Selection of uncertain differential equations using cross validation

Z. Liu and Y. Yang

Chaos, Solitons & Fractals, 2021, vol. 148, issue C

Abstract: Uncertain differential equations have been widely applied to modelling dynamic phenomena with noises. Facing with the same dynamic phenomenon, different scholars may adopt different uncertain differential equations. Naturally, there is a crucial question about which of these equations is most suitable to describe the given dynamic phenomenon. A desired uncertain differential equation should have a good prediction ability, that is, it performs well in a new dataset. As a model selection technique, cross validation assesses the model’s ability to predict new data in order to avoid overfitting. This paper applies k fold cross validation to the selection of uncertain differential equations. Observations in training sets and testing sets are used to calculate generalized moment estimations of unknown parameters and testing errors for uncertain differential equations, respectively. Then the uncertain differential equation with the smallest total testing error is selected. A numerical example and a real data example using closing prices of Industrial and Commercial Bank of China (ICBC) stock illustrate our methods in detail.

Keywords: Uncertain differential equation; Generalized moment estimation; Cross validation; Uncertainty theory (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077921004033
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:148:y:2021:i:c:s0960077921004033

DOI: 10.1016/j.chaos.2021.111049

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. ().