total_mixed_c_correlation_1: Computes the total mixed cumulative linear correlation...

In otsfeatures: Ordinal Time Series Analysis

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
)

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.

Details

Given a OTS of length T with range \mathcal{S}=\{s_0, s_1, …, s_n\}, \overline{X}_t=\{\overline{X}_1,…, \overline{X}_T\}, and the cumulative binarized time series, which is defined as \overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, …, \overline{\boldsymbol Y}_T\}, with \overline{\boldsymbol Y}_k=(\overline{Y}_{k,0}, …, \overline{Y}_{k,n-1})^\top such that \overline{Y}_{k,i}=1 if \overline{X}_k ≤q s_i (k=1,…,T , i=0,…,n-1), the function computes the estimated TMCLC given by

\widehat{Ψ}_1^m(l)=\frac{1}{n}∑_{i=0}^{n-1}\widehat{ψ}_{i}^*(l)^2,

where \widehat{ψ}_{i}^*(l)=\widehat{Corr}(Y_{t,i}, Z_{t-l}), with \overline{Z}_t=\{\overline{Z}_1,…, \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{ψ}_{i}(l), i=0,1, …,n-1.

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.

Author(s)

Ángel López-Oriona, José A. Vilar

Examples

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

otsfeatures documentation built on March 7, 2023, 7:38 p.m.