joint_probabilities {ctsfeatures}

Computes the joint probabilities of a categorical time series

Description

joint_probabilities returns a matrix with the joint probabilities of a categorical time series

Usage

joint_probabilities(series, lag = 1)

Arguments

series

An object of type tsibble (see R package tsibble), whose column named Value contains the values of the corresponding CTS. This column must be of class factor and its levels must be determined by the range of the CTS.

lag

The considered lag (default is 1).

Details

Given a CTS of length T with range \mathcal{V}=\{1, 2, \ldots, r\}, \overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}, the function computes the matrix \widehat{\boldsymbol P}(l) = \big(\widehat{p}_{ij}(l)\big)_{1 \le i, j \le r}, 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})=(i,j) in the realization \overline{X}_t.

Value

A matrix with the joint probabilities.

Author(s)

Ángel López-Oriona, José A. Vilar

References

Weiß CH, Göb R (2008). “Measuring serial dependence in categorical time series.” AStA Advances in Statistical Analysis, 92, 71–89.

Examples

sequence_1 <- GeneticSequences[which(GeneticSequences$Series==1),]
matrix_jp <- joint_probabilities(series = sequence_1) # Computing the matrix of
# joint probabilities for the first series in dataset GeneticSequences