Generalized divergences for statistical evaluation of uncertainty in long-memory processes

Hidekazu Yoshioka and Yumi Yoshioka

Chaos, Solitons & Fractals, 2024, vol. 182, issue C

Abstract: Environmental variables such as streamflow discharge and water quality indices vary stochastically over time and often exhibit long (subexponential) memory. Their dynamics are described by stochastic differential equations that are superposed with respect to a probability measure of the reversion speeds, called the reversion measure. The reversion measure governs their statistics; however, as its accurate estimation is not always successful owing to data limitations, possible misspecifications should be assumed. In particular, bounding their statistics from below and above should be performed robustly within a unified mathematical framework, which still remains challenging. We propose bounding the statistics of long-memory processes by a pair of risk measures based on the Kaniadakis or α divergence, which are generalizations of the Kullback–Leibler divergence. We obtain a series of mathematical results for the upper- and lower-bounding divergence risk measures of the reversion measure based on these divergences in proper Orlicz spaces, along with their continuous embedding relationships. These results clarify the advantages and disadvantages of the two divergences in applications. A multifractional limit of the long-memory process under misspecification is also considered to investigate behavior of the scaling function and its correspondence with an anomalous diffusion. We also show that the recently proposed generalized Lorenz curve allows for a deeper comprehension of the bounds. Finally, we apply our mathematical framework to hourly streamflow discharge data with a record length of about 20 years.

Keywords: Kaniadakis divergence; α divergence; Generalized Lorenz curve; Long-memory process; Streamflow discharge (search for similar items in EconPapers)
Date: 2024
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/S0960077924001784
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:chsofr:v:182:y:2024:i:c:s0960077924001784

DOI: 10.1016/j.chaos.2024.114627

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().