mddm function

Martingale Difference Divergence Matrix

mddm extends martingale difference divergence from a scalar to a matrix. It encodes the linear combinations of all univariate components in Y

that are conditionally mean independent of X. Only the double-centering approach is applied.

mddm(X, Y, compute = "C")

Arguments

• X: A vector, matrix or data frame, where rows represent samples, and columns represent variables.

• Y: A vector, matrix or data frame, where rows represent samples, and columns represent variables.

• compute: The method for computation, including

  • C: computation implemented in C code;
  • R: computation implemented in R code.

Returns

mddm returns the martingale difference divergence matrix of Y given X.

Examples

# X, Y are vectors with 10 samples and 1 variable
X <- rnorm(10)
Y <- rnorm(10)

mddm(X, Y, compute = "C")
mddm(X, Y, compute = "R")

# X, Y are 10 x 2 matrices with 10 samples and 2 variables
X <- matrix(rnorm(10 * 2), 10, 2)
Y <- matrix(rnorm(10 * 2), 10, 2)

mddm(X, Y, compute = "C")
mddm(X, Y, compute = "R")

References

Lee, C. E., and Shao, X. (2017). Martingale Difference Divergence Matrix and Its Application to Dimension Reduction for Stationary Multivariate Time Series. Journal of the American Statistical Association, 1-14. http://dx.doi.org/10.1080/01621459.2016.1240083.