A SIMPLIFIED PERIODICAL DETECTION METHOD FOR LONG TERM SEQUENCES BASED ON RESCALED RANGE ANALYSIS

摘要

Rescaled range (R/S) analysis is a non-parameter method for persistence detection in time series based on fractal theory, it was applied in a short series and a long record about floods and droughts of Huaihe River basin in Henan province. The short one is standardized precipitation index (SPI) series of 1957-2008, and the long one is a drought and waterlogging grade sequence of 1470-1980. The short record presents strong anti-persistenc and without significant trend for the existence. But the long record presents a significant trend of drought and with strong persistence. For quantified relation exists between Hausdorff dimension D_0 used in the R/S analysis and generalized entropy S_0, by build link between method of principle of maximum entropy (POME) and the R/S analysis, this paper got a new period detection method of extremes, it computes So of every section in a sequence and increment ΔS_0(i) of every point to its previous time, for change happen at position with large ΔS_0(i), section between two change points can take as a period with one trend, and significant of a change can be measure with the quantile. The method has been applied in the records and found that periods of the long record almost cover periods of the short records, and the long term periods composed with the short term periods. This result inferred that though long term series and short term series of extremes present different persistence, the short one can be taken as a part of the lone one, or a fractal of it. Short term events have cumulative effect to future.