SEQUENTIAL ANALYSIS FOR FINANCIAL TIME SERIES
Project/Area Number  03630011 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
Economic statistics

Research Institution  HITOTSUBASHI UNIVERSITY 
Principal Investigator 
TAKAHASHI Hajime HITOTSUBASHI UNIVERSITY ECONOMICS DEPARTMENT PROFESSOR, 経済学部, 教授 (70154838)

Project Fiscal Year 
1991 – 1992

Project Status 
Completed(Fiscal Year 1992)

Budget Amount *help 
¥1,500,000 (Direct Cost : ¥1,500,000)
Fiscal Year 1992 : ¥600,000 (Direct Cost : ¥600,000)
Fiscal Year 1991 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  FINANCIAL TIME SERIES / SEQUENTIAL ANALYSIS / 金融時系列 / 逐次分析 / 遂次分析 / 時系列 / 金融デタ / 構造変化 
Research Abstract 
We considered two problems in this project. The first one is a technical one arising from the change point problem in the normal random walk. Let x_1, x_2,... be a sequence of independent and normally distributed random variables with mean theta and variance 1. We let s_n = x_1+...+x_n for n * 1. A sequential test for the hypothesis H_0:theta =0 against the alternative H_1 : theta >0 consists of rejecting H_0 in favor of H_1 if and only if t * m, where the stopping time t = inf{n* 1; s_n* (2a(n+c))^<1/2>} is defined for constants a>0, c * 0, and m is a positive integer. Using the nonlinear renewal theory Siegmund(1977,1978,Biometrika) calculate the limits of the expected value of t(m) = min{t,m} at the various theta values as m=m(a) ** , a ** in such a way that 2a/m is fixed (=theta_0). We calculated asymptotic expantions for E_*{t(m)} for all theta =theta_0(1+u/(2a)^<1/2>). We let a goes to infinity throught the integral multiple of theta_0^2/2, so that m=2a/theta_0^2 are integer. For each theta , we let N = [2a/theta^2] and rho = (2a/theta^2)  N. Our main results is given in theorem 2 of Takahashi(1993), where the constant rho playes an important role. Another problem we considered in this project is to analyze daily Nikkei 225 for 3 years from 1987 to 1989. We extract several factors from the randomly selected 100 stock's time series data, and then fit AR model to these factors. Finally we adopt Kalman filter to estimate the parameters in the model. The results are found in Takubo, Tanaka and Takahashi(1993).

Report
(4results)
Research Output
(4results)