The Study Of Stock Price Prediction Based On Wavelet-Particle Filter Algorithm

The paper is mainly focusing on establishing a price volatility model of the stock and using the normal particle filter algorithm and the particle filter algorithm which uses the way of wavelet threshold denoising in the prediction of stock prices.Firstly, Particle filter is a kind of approximately solutions of Bayes estimate based on sample theory. It is compounded by Monte Carlo Methods and Bayes Theory. The based manner is trying to find out a series of random samples from the state space and to approximate the posterior probability p ( x0 :n | y1 :n). The mean of samples takes the place of [ ]E g ( x0 :n ) |y1 :n, and the minimum variance estimate is obtained. The key of this method is finding the random samples according to p ( x0 :n | y1 :n). These samples are called particles vividly. As far as the meanings, Particle Filter Method is one of approximate Bayes estimate methods using adaptive method of lattice. The technology is adapted to any non-linear and non-Gauss systems that can be indicated by dynamic space model and traditional Kalman filter. The precision is close to the best.The main steps of particle filter are system initialization, sampling from the important particles, threshold decision, and resample. The system initialization aims to start the computation by setting an initialization. As far as the samples from important ones, the prior probability function is often used as the important density function to get the needed ones. And then the weights are got. For improving the algorithm efficiency and the sample representation, the samples with bigger weight is reserved. There are many improved particle filter algorithms, including: Auxiliary particle filter, regularization particle filter and EKF particle filter.The idea of Auxiliary particle filter uses a variableμk (which is drawn from p ( X k X ki)), and changes the weights two times to make the weights stablely and makes RMS error smaller, the particles are more close to reality value. The regularization particle filter resamples from the samples continuously, and gets the posterior probability from them. This way conquers the degeneration of sample. EKF particle filter makes the model be lined to improve the performance of the particle filter, using the EKF to have the posterior probability. The simulations indicate that the particle filter and improved particle filter have a superior performance in dealing with nonlinear and non-Gaussian noise problems.Secondly, people never stop the study of the the price of the stock since the stock market begins. There are many models to describe the price of stock, such as the random walk model , geometric Brownian motion model, and so on.Different ways to solve different problems.The paper treat the price of the stock as a mobile object, the price as the displacement, the changes as the speed, and the volatility of the price as a mobile model.This model adds a factor (SoA) to delegate the investors'confidence in stock about the space of advance, the higher the stock price is, the smaller space is, and the smaller the investors'confidence is. Using the EKF to predict the price of stock makes the investors grasp the laws of variety of the price better.Thirdly, the current improved particle filter focuses on improving the important density function, and not on the particles and their relevent weights. Therefore, the paper uses the wavelet threshold denoising to improve the particle filter-transforming the initial particles using wavelet and setting a threshold to the weights. Using the ways of wavelet threshold denoising can reduce the variance of the weights and rise the accuracy of the forecasting. The simulations show that the particle filter get a better accuracy by using the way of wavelet threshold denoising.Finally, the particle filter and the particle filter by using wavelet threshold denoising apply to predict the stock price. The model uses the non-linear one which was described in the fourth paragraph. The results of simulation show that the particle filter and wavelet - particle filter are better than the EKF for predicting the stock price.There is some referenced value for investors by using the prediction price.Above all, the paper gives some simulations on the four following aspects:1. Compare the predictable accuracy of KF, EKF, PF, APF, RPF EKFPF by using a nonlinear problem.2. Deal with the particle weights by using wavelet threshold denoising to show the higher accuracy of the wavelet-filter. Change the value of the threshold to discuss the effect of the threshold.3. Establish a stock price volatility model, and predict the price by using EKF.4. Predict the stock price by using the particle filter and the improved particle filter, the wavelet-particle filter and other improved wavelet-particle filter. Discuss the influence on investors'decisions.