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

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 e...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 39; no. 3; pp. 309 - 320
Main Author Artemov, A. V.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.04.2018
Springer Nature B.V
Subjects
Algebra
Analysis
Digital signal processors
Flow control
Geometry
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Numerical analysis
Numerical methods
Polynomials
Probability Theory and Stochastic Processes
Smooth trend
fractional Brownian motion
long-range dependence
local polynomial estimate
signal extraction
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Summary: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.
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080218030101