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otsfeatures (version 1.0.0)

total_mixed_c_correlation_1: Computes the total mixed cumulative linear correlation (TMCLC) between an ordinal and a real-valued time series

Description

total_mixed_c_correlation_1 returns the TMCLC between an ordinal and a real-valued time series

Usage

total_mixed_c_correlation_1(
  o_series,
  n_series,
  lag = 1,
  states,
  features = FALSE
)

Value

If features = FALSE (default), returns the value of the TMCLC. Otherwise, the function returns a vector of features, i.e., the vector contains the features employed to compute the TMCLC.

Arguments

o_series

An OTS.

n_series

A real-valued time series.

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 TMCLC is returned. Otherwise, the function returns a vector with the individual components of the TMCLC.

Author

Ángel López-Oriona, José A. Vilar

Details

Given a 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 TMCLC given by $$\widehat{\Psi}_1^m(l)=\frac{1}{n}\sum_{i=0}^{n-1}\widehat{\psi}_{i}^*(l)^2,$$ where \(\widehat{\psi}_{i}^*(l)=\widehat{Corr}(Y_{t,i}, Z_{t-l})\), with \(\overline{Z}_t=\{\overline{Z}_1,\ldots, \overline{Z}_T\}\) being a \(T\)-length real-valued time series. If features = TRUE, the function returns a vector whose components are the quantities \(\widehat{\psi}_{i}(l)\), \(i=0,1, \ldots,n-1\).

Examples

Run this code
tmclc <- total_mixed_c_correlation_1(o_series = SyntheticData1$data[[1]],
n_series = rnorm(600), states = 0 : 5) # Computing the TMCLC
# between the first series in dataset SyntheticData1 and white noise
feature_vector <- total_mixed_c_correlation_1(o_series = SyntheticData1$data[[1]],
n_series = rnorm(600), states = 0 : 5, features = TRUE) # Computing the corresponding
# vector of features

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