FRACTIONAL STATE SPACE ANALYSIS OF TEMPERATURE TIME SERIES

被引：19

作者：

Tenreiro Machado, J. A. ^{[1
]}

Lopes, Antonio M. ^{[2
]}

机构：

[1] Polytech Porto, Inst Engn, Dept Elect Engn, P-4249015 Oporto, Portugal

[2] Univ Porto, Fac Engn, Inst Engn Mech, P-4200465 Oporto, Portugal

来源：

FRACTIONAL CALCULUS AND APPLIED ANALYSIS | 2015年 / 18卷 / 06期

关键词：

state space portrait; fractional calculus; multidimensional scaling; clustering; time series; VISUALIZATION; CALCULUS; DYNAMICS; MODELS;

D O I：

10.1515/fca-2015-0088

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Atmospheric temperatures characterize Earth as a slow dynamics spatio-temporal system, revealing long-memory and complex behavior. Temperature time series of 54 worldwide geographic locations are considered as representative of the Earth weather dynamics. These data are then interpreted as the time evolution of a set of state space variables describing a complex system. The data are analyzed by means of multidimensional scaling (MDS), and the fractional state space portrait (fSSP). A centennial perspective covering the period from 1910 to 2012 allows MDS to identify similarities among different Earth's locations. The multivariate mutual information is proposed to determine the "optimal" order of the time derivative for the fSSP representation. The fSSP emerges as a valuable alternative for visualizing system dynamics.

引用

页码：1518 / 1536

页数：19

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