RUSSIAN JOURNAL OF EARTH SCIENCES VOL. 11, RE4001, doi:10.2205/2009ES000436, 2010

Smoothing of time series by the methods of Discrete Mathematical Analysis

Geophysical Center RAS, Moscow, Russia

Abstract

Discrete Mathematical Analysis is a new approach to discrete data, based on modeling of discrete analogues of such fundamental notions as limit, continuity, connectedness, trend by using artificial intelligence and fuzzy logic. It is the series of algorithms, aimed at solving such fundamental tasks of data analysis as clusterization, tracing, smoothing and forecasting of time series, morphological analysis, search of trends etc. All algorithms of DMA have universal character and are based on a finite limit. This article is devoted to solving the problem of smoothing of time series within the bounds of DMA. As a result, so-called gravitational smoothing was got. This smoothing is based on the methods of artificial intelligence and fuzzy logic. It was also compared with wavelet-smoothing.

Received 25 December 2009; accepted 12 March 2010; published 19 March 2010.

Keywords: Discrete Mathematical Analysis, gravitational smoothing, the misalignment of smoothness

Citation: Agayan S. M., Sh. R. Bogoutdinov, A. D. Gvishiani, and A. I. Kagan (2010), Smoothing of time series by the methods of Discrete Mathematical Analysis, Russ. J. Earth Sci., 11, RE4001, doi:10.2205/2009ES000436.