ordinal_dispersion_2: Computes the estimated dispersion of an ordinal time series...

In otsfeatures: Ordinal Time Series Analysis

Computes the estimated dispersion of an ordinal time series according to the approach based on the diversity coefficient (DIVC)

Description

ordinal_dispersion_2 computes the estimated dispersion of an ordinal time series according to the approach based on the diversity coefficient

Usage

ordinal_dispersion_2(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 dispersion is returned. Otherwise, the function returns the normalized estimated dispersion.

Details

Given an OTS of length T with range \mathcal{S}=\{s_0, s_1, s_2, …, s_n\} (s_0 < s_1 < s_2 < … < s_n), \overline{X}_t=\{\overline{X}_1,…, \overline{X}_T\}, the function computes the DIVC estimated dispersion given by \widehat{disp}_{d}=\frac{T}{T-1}∑_{i,j=0}^nd\big(s_i, s_j\big)\widehat{p}_i\widehat{p}_j, 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. If normalize = TRUE, and distance = "Block" or distance = "Euclidean", then the normalized versions are computed, that is, the corresponding estimates are divided by the factors 2/m or 2/m^2, respectively.

Value

The estimated dispersion according to the approach based on the diversity coefficient.

Author(s)

Ángel López-Oriona, José A. Vilar

References

\insertRef

weiss2019distanceotsfeatures

Examples

estimated_dispersion <- ordinal_dispersion_2(series = AustrianWages$data[[100]],
states = 0 : 5) # Computing the DIVC dispersion estimate
# for one series in dataset AustrianWages using the block distance

otsfeatures documentation built on March 7, 2023, 7:38 p.m.