ordinal_dispersion_1 {otsfeatures}

Computes the standard estimated dispersion of an ordinal time series

Description

ordinal_dispersion_1 computes the standard estimated dispersion of an ordinal time series

Usage

ordinal_dispersion_1(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 standard estimated dispersion is returned. Otherwise, the function returns the normalized standard estimated dispersion.

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 standard estimated dispersion given by \widehat{disp}_{loc, d}=\frac{1}{T}\sum_{t=1}^Td\big(\overline{X}_t, \widehat{x}_{loc, d}\big), where \widehat{x}_{loc, d} is the standard estimate of the location and d(\cdot, \cdot) is a distance between ordinal states. If normalize = TRUE, then the normalized dispersion is computed, namely \widehat{disp}_{loc, d}/max_{s_i, s_j \in \mathcal{S}}d(s_i, s_j).

Value

The standard estimated dispersion.

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

estimated_dispersion <- ordinal_dispersion_1(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the standard dispersion estimate
# for one series in dataset AustrianWages using the block distance