Lobachevskii Journal of Mathematics

, Volume 39, Issue 3, pp 309–320 | Cite as

Effective Signal Extraction Via Local Polynomial Approximation Under Long-Range Dependency Conditions

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Abstract

We study the signal extraction problemwhere a smooth signal is to be estimated against a long-range dependent noise. We consider an approach employing local estimates and derive a theoretically optimal (maximum likelihood) filter for a polynomial signal. On its basis, we propose a practical signal extraction algorithm and adapt it to the extraction of quasi-seasonal signals. We further study the performance of the proposed signal extraction scheme in comparison with conventional methods using the numerical analysis and real-world datasets.

Keywords

Smooth trend signal extraction long-range dependence local polynomial estimate fractional Brownian motion 

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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityComplex Systems Modeling LaboratoryMoscowRussia
  2. 2.Yandex Data FactoryMoscowRussia

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