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Nonlinear time series prediction based on a power-law noise model

Research output: Contribution to journalArticleScientificpeer-review


Original languageEnglish
Pages (from-to)1839-1852
Number of pages14
JournalInternational Journal of Modern Physics C
Issue number12
Publication statusPublished - Dec 2007
Externally publishedYes
Publication typeA1 Journal article-refereed


In this paper we investigate the influence of a power-law noise model, also called noise, on the performance of a feed-forward neural network used to predict time series. We introduce an optimization procedure that optimizes the parameters the neural networks by maximizing the likelihood function based on the power-law model. We show that our optimization procedure minimizes the mean squared leading to an optimal prediction. Further, we present numerical results applying method to time series from the logistic map and the annual number of sunspots demonstrate that a power-law noise model gives better results than a Gaussian model.


  • time series prediction, maximum likelihood, Monte Carlo method, feed-forward, neural network., SELF-ORGANIZED CRITICALITY, NEURAL-NETWORKS, OPTIMIZATION, EXPLANATION