金融時系列の分散構造変化問題

本文讨论了用连续时间过程逼近离散时间过程的问题。关键的一步是在Ito公式中引入新的项，并且它的一些结果可以在“On the discrete Ito formula and one factor interest rate model”（1996）Ruee Working paper #96-64 Faculty of Economics Hitotsubashi University，国町东京，日本中找到。这一结果使人们有可能修正现有的利率期限结构模型，如Vasicek（1977）和Heath，Jarrow和Morton（1992），使之更符合实际。我们还在一桥大学研究丛书经济学第37卷第87 -125页的“关于利率期限结构的一些模型”（1966年）和成城大学经济研究所年度公报的“关于利率期限结构的一些模型II”（1966年）中总结了这些模型。Vol.9103 - 129.关于寻找正态随机游动的方差变点的问题，我们发现这个问题与检验正态方差的Bays过程的检验过程的布朗运动逼近有很深的关系。(This这是沃尔夫教授向我们指出的）。我们现在考虑这个问题的序贯测试，我们现在得到有关的结果，通过逆向归纳法。

We have considered the problem of approximating the discrete time processes by the continuous time processes. The key step is to introduce the new term in the Ito formula and the some of its results are found in "On the discrete Ito formula and one factor interest rate model" (1996) Ruee Working paper #96-64 Faculty of Economics Hitotsubashi University, Kunitachi Tokyo, Japan. The results make it possible to modify the existing models on the term structure of interests rates, such as Vasicek (1977), and Heath, Jarrow and Morton (1992), discritize in more realistic fashon. We also summarized these models in the papers "On some model for the term structure of interest rates" (1966) Hitotsubashi University Research Series, Economics Vol.37,87-125, and "On some model for the term structure of interest rates II" (1966) The Annual Bulleti of the Institute for Economic Studies, Seijo University, Vol.9 103-129.As to the problems of finding the change point of the variance of the normal random walks, we found the problem is deeply related with the Brownian motion approximation for the test process of Bays procedure which tests the normal variances. (This is pointed out to us by Prof.Chernoff). We are now considering the problem in terms of the sequential test and we are now obtaining the relevant results via the methods of backward induction.