Statistical Sequential Analysis for Stochastic Processes and Its Application to Risk Management

本研究的目的是将Lai和Siegmund(1983)提出的自回归参数的统计序贯估计推广到单位根检验问题。本文研究了与随机过程有关的停机次数统计推断理论，并将其应用于在线风险管理。主要研究内容如下：1.平稳时间序列的在线监测问题1.经济时间序列的在线监测问题2.监控关键分支流程3.一般离散时间马尔可夫过程的监控问题在线监控破产、合并和上市

The aim of this study is to develop the statistical sequential estimation of auto-regressive parameter initiated by Lai and Siegmund(1983) to unit root testing problem. In this study, statistical inference theory via stopping times relating to stochastic process is investigated and applied to online risk management. The following topics are the focus of the study:1. Online monitoring problem of stationary 1. economic time series2. Monitoring critical branching processes3. Monitoring problem of general discrete-time Markov processes4. Online monitoring for bankruptcy, merger, and listing