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).

我们考虑了这个项目中的两个问题。第一个是在正常随机步行中的变更点问题引起的技术。令x_1，x_2，...为一系列单体和正态分布的随机变量，具有平均theta和差异1。我们让s_n = x_1+...+x_n for n * 1。假设H_0：theta = 0的顺序测试fits h_1：the fime fieptiative h_1： inf {n* 1; s_n *（2a（n+c））^<1/2>}定义为常数a> 0，c * 0，而m是一个正整数。使用非线性更新理论Siegmund（1977,1978，Biometrika）在各种theta值上计算t（m）= min {t，m}的期望值的限制为m = m = m（a）**，a **，以某种方式固定了2a/m的方式（= theta__0）。我们计算了所有theta = theta_0（1+u/（2a）^<1/2>）的e _*{t（m）}的渐近实验。我们让A通过Theta_0^2/2的积分倍数到Infinity，以便M = 2A/Theta_0^2是整数。对于每个theta，我们让n = [2a/theta^2]和rho =（2a/theta^2） - n。我们的主要结果是在Takahashi（1993）的定理2中给出的，不断的Rho扮演着重要的问题。在该项目中，我们考虑的其他问题是从1987年开始进行了每天的库存225，我们在1987年进行了几个库存。这些因素。最后，我们采用卡尔曼过滤器来估计模型中的参数。结果可在Takubo，Tanaka和Takahashi（1993）中找到。