c_conditional_probabilities function

Computes the cumulative conditional probabilities of an ordinal time series

c_conditional_probabilities returns a matrix with the cumulative conditional probabilities of an ordinal time series UTF-8

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.

Returns

A matrix with the conditional probabilities.

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 $\overline{X}_{t-l} \le s_j$.

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

References

Rdpack::insert_ref(key="weiss2019distance",package="otsfeatures")

Author(s)

Ángel López-Oriona, José A. Vilar