Research On The Problem Of Financial Time Series Data Base On Theory Of Multifractal And Self-organized Criticality

We are constantly using science of complex to research on the complex phenomenon and complex systems in order to dig out the general laws of the nature. Science of complex are consist of many jump up new knowledge such as Infomation Theory,Cybernetics,Genetics,Chaos,Fractal and Self-organized Criticality etc。These theories and concepts mainly emphasize different sides of the complex theory reflect principal guidance and research method in recent science of complex study.By using the Theory of SOC,Multifractal analysis and Memory theory,we study several complex systems,and gain some irradiative resultWe combine the theory of Generalized infomational dimension and multifractal in order to analyse fluctuante singularity,put forward two new rick measurementsΔα,Δf,find out their underlying fluctuante law and financial significance empirically, and test its availability.The new risk measurements which are not base on the hypothesis of EMH and this is to say there is no limit on the return distributing,so this risk measurement can fetch up the deficiency of the tradional risk measurements.We integrate fractal,chaos and wavelet theory to forecast the index of stock market on multi steps.After comparing with other methods,we find out methond conbining fractal and wavelet is nice way,has more precision than chaos forcecast method and better adaption and nicety.We study SOC in economic system and build "sand-pile model" in the stock market,deduce that if return density fuction satisfy scale property p_r(r)∝r^-Ï„,and P_|r|(r),p_rⁿ|(r),1-P{|x|＞r} all fit the scale property and scale value isÏ„,(1-n-Ï„)/ n,(1 -Ï„),this phenomenon means fluctuante statics are interassociate.After caculating soc characteristic and Hurst value of 1A0001 when its index below 1000 since 1999,we find out the relationship of index changing and characteristics has very realisic meaning in preventing large mount of price fluctuante.