The chaotic attractor analysis of DJIA based on manifold embedding and Laplacian eigenmaps
type: Item
instance of: scholarly article
title: The chaotic attractor analysis of DJIA based on manifold embedding and Laplacian eigenmaps
zbMATH Open document ID: 1400.37038
DOI: 10.1155/2016/8087178
author: Xiaohua Song
author: Dongxiao Niu
author: Yulin Zhang
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: Summary: By using the techniques of Manifold Embedding and Laplacian Eigenmaps, a novel strategy has been proposed in this paper to detect the chaos of Dow Jones Industrial Average. Firstly, the chaotic attractor of financial time series is assumed to lie on a low-dimensional manifold that is embedded into a high-dimensional Euclidean space. Then, an improved phase space reconstruction method and a nonlinear dimensionality reduction method are introduced to help reveal the structure of the chaotic attractor. Next, the empirical study on the financial time series of Dow Jones Industrial Average shows that there exists an attractor which lies on a manifold constructed by the time sequence of Moving average convergence divergence; finally, Determinism Test, Poincaré section, and translation analysis are used as test approaches to prove both whether it is a chaos and how it works.
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 62M20
Mathematics Subject Classification ID: 91B84
zbMATH DE Number: 6953612
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/8087178
OpenAlex ID: W2468609232
Wikidata QID: Q59141261
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description: scientific article; zbMATH DE number 6953612