| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| 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
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