ordinal_skewness function

Computes the estimated skewness of an ordinal time series

ordinal_skewness computes the estimated skewness of an ordinal time series UTF-8

ordinal_skewness(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 skewness is returned. Otherwise, the function returns the normalized estimated skewness.

Returns

The estimated skewness.

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 skewness given by $\widehat{skew}_{d}=\sum_{i=0}^n\big(d(s_i,s_n)-d(s_i,s_0)\big)\widehat{p}_i$, where $d(\cdot, \cdot)$ is a distance between ordinal states and $\widehat{p}_k$ is the standard estimate of the marginal probability for state $s_k$ computed from the realization $\overline{X}_t$.

Examples

estimated_skewness <- ordinal_skewness(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the skewness 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