Research On The Modeling Methods For Nonlinear Cointegration And Nonlinear Volatility Co-persistence

This dissertation mainly studies nonlinear relationship in econometric system offinancial market and financial theory based on nonlinear econometric characters,weestablish nonlinear time series model and nonlinear financial volatility model usedavoiding risk。This dissertation studies nonlinear cointegrated relationship andnonlinear error correction model;establishing CAPM with Markov switching model;modeling nonlinear co-persistence on the portfolio investment;researching internalrelationship between cointegration and co-persistence;setting up co-persistence of themultivariate GARCH model and applying these models in China Stocks. The mainwork and innovations of the dissertation include:This dissertation presents out using wavelet neural network studying nonlinearerror correction model aiming at linear cointegrated theory limitation and gives outmodeling nonlinear error correction model methods,perfects nonlinear cointegratedtheory;This dissertation give full narration about limitation of classical CAPM aboutmarket changes. A CAPM with Markov switching is established and the iterativecalculation maximum likelihood function is given out. At the same time we putforward taboo search genetic algorithm to optimize likelihood function. We comparewith classical CAPM to show us the parameter of maximum likelihood estimator ofCAPM with Markov switching has much better forecast effect;This dissertationdiscuss volatility persistence meaning and analyze the persistence of individual stockin Shanghai Stock Market, and persistence is eliminated by portfolio investment ofstocks to in order to avoid risk according to co-persistence. At results the persistenceof linear combination increases not drops by analyzing the example in the ShanghaiStock Market. In further, this paper considers nonlinear nature of financial market,puts forward the nonlinear co-persistence of investment combination, and extends thenotion of co-persistence and gives out modeling method. The Nonlinearco-persistence riches the dynamic portfolio investment theory;This dissertation firstlyintroduces the signification of persistence and co-persistence. We proves internalrelationship for two given co-persistence in documents,further establishes therelationship between cointegration and co-persistence, gives the condition of thevector GARCH process about co-persistence, and combines cointegration andco-persistence based on the matrix and gives estimation and test means;Thisdissertation extends the multivariate GARCH co-persistence and pretends themultivariate GARCH nonlinear co-persistence based on the nonlinear equilibriumrelationship in the components of multivariate volatility series. We make use of thewavelet neural network to approach the nonlinear co-persistence function. Theexperiments find multivariate volatility persistence can not be eliminated by linearportfolio investment, we testify there is not linear co-persistence relationship, butnonlinear co-persistence relationship. We check out the nonlinear character ofeconometric system.