dCovTS (version 1.0)

mADCV: Distance Covariance Matrix

Description

Computes the sample distance covariance matrices of a multivariate time series.

Usage

mADCV(x, lags, output=TRUE)

Arguments

x

multivariate time series.

lags

lag order at which to calculate the mADCV. No default is given.

output

logical value. If output=FALSE, no output is given. Default value is TRUE.

Value

• Returns the sample auto-distance covariance matrix at lag, $j$, determined by the argument lags.

Details

Suppose that $\textbf{X}_t=(X_{t;1}, \dots, X_{t;d})'$ is a multivariate time series of dimension $d$. Then, mADCV computes the $d \times d$ sample distance covariance matrix, $\hat{V}(\cdot)$, of $\textbf{X}_t$ given by $$\hat{V}(j) = [\hat{V}_{rm}(j)]_{r,m=1}^d , j~~=~~0, \pm 1, \pm 2, \dots$$ where $\hat{V}_{rm}(j)$ denotes the pairwise sample auto-distance covariance function between $X_{t;r}$ and $X_{t-|j|;m}$ whose definition is given analogously as in the univariate case ADCV. Formal definitions and theoretical properties of mADCV can be found in Fokianos and Pitsillou (2016).

References

Fokianos K. and M. Pitsillou (2016). On multivariate auto-distance covariance and correlation functions. Submitted for publication.

See Also

ADCV,mADCF

Examples

x <- MASS::mvrnorm(100,rep(0,2),diag(2))
mADCV(x,lags=1)
mADCV(x,lags=15)

y <- as.ts(swiss)
mADCV(y,15)