The chaotic and random components in time series data
Abstract
We proposed a method for determining the ratio of deterministic and stochastic components for observed real data. We illustrated a number of numerical experiments which used simulation modelling of the logistic chaotic sequence and the values of fractional Brownian motion with different values of Hurst exponent H. In the additive mixture, the ratio of the energies of deterministic and random components are defined. The chaotic term turns out to be more aggressive for large values of Hurst exponent: the control statistics of the mixture are different from the reference values corresponding to the fractional Brownian motion. Another situation takes place for small values of H (antipersistent case). The considered examples of time series data are described by an antipersistent model.References
Kuznetsov S.P. Dinamicheskiy khaos. — M.: Fizmatlit, 2006. — 296 s.
Mishura Y. Stochastic Calculus for Fractional Brownian Motion and Related Processes. Lecture Notes in Mathematics. V. 1929 // Springer–Verlag, 2008. — 392 p.
Beran J. Statisticsfor Long-Memory Processes / Beran J. — Chapmanand Hall. — 1995. — 315 p.
Bondarenko V.V. Iteratsionnyy algoritm otsenivaniya parametrov fraktal’nogo brounovskogo dvizheniya // Problemy upravleniya i informatiki. — 2012. — № 4. — S. 28–33.
Bondarenko V.V. Аpproksimatsiya vremennogo ryada stepennoy funktsiyey fraktal’nogo brounovskogo dvizheniya // Problemy upravleniya i informatiki. — 2013. — № 3. — S. 113–116.
Nourdin I., Nualart D., Tudor C. Central and non-central limit theorems for weighted power variations of fractional Brownian motion // Ann. Institute H. Poincaré Probab Statist. — 2010 — 46, № 4. — P. 1055–1079.
Bondarenko V.V. Proverka kachestva approksimatsii vremennogo ryada fraktal’nym brounovskim dvizheniyem // Problemy upravleniya i informatiki. — 2014. — № 3. — S. 102–108.
Dannyye Nauchno-prakticheskogo tsentra АN Respubliki Belarus’. — http://biobel.bas-net.by/zoo.
University of Arisona Tree Ring Data: http://rda.ucar.edu/#!lfd?nb=y&b=topic&v=Paleoclimate.
Climate Prediction Center(USA). — http://www.cpc.ncep.noaa.gov/products/precip/Cwlink/pna/pna.shtml.
