Statistical Sequential Analysis via Stochastic Calculus and It's Application

2017 Fiscal Year Final Research Report

• Project/Area Number: 15K03395
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Economic statistics
• Research Institution: Yokohama National University
• Principal Investigator: NAGAI KEIJI 横浜国立大学, 大学院国際社会科学研究院, 教授 (50311866)
• Project Period (FY): 2015-04-01 – 2018-03-31
• Keywords: 時系列解析 / 統計的逐次解析 / 停止時刻 / ｐ階自己回帰過程 / 単位根検定 / 局所漸近正規 / 汎関数中心極限定理 / 確率解析

Outline of Final Research Achievements

We consider a sequentially observed unstable AR(p) process with a unit root or a near unit root and provide a sequential testing procedure corresponding to the augmented Dickey-Fuller test in non-sequential sampling. Modifying the stopping time for AR(1) in Lai and Siegmund (1983), we introduce a stopping time based on observed Fisher information for AR(p). The sequential testing procedure has LAN(local asymptotic normality), which can be shown by the time change of the score process using its quadratic variation in Ornstein-Uhlenbeck process. The asymptotic property of the stopping time is characterized by the Bessel process, which makes possible to obtain its asymptotic moments. A testing procedure using the quantile of the asymptotic distribution of the stopping time is a

Free Research Field

数理統計学