ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Bobrov K. E., Iskoldsky A. M. Stability оf numerical estimations of time series characteristics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 1, pp. 127-136. DOI: 10.18500/0869-6632-2002-10-1-127-136

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Language: 
Russian
Heading: 
Methodical Papers on Nonlinear Dynamics
Article type: 
Article
UDC: 
681.3, 519.67
DOI: 
10.18500/0869-6632-2002-10-1-127-136

Stability оf numerical estimations of time series characteristics

Autors: 
Bobrov Konstantin Evgenevich, The Institute of Electrophysics of the UB RAS
Iskoldsky Aleksandr Mihailovich, The Institute of Electrophysics of the UB RAS
Abstract: 

The numerical methods of a data analysis (finite ordered sequences of natural binary codes), corresponding to fragments оf trajectories, obtained by the numerical solving of а finite number of nonlinear ordinary differential equations are discussed. These equations represent the determined dissipative chaotic dynamic systems.

Measuring properties of such sequences are characterized by the estimation which assumes the code, obtained as a result of processing of source sequence of data by given algorithm, realized on the computer and not supposing the participation of the expert. The concept оf stability оf the estimation is formalized. The stability of obtained estimations in relation to numerically simulated small variations оf registration scheme parameters and to parameters of the algorithm of processing is investigated. Examples of data sequences with typical parameters (digit capacity, time step, length of sequence) for many real experiments are considered.

It is shown that estimation, obtained by the algorithm based on the analysis оf properties essentially depended оn behavior оf trajectory in every point, is unstable. At the same time, the estimation, obtained by the algorithm based on the analysis of properties, essentially depended оn some «average» for different points behavior оf trajectory, is stable.

Key words: 
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Received: 
04.07.2001
Accepted: 
17.05.2002
Available online: 
13.12.2023
Published: 
31.07.2002
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