ADCF(x, MaxLag)ADCF. Default is 15.MaxLag, and contains the estimated ADCF.ADCF computes the auto-distance correlation function, $R_X(j)$, between ${X_t}$ and ${X_{t-|j|}}$,
whereas ADCV computes the auto-distance covariance function between them, denoted by $V_X(j)$. Formal definition
of $R_X(\cdot)$ and $V_X(\cdot)$ can be found in Zhou (2012) and Fokianos and Pitsillou (2016). The empirical auto-distance correlation function, $\hat{R}_X(j)$, is computed as the square root of
$$\hat{R}_X^2(j)=\frac{\hat{V}_X^2(j)}{\hat{V}_X^2(0)}, ~~~~~j=0, \pm 1, \pm 2, \dots$$
for $\hat{V}_X^2(0) \neq 0$ and zero otherwise, where $\hat{V}_X(\cdot)$ is a function of the double
centered Euclidean distance matrices of the sample $X_t$ and its lagged sample $X_{t-|j|}$ (see ADCV for more details).
Theoretical properties of this measure can be found in Fokianos and Pitsillou (2016).
mADCF computes the auto-distance correlation function of a multivariate time series.ADCFplot, ADCV, mADCFx <- rnorm(1000)
ADCF(x)
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