elbouch.statistic {nortsTest}

Computes El Bouch, et al.'s z statistic.

Description

Computes the El Bouch, Michel, & Comon's z test statistic for normality of a univariate or bivariate time series.

Usage

elbouch.statistic(y, x = NULL)

Arguments

y

a numeric vector or an object of the ts class containing a stationary time series.

x

a numeric vector or an object of the ts class containing a stationary time series.

Details

This function computes Mardia's standardized 'z = (B - E_B)/ sd_B' statistic corrected by El Bouch, et al. (2022) for stationary bivariate time series. Where: 'B' is the square of a quadratic form of the process 'c(y, x)'; 'E_B' and 'sd_B' are the estimator's expected value and standard error respectively. If 'x' is set to 'NULL', the test computes the univariate counterpart.

Value

a real value with El Bouch test's statistic.

Author(s)

Asael Alonzo Matamoros.

References

El Bouch, S., Michel, O. & Comon, P. (2022). A normality test for Multivariate dependent samples. Journal of Signal Processing. Volume 201.

Mardia, K. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57 519-530

Lobato, I., & Velasco, C. (2004). A simple test of normality in time series. Journal of econometric theory. 20(4), 671-689.

See Also

lobato.statistic

Examples

# Genere an univariate stationary ARMA process
y = arima.sim(100,model = list(ar = 0.3))
elbouch.statistic(y)

# Generate a bivariate Gaussian random vector
x = rnorm(200)
y = rnorm(200)
elbouch.statistic(y = y, x = x)