| 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)
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| 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 non-linear 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).
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