Computes the distance correlation matrix of a multivariate time series.
Usage
mADCF(x, lags, output=TRUE)
Arguments
x
multivariate time series.
lags
lag order at which to calculate the mADCF. No default is given.
output
logical value. If output=FALSE, no output is given. Default value is TRUE.
Value
Returns the sample auto-distance correlation matrix at lag, $j$, determined by the argument lags.
Details
If $\textbf{X}_t=(X_{t;1}, \dots, X_{t;d})'$ is a multivariate time series of dimension $d$, then mADCF
computes the sample distance correlation matrix, $\hat{R}(\cdot)$, of $\textbf{X}_t$. It is defined by
$$\hat{R}(j) = [\hat{R}_{rm}(j)]_{r,m=1}^d ~~~~, j~~=~~0, \pm 1, \pm 2, \dots$$
where $\hat{R}_{rm}(j)$ is the sample auto-distance correlation function between $X_{t;r}$ and $X_{t-|j|;m}$ given as
the positive square root of
$$\hat{R}_{rm}^2(j) = \frac{\hat{V}_{rm}^2(j)}{\hat{V}_{rr}(0)\hat{V}_{mm}(0)}$$
for $\hat{V}_{rr}(0)\hat{V}_{mm}(0) \neq 0$ and zero otherwise.
$\hat{V}_{rm}(j)$ is the $(r,m)$-element of the corresponding mADCV matrix at lag $j$. Formal definition and
more details 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.