total_mixed_c_correlation_2: Computes the total mixed cumulative quantile correlation...

In otsfeatures: Ordinal Time Series Analysis

Computes the total mixed cumulative quantile correlation (TMCQC) between an ordinal and a real-valued time series

Description

total_mixed_c_correlation_2 returns the TMCQC between an ordinal and a real-valued time series

Usage

total_mixed_c_correlation_2(
  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 TMCQC.

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 TMCQC given by

\widehat{Ψ}_2^m(l)=\frac{1}{n}∑_{i=0}^{n-1}\int_{0}^{1}\widehat{ψ}^ρ_{i}(l)^2dρ,

where \widehat{ψ}_{i}^ρ(l)=\widehat{Corr}\big(Y_{t,i}, I(Z_{t-l}≤q q_{Z_t}(ρ)) \big), with \overline{Z}_t=\{\overline{Z}_1,…, \overline{Z}_T\} being a T-length real-valued time series, ρ \in (0, 1) a probability level, I(\cdot) the indicator function and q_{Z_t} the quantile function of the corresponding real-valued process. If features = TRUE, the function returns a vector whose components are the quantities \int_{0}^{1}\widehat{ψ}^ρ_{i}(l)^2dρ, i=0,1, …,n-1.

Value

If features = FALSE (default), returns the value of the TMCQC. 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_2(o_series = SyntheticData1$data[[1]],
n_series = rnorm(600), states = 0 : 5) # Computing the TMCQC
# between the first series in dataset SyntheticData1 and white noise
feature_vector <- total_mixed_c_correlation_2(o_series = SyntheticData1$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.