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otsfeatures (version 1.0.0)

c_joint_probabilities: Computes the cumulative joint probabilities of an ordinal time series

Description

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

Usage

c_joint_probabilities(series, lag = 1, states)

Value

A matrix with the jcumulative oint probabilities.

Arguments

series

An OTS.

lag

The considered lag (default is 1).

states

A numerical vector containing the corresponding states.

Author

Ángel López-Oriona, José A. Vilar

Details

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

References

weiss2019distanceotsfeatures

Examples

Run this code
matrix_cjp <- c_joint_probabilities(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the matrix of
# cumulative joint probabilities for one series in dataset AustrianWages

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