Stochastic Interacting Financial Modelling, Statistical Analysis And Prediction

Financial market is a complex system, its price variations usually exhibit many interesting statistical properties that are highly concerned about. Modelling and statis-tical analysis of financial fluctuation behaviors is one of the most important research topics in recent years. Especially with the rapid development of "Econophysics", more and more micro price models are being proposed. In this thesis, we mainly apply the underlying mechanisms of several stochastic statistical physics systems (voter system, oriented percolation system and continuum percolation system) to describe the inter-action behaviors among the investors in the financial markets, and establish the price models. Then we explore and study the statistical properties that are revealed in the simulated data of the proposed models. Through the comparison analysis with the real market data, we illustrate that the proposed price model is reasonable and effective. Be-sides we improve the neural network’s forecasting algorithm and discuss its prediction of financial price time series. The main work in this thesis is as follows:In Chapter 1, we give a brief introduction of this paper’s backgrounds, some im-portant basic theories and the main research results.In Chapter 2, we introduce the process of applying the biased voter interacting par-ticle system to construct the financial price fluctuation model. Voter interacting system is one of the most important statistical physics systems, the interaction process of its particles are used to depict the interactions of the investment attitudes or the informa-tion among the investors. To illustrate that the constructed price model can reflect the statistical characteristics of the financial market, we perform a series of important and typical statistical analysis.In Chapter 3, we aim to apply the two-dimensional oriented percolation system to establish the financial price model, in which the percolation cluster is assumed to be the investors holding the same investment opinions. Then compared with the Hang Seng Index, we discuss the complex chaos characteristics of simulation data under different percolation probabilities.In Chapter 4, we aim to apply the two-dimensional continuum percolation system to the modelling of financial price fluctuations. Then the multifractal properties hidden in the simulation returns with various parameter sets are discussed. Further, the recur-rence plot and recurrence quantification analysis techniques are applied to investigate the complex determinism dynamics of the simulated returns from the price model and Shanghai Composite Index, as well as in their different intrinsic mode functions (IMFs) decomposed from the empirical mode decomposition method. Finally, the statistical test and MF-DCCA method are respectively utilized to study the cross-correlations of two simulated returns and the multifractality on the this relationship.In Chapter 5, we for the first time apply the composite multiscale entropy (CMSE) technique to the financial market, mainly testing its effectiveness in the entropy’s esti-mation of short-term financial time series. That is, compared with the traditional MSE method, the CMSE technique can reduce the errors or variations in estimating the sam-ple entropy. We adopt two Chinese stock indexes to perform the empirical testing. Then we adopt the CMSE’method to investigate the complexity behaviors of the returns and their various volatility series of financial stock indexes from different world financial markets.In Chapter 6, we introduce a new concept of daily return volatility duration, which is defined as the shortest passage time when the future volatility intensity is above or below the current volatility intensity (without predefining a threshold). The statistical properties of the daily return volatility durations for seven representative stock indices from the world financial markets are investigated. Some useful and interesting empirical results of these volatility duration series about the probability distributions, memory effects and multifractal properties are obtained.In Chapter 7, we introduce an improved RBF neural network. That is, a random time-data effective function composed of a drift function and a random Brownian func-tion is introduced into the gradient descent optimization algorithm in training the neural network model. By empirical prediction of the financial time series, we confirm that the proposed RBF neural network model can indeed enhance the forecasting precision.