joint_probabilities: Computes the joint probabilities of an ordinal time series

In otsfeatures: Ordinal Time Series Analysis

Computes the joint probabilities of an ordinal time series

Description

joint_probabilities returns a matrix with the joint probabilities of an ordinal time series

Usage

joint_probabilities(series, lag = 1, states)

Arguments

series	An OTS.
lag	The considered lag (default is 1).
states	A numerical vector containing the corresponding states.

Details

Given an OTS of length T with range \mathcal{S}=\{s_0, s_1, s_2, …, s_n\} (s_0 < s_1 < s_2 < … < s_n), \overline{X}_t=\{\overline{X}_1,…, \overline{X}_T\}, the function computes the matrix \widehat{\boldsymbol P}(l) = \big(\widehat{p}_{i-1j-1}(l)\big)_{1 ≤ i, j ≤ n+1}, with \widehat{p}_{ij}(l)=\frac{N_{ij}(l)}{T-l}, where N_{ij}(l) is the number of pairs (\overline{X}_t, \overline{X}_{t-l})=(s_i,s_j) in the realization \overline{X}_t.

Value

A matrix with the joint probabilities.

Author(s)

Ángel López-Oriona, José A. Vilar

References

\insertRef

weiss2019distanceotsfeatures

Examples

matrix_jp <- joint_probabilities(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the matrix of
# joint probabilities for one series in dataset AustrianWages

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