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SEQUENTIAL ANALYSIS FOR FINANCIAL TIME SERIES

金融时间序列的序贯分析

基本信息

批准号：
03630011
负责人：
TAKAHASHI Hajime
金额：
$ 0.96万
依托单位：
HITOTSUBASHI UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1991
资助国家：
日本
起止时间：
1991 至 1992
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03630011/
关键词：
FINANCIAL TIME SERIES SEQUENTIAL ANALYSIS 遂次分析時系列金融デ-タ構造変化

项目摘要

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).

我们在这个项目中考虑了两个问题。第一个问题是技术问题，它源于正常随机游动中的变点问题。设x_1，x_2，.是一个独立的正态分布的随机变量序列，平均值为θ，方差为1。我们设s_n = x_1+.+ x_n对于n * 1。假设H_0：theta =0与另一个假设H_1：theta >0的序贯检验包括拒绝H_0而支持H_1当且仅当t * m，其中停时t = inf{n* 1; s_n*（2a（n+c））^<1/2>}定义为常数a>0，c * 0，m为正整数。使用非线性更新理论Siegmund（1977，1978，Biometrika）计算t（m）= min{t，m}在各种θ值下的期望值的极限，如m=m（a）**，a **，以使得2a/m固定（=theta_0）。我们计算了E_*{t（m）}对所有θ = θ_0（1+u/（2a）^<1/2>）的渐近展开式。设a是θ_0^2/2的整数倍，则m=2a/θ_0^2为整数。对于每个θ，我们设N = [2a/θ ^2]，rho =（2a/θ ^2）- N。我们的主要结果在Takahashi（1993）的定理2中给出，其中常数ρ起着重要的作用。我们在这个项目中考虑的另一个问题是分析日经225指数从1987年到1989年的三年。从随机抽取的100只股票的时间序列数据中提取多个因子，并对这些因子进行AR模型拟合。最后采用卡尔曼滤波对模型中的参数进行估计。结果见Takubo、Tanaka和Takahashi（1993）。