Generalized ordinal patterns allowing for ties and their applications in hydrology

Alexander Schnurr and Svenja Fischer

Computational Statistics & Data Analysis, 2022, vol. 171, issue C

Abstract: When using ordinal patterns, which describe the ordinal structure within a data vector, the problem of ties appears permanently. So far, model classes were used which do not allow for ties; randomization has been another attempt to overcome this problem. Often, time periods with constant values even have been counted as times of monotone increase. However, ties can contain valuable information which is disregarded by all of these approaches. To overcome this, a new approach is proposed: it explicitly allows for ties and, hence, considers more patterns than before. Ties are no longer seen as nuisance, but the information they carry is taken into account explicitly. Limit theorems in the new framework are provided, both, for a single time series and for the dependence between two time series. The methods are applied to hydrological data sets. In hydrology, it is common to distinguish five flood classes (plus ‘absence of flood’). Considering data vectors of these classes at a certain gauge in a river basin, one will usually encounter several ties. Co-monotonic behavior between the data sets of two gauges (increasing, constant, decreasing) can be detected by the method as well as spatial patterns. Thus, it helps to analyze the strength of dependence between different gauges in an intuitive way. This knowledge can be used to assess risk and to plan future construction projects.

Keywords: Ordinal data analysis; Discrete time series; Limit theorems; Flood events (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167947322000524
Full text for ScienceDirect subscribers only.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:171:y:2022:i:c:s0167947322000524

DOI: 10.1016/j.csda.2022.107472

Access Statistics for this article

Computational Statistics & Data Analysis is currently edited by S.P. Azen

More articles in Computational Statistics & Data Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().