Measuring the distance between time series

Richard Moeckel; Brad Murray

doi:10.1016/S0167-2789(96)00154-6

Measuring the distance between time series

Richard Moeckel
, Brad Murray

School of Mathematics

Research output: Contribution to journal › Article › peer-review

64 Scopus citations

Abstract

To evaluate models of dynamical systems, researchers have traditionally used quantitative measures of short term prediction errors. However, for chaotic or stochastic systems, comparison of long term, qualitative behaviors may be more relevant. Let x = (x₀. . . . , x_n) be a sequence of real numbers generated by sampling a dynamical system or stochastic process and suppose y = (y₀, . . . . y_n) is another sequence, generated by a mathematical model of the process which generated x. In this paper we consider several ways of assigning a distance d(x, y) which measures the difference in long term behavior.

Original language	English (US)
Pages (from-to)	187-194
Number of pages	8
Journal	Physica D: Nonlinear Phenomena
Volume	102
Issue number	3-4
DOIs	https://doi.org/10.1016/S0167-2789(96)00154-6
State	Published - 1997

Bibliographical note

Funding Information:
I Research supported by the NSF grants DMS 93-16078 and EAR 94-05807 and by the Graduate School and the GEO FLU1DS program at the University of Minnesota.

Funding Information:
The simplest way to measure the distance is to think of x and 3' as ordinary vectors in \[R" +l and to use one of the familiar metrics in \[R" +1 , for example, the usual Euclidean distance between x and y. This approach * Corresponding author. Research supported by the NSF grants DMS 93-16078 and DMS 92-06957.

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abstract = "To evaluate models of dynamical systems, researchers have traditionally used quantitative measures of short term prediction errors. However, for chaotic or stochastic systems, comparison of long term, qualitative behaviors may be more relevant. Let x = (x0. . . . , xn) be a sequence of real numbers generated by sampling a dynamical system or stochastic process and suppose y = (y0, . . . . yn) is another sequence, generated by a mathematical model of the process which generated x. In this paper we consider several ways of assigning a distance d(x, y) which measures the difference in long term behavior.",

author = "Richard Moeckel and Brad Murray",

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doi = "10.1016/S0167-2789(96)00154-6",

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volume = "102",

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PY - 1997

Y1 - 1997

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AB - To evaluate models of dynamical systems, researchers have traditionally used quantitative measures of short term prediction errors. However, for chaotic or stochastic systems, comparison of long term, qualitative behaviors may be more relevant. Let x = (x0. . . . , xn) be a sequence of real numbers generated by sampling a dynamical system or stochastic process and suppose y = (y0, . . . . yn) is another sequence, generated by a mathematical model of the process which generated x. In this paper we consider several ways of assigning a distance d(x, y) which measures the difference in long term behavior.

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ER -

Measuring the distance between time series

Abstract

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