Mixed Garch Model And Fractal Brown Motion

Non-linear stochastic process can describe the deep connotation of non-linear systems, and provide theory and methods for dealing with the non-linear dynamic data. In recent years, the study on the non-linear stochastic process mainly concentrates on the theory and methods of the typical models. In this paper, two important non-linear stochastic process models, namely mixture generalized autoregressive conditional heteroscedastic model(the abbreviation is MGARCH) and nth-order fractional Brownian motion(the abbreviation is nth-order fBm) have been studied, some results have been obtained, the details are:1. MGARCH model was proposed firstly;2. The stationary conditions of MGARCH was proved;3. The EM parameter estimation algorithm of MGARCH was provided;4. A new variance estimation of the Hurst parameter of nth-order fBm was provided;5. That a weakly stationary process transformed by wavelet is still a weakly tationary process on the same scale was proved;6. A number of simulation examples and real data analysis have been done, the results obtained from different models were compared, all the results proved the models and methods in this paper superior and workable.