total_c_correlation function

Computes the total cumulative correlation of an ordinal time series

total_c_correlation returns the value of the total cumulative correlation for an ordinal time series UTF-8

total_c_correlation(series, lag = 1, states, features = FALSE)

Arguments

• series: An OTS.
• lag: The considered lag (default is 1).
• states: A numerical vector containing the corresponding states.
• features: Logical. If features = FALSE (default), the value of the total cumulative correlation is returned. Otherwise, the function returns a matrix with the individual components of the total cumulative correlation

Returns

If features = FALSE (default), returns the value of the total cumulative correlation. Otherwise, the function returns a matrix of features, i.e., the matrix contains the features employed to compute the total cumulative correlation.

Details

Given an OTS of length $T$ with range $\mathcal{S}=\{s_0, s_1, \ldots, s_n\}$, $\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}$, and the cumulative binarized time series, which is defined as $\overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, \ldots, \overline{\boldsymbol Y}_T\}$, with $\overline{\boldsymbol Y}_k=(\overline{Y}_{k,0}, \ldots, \overline{Y}_{k,n-1})^\top$

such that $\overline{Y}_{k,i}=1$ if $\overline{X}_k\leq s_i$ (c("$k=1,\\ldots,T,\n$", "$, i=0,\\ldots,n-1$")), the function computes the estimated average $\widehat{\Psi}(l)^c=\frac{1}{n^2}\sum_{i,j=0}^{n-1}\widehat{\psi}_{ij}(l)^2$, where $\widehat{\psi}_{ij}(l)$ is the estimated correlation $\widehat{Corr}(Y_{t, i}, Y_{t-l, j})$, $i,j=0, 1,\ldots,n-1$. If features = TRUE, the function returns a matrix whose components are the quantities $\widehat{\psi}_{ij}(l)$, $i,j=0,1, \ldots,n-1$.

Examples

tcc <- total_c_correlation(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the total cumulative correlation
# for one of the series in dataset AustrianWages
feature_matrix <- total_c_correlation(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the corresponding matrix of features

Author(s)

Ángel López-Oriona, José A. Vilar