Study On Memory, Persistence And Fractal Properties In Financial Market Volatility

The dissertation studies on the properties and law of financial market time seriesby analyzing the properties of memory ,persistence and fraction.Firstly ,former research results about memory and persistence properties of timeseries are presented. The varieties definitions about memory and persistenceproperties are given in Chapter 2.Based on these ,the dissertation discusses therelations about memory and persistence properties of time series.In Chapter 3, some common discrete and continuous time series models arediscussed .The memory of continuous time series model FRACIMA and the discretetime series model ARFIMA are compared .The autoregressive conditional heteroscedasticity (ARCH) models and itsderivative models are introduced in the Chapter 4.The persistence of ARCH modelwas discovered in the researches of economic and financial time series ,which is acommon phenomenon in economy and finance market. Because of the similarity ofthe structure , the research methods of time series conditional mean long memoryare applied on the research of ARCH model persistence properties. Because there isno unified definition of time series persistence properties, the dissertation presentsdifferent definitions on different ARCH type models, and probes the persistence andco-persistence properties of ARCH type models and vector ARCH models.The fifth part of the dissertation studies on the stochastical volatility (SV) modelsand their memory, persistence and co-persistence properties.The fractal market theory and fractal market analysis are introduced in detail inthe sixth section of the dissertation. Fractal Market Hypothesis(FMH),FractionalBrownian Motion(FBM),the conditionally Exponential Dependence(CED) andFractional Market Dynamics (FMD) models are applied to analyze the structure ofthe financial market in the same section.Finally , the empirical researches of exchanges(US dollar to Euro, US dollar topound ) ,Shanghai stock market composite exponents and Shenzhen stock market arepresented in the Chapter 7.