu

References

Trapani, L. (2016). Testing for (in) finite moments. Journal of Econometrics, 191(1), 57-68.

Examples

x=rt(10000,5)
moment.test(x,4)

x=rt(10000,4)
moment.test(x,4)