An Asymptotic Distribution Of Stock Price-Volume And Its Chang-point Detecting By Statistical Process Control

This dissertation is composed of two parts.In the first part, we investigate the relationship between the stock price and tradingvolume of stock market . There is a logion in the stock market that"It takes volumeto price move", it show that there is certainly relationship between the stock price andtrading volume. There is an extensive research into the theoretical and empirical aspectsof the stock price and trading volume relationship. Theoretical models, such as the"MDH"(mixture of distribution hypothesis) model,"SIF"(the sequential information?ow) model and framework in Noisy rational expectation equilibrium bivariate model, andso on, suggest that volume and price are jointly determined. Relying on the motivationof these models, most of the empirical literatures test and consistently find evidence for apositive contemporaneous correlation between volume and the price variability. Most ofthese models use indirect variable to explain the price-volume relationship, and therefore,the original data are fully changed in these models. It is di?cult to explain how thevolume e?ect this Statistical characteristic.In the second chapter, we propose a general non-linear statistical model, by the factthat a stock's price can be e?ected not only by itself historical volumes and prices, butalso by the other stocks'volumes and prices. Then, we study the asymptotic distributionof a sequence of the return by analyzing the relationship between the return, relative rateof trading volume and its residues.In the chapter 3, we use the newly method of time series analysis to test the shanghai'sstock index by the hypothesis tests based on stationarity, heteroskedasticity ,long memory,and so on. For the model put forwards in the chapter two, we make empirical analysis,and obtain some forecast results of shock price better than the guess result considering oftrading volume.The chapter 4 and chapter 5 are the other part. We study Mainly using Statisticalprocess control (SPC) theory to detecting several known or unknown mean shifts.In the chapter 4, we study a multi-chart basically consists of multiple control chartswith di?erent reference valuesδ, and prove the ARL of multi-chart is less than the averageARLs of its constituent charts, and prove the asymptotic optimality of the CUSUM Multi-chart.For the case of known mean shifts, we prove CUSUM multi-chart can fast attain itsoptimality lower limit. For the case of unknown mean shifts, we find the expression of anoptimal design of the CUSUM multi-chart, and prove the CUSUM multi-chart has betterperformance than that of any single constituent CUSUM chart in detecting an unknownmean shift.Further, By Monte Carlo simulating, make sure the CUSUM multi-chart with meritof the fast detecting a range of mean shifts, and design simply and ?exible, decreasecomputational complexity, and the CUSUM multi-chart is superior (rapid and robust)on the whole to the CUSUM, EWMA, EWMA multi-chart, and GLR chart in detectingvarious mean shifts.In the chapter 5, by CUSUM chart, we detect the mean shifts of series of shanghai'sstock return in several stages, give out a design of CUSUM chart based on considering of trading volume. BY CUSUM chart exceeding upper control limit or lower control limit,combining contemporaneous the rate of trading volume, we give a rule of judgement whenthe stock will buy or sale. we compare the value of detecting mean shifts with the returnof stock at the next time, and think that our model for forecasting is relatively satisfied.