Test and Estimation for the Structual Change in Econometric Model
Project/Area Number  01530013 
Research Category 
GrantinAid for General Scientific Research (C)

Allocation Type  Singleyear Grants 
Research Field 
統計学

Research Institution  Hitotsubashi University 
Principal Investigator 
TAKAHASHI Hajime Hitotsubashi Univ., Economics Dept., Professor, 経済学部, 教授 (70154838)

CoInvestigator(Kenkyūbuntansha) 
TAKAHASHI Hajime Hitotsubashi Univ., Economics Dept., Professor (70154838)

Project Period (FY) 
1989 – 1990

Project Status 
Completed(Fiscal Year 1990)

Budget Amount *help 
¥1,700,000 (Direct Cost : ¥1,700,000)
Fiscal Year 1990 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1989 : ¥900,000 (Direct Cost : ¥900,000)

Keywords  Structual change / Sequential analysis / Renewal theory / Cusum test / RENEWAL THEORY 
Research Abstract 
We obtained the asymptotic expansions of the expected values of the truncated stopping time and the sample mean of the randomly stopped sequence of independent normally distributed random variables. The results may be applied to obtain the statistical characteristics of the Cusum test for detecting the mean changes, such as error probabilities and the expected sample sizes. The results may be used to estimate the time at which the change occurs after having rejected the null hypothesis of no mean changes. We also applied the Cusum test for the detection of the mean change to the Gammamormal mixture model which is suitable for the data with heavier tail than that of the normal distribution. And recent empirical studies of the Financial Time Series show that the underlying distribution tends to have bigger kurtosis. We also applied the method to obtain the similar sequential procedure for detecting the variance change, for the variance may be more important in practice. We used Brownian motion approximation to obtain the probabilities as a first step. We are now working to get the more accurate results by using the (nonlinear) renewal theory with which we will evaluate the asymptotic distribution of the excess over the boundaries. We believe that we have obtained somehow satisfactory results for the detection of the mean change of the sequence of the independent random variables. But the case for the time series data is just started and have not got any satisfactoryresults yet. Although some results concerning the detection of the change of variance was obtained, we are still long way up to the final goal.

Report
(3results)
Research Output
(11results)