ordinal_asymmetry function

Computes the estimated asymmetry of an ordinal time series

ordinal_asymmetry computes the estimated asymmetry of an ordinal time series UTF-8

ordinal_asymmetry(series, states, distance = "Block", normalize = FALSE)

Arguments

• series: An OTS.
• states: A numerical vector containing the corresponding states.
• distance: A function defining the underlying distance between states. The Hamming, block and Euclidean distances are already implemented by means of the arguments "Hamming", "Block" (default) and "Euclidean". Otherwise, a function taking as input two states must be provided.
• normalize: Logical. If normalize = FALSE (default), the value of the estimated asymmetry is returned. Otherwise, the function returns the normalized estimated asymmetry.

Returns

The estimated asymmetry.

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 estimated asymmetry given by $\widehat{asym}_{d}=\widehat{\boldsymbol p}^\top (\boldsymbol J-\boldsymbol I)\boldsymbol D\widehat{\boldsymbol p}$, where $\widehat{\boldsymbol p}=(\widehat{p}_0, \widehat{p}_1, \ldots, \widehat{p}_n)^\top$, with $\widehat{p}_k$ being the standard estimate of the marginal probability for state $s_k$, $\boldsymbol I$ and $\boldsymbol J$ are the identity and counteridentity matrices of order $n + 1$, respectively, and $\boldsymbol D$ is a pairwise distance matrix for the elements in the set $\mathcal{S}$ considering a specific distance between ordinal states, $d(\cdot, \cdot)$. If normalize = TRUE, then the normalized estimate is computed, namely $\frac{\widehat{asym}_{d}}{max_{s_i, s_j \in \mathcal{S}}d(s_i, s_j)}$.

Examples

estimated_asymmetry <- ordinal_asymmetry(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the asymmetry estimate
# for one series in dataset AustrianWages using the block distance

References

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

Author(s)

Ángel López-Oriona, José A. Vilar