IJPAM: Volume 73, No. 3 (2011)
BEHIND THE PERIODIC TIME SERIES AND ITS
APPLICATION TO SOLAR CYCLE PREDICTION
5-3-1 Akasaka, Minato-Ku
Tokyo, 107-6322, JAPAN
Graduate School of Advanced Mathematical Sciences
1-1-1 Higashimita, Tamaku, Kawasaki, 214-8571, JAPAN
Abstract. This paper proposes a method for detecting a change in non-linear dynamics behind periodic time series. In order to develop this method, we define the smoothed pseudo determinacy function (SPDF) based on the theory of KMO-Langevin equations. Because SPDF has information about non-linear dynamics, the proposed method detects a change in non-linear dynamics in comparison to previous methods such as Time-Frequency Analysis and Wavelet Analysis. We confirmed its practicality by applying the method to monthly sunspot number. The result shows that one of the changes in non-linear dynamics at year 2004 is detected and the dynamics is changing into the same as ``Dalton Minimum" from year 1790 to 1820. From this result, we suggest that maximum of the next cycle will be as same as ``Dalton Minimum". This result supports some previous works.
Received: October 28, 2011
AMS Subject Classification: 62M10, 62M15
Key Words and Phrases: time series, non-linear, periodicity, sunspot, solar cycle prediction
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395