| c_conditional_probabilities {otsfeatures} | R Documentation |
Computes the cumulative conditional probabilities of an ordinal time series
Description
c_conditional_probabilities returns a matrix with the cumulative conditional
probabilities of an ordinal time series
Usage
c_conditional_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 F}^c(l) = \big(\widehat{f}^c_{i-1j-1}(l)\big)_{1 \le i, j \le n},
with \widehat{f}^c_{ij}(l)=\frac{TN_{ij}(l)}{(T-l)N_i}, where
N_i is the number of elements less one or equal to s_i in the realization \overline{X}_t and 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.
Value
A matrix with the conditional 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_ccp <- c_conditional_probabilities(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the matrix of
# cumulative conditional probabilities for one series in dataset AustrianWages