| total_c_correlation {otsfeatures} | R Documentation |
Computes the total cumulative correlation of an ordinal time series
Description
total_c_correlation returns the value of the total cumulative correlation for
an ordinal time series
Usage
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 |
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 (k=1,\ldots,T,
, 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.
Value
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.
Author(s)
Ángel López-Oriona, José A. Vilar
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