Topological diagnostics of the cyclic component of the time series associated with helium


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Abstract

Detection of the deterministic component from noised time series is a common procedure in the solar–terrestrial coupling problem when climate is modeled, solar activity is analyzed, or a signal associated with helium is extracted. Such series are mostly generated by the superposition of different processes for which the concept of a noise component cannot be determined formally. A method based on the combination of time-series topological embedding in Euclidean space and the identification of a persistent cycle by homology theory methods is proposed. The method application is demonstrated based on actual data.

About the authors

I. S. Knyazeva

Main Astronomical (Pulkovo) Observatory; St. Petersburg State University

Author for correspondence.
Email: iknyazeva@gmail.com
Russian Federation, St. Petersburg, 196140; St. Petersburg

Yu. A. Nagovitsyn

Main Astronomical (Pulkovo) Observatory; St. Petersburg State University of Aerospace Instrumentation

Email: iknyazeva@gmail.com
Russian Federation, St. Petersburg, 196140; St. Petersburg, 190000

F. A. Urt’ev

Main Astronomical (Pulkovo) Observatory

Email: iknyazeva@gmail.com
Russian Federation, St. Petersburg, 196140

N. G. Makarenko

Main Astronomical (Pulkovo) Observatory

Email: iknyazeva@gmail.com
Russian Federation, St. Petersburg, 196140

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