Improvement in global forecast for chaotic time series

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• 作者：P.R.L. Alves ; ^{pauloricardo@uerj.br" class="auth_mail" title="E-mail the corresponding author} ; L.G.S. Duarte ^{lgsduarte@gmail.com.br" class="auth_mail" title="E-mail the corresponding author} ; L.A.C.P. da Mota ^{lacpdamota@uerj.br" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Time series analysis ; Global fitting ; Predictability ; Chaos ; Symbolic computation
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：October 2016
• 年：2016
• 卷：207
• 期：Complete
• 页码：325-340
• 全文大小：668 K

文摘

In the Polynomial Global Approach to Time Series Analysis, the most costly (computationally speaking) step is the finding of the fitting polynomial. Here we present two routines that improve the forecasting. In the first, an algorithm that greatly improves this situation is introduced and implemented. The heart of this procedure is implemented on the specific routine which performs a mapping with great efficiency. In comparison with the similar procedure of the TimeS package developed by Carli et al. (2014), an enormous gain in efficiency and an increasing in accuracy are obtained. Another development in this work is the establishment of a level of confidence in global prediction with a statistical test for evaluating if the minimization performed is suitable or not. The other program presented in this article applies the Shapiro–Wilk test for checking the normality of the distribution of errors and calculates the expected deviation. The development is employed in observed and simulated time series to illustrate the performance obtained.

Program summary

Program title: LinMapTS

Catalogue identifier: AFAJ_v1_0

Program summary URL:class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/summaries/AFAJ_v1_0.html">http://cpc.cs.qub.ac.uk/summaries/AFAJ_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: Standard CPC licence, class="interref" data-locatorType="url" data-locatorKey="http://cpc.cs.qub.ac.uk/licence/licence.html">http://cpc.cs.qub.ac.uk/licence/licence.html

No. of lines in distributed program, including test data, etc.: 9850

No. of bytes in distributed program, including test data, etc.: 223921

Distribution format: tar.gz

Programming language: Maple 16.

Computer: Any capable of running Maple.

Operating system: Any capable of running Maple. Tested on Windows ME, Windows XP, Windows 7.

RAM: 128 MB bytes

Classification: 4.3, 4.9, 5.

Nature of problem:

Time series analysis and improving forecast capability.

Solution method:

The basis of the solution method is the result published in [1].

Restrictions:

Global variables X [i] are used in the generated map; If more than 2000 vectors are employed in the global mapping the normality test is not applicable.

Unusual features:

When many polynomial coefficients are calculated (e.g., 55) their values can be different in distinct computers. These discrepancies do not affect significantly the accuracy in forecasting.

Running time:

A few seconds are required for the usual applications.

References:

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class="label">[1]

H. Carli, L. Duarte, L. da Mota, A maple package for improved global mapping forecast, Comp. Phts. Comm. 185(2014)1115