cvm_3series {IndGenErrors}

Cramer-von Mises Moebius statistics for testing independence between the innovations of 3 series of same length

Description

This function computes the Cramer-von Mises statistics between x(t), y(t-l2), z(t-l3), for l2=-lag2,.., lag2, l3=-lag3,.., lag3,and also the combinations of these statistics.

Usage

cvm_3series(x, y, z, lag2, lag3)

Arguments

x

Pseudo-observations (or residuals) of first series.

y

Pseudo-observations (or residuals) of second series.

z

Pseudo-observations (or residuals) of third series.

lag2

Maximum number of lags around 0 for pairs of series.

lag3

Maximum number of lags around 0 for the three series.

Value

cvm

Cramer-von Mises statistics for all lags and for all subsets

Wstat

Sum of (unbiased) Cramer-von Mises statistics for all subsets

Fstat

Combination of p-values of the Cramer-von Mises statistics

pvalue

List of p-values for the cvm, Wstat, and Fstat

References

Duchesne, Ghoudi & Remillard (2012). On Testing for independence between the innovations of several time series. CJS, vol. 40, 447-479.

Examples

set.seed(1)
x0 = rnorm(100); y = rnorm(100); z = rnorm(100);