| joint_probabilities {otsfeatures} | R Documentation |
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, \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 P}(l) = \big(\widehat{p}_{i-1j-1}(l)\big)_{1 \le i, j \le 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
Weiß CH (2019). “Distance-based analysis of ordinal data and ordinal time series.” Journal of the American Statistical Association.
Examples
matrix_jp <- joint_probabilities(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the matrix of
# joint probabilities for one series in dataset AustrianWages