长记忆指数变点的统计推断

发布时间：2018-03-06 16:57

本文选题：长记忆序列　切入点：结构变点　出处：《西安科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：自20世纪80年代以来,长记忆时间序列理论开始在计量经济学领域中得到快速发展,并广泛应用在经济、金融等研究领域;与此同时,变点检测问题也同样受到经济学家的高度重视。时下,越来越多的金融数据呈现长记忆特性,而且结构变点在金融时间序列中经常出现。鉴于此,研究长记忆序列指数变点检验问题显得十分重要。本文的创新点如下:首先,建立含指数变点的长记忆序列回归模型,基于ratio检验统计量检验序列的指数变点。研究发现:在原假设下,ratio检验统计量收敛到一个分数布朗桥,在备择假设下,ratio检验统计量是发散的。数据模拟结果表明:在原假设下,拒绝率随样本量的增大而增大,基本接近5%,在备择假设下,拒绝率随样本量的增大以及指数跳跃幅度的增大而增大,最高达到66.3%。此外,变点的估计依赖于不同的长记忆时间序列和样本量,更加准确地说,随着指数跳跃幅度的增大,变点的估计值会更加精确,接近真实值。通过蒙特卡罗模拟说明理论与实验模拟相吻合。其次,建立含均值变点、指数变点的长记忆序列回归模型,基于ratio检验统计量检测序列的指数变点。研究发现:在原假设下,ratio检验统计量是以021 dT-的速率发散,在备择假设下,ratio检验统计量趋于无穷。数据模拟结果表明:在原假设下,拒绝率随着均值跳跃幅度的增大而增大,随着长记忆指数的增大而减小,且均值起决定性作用,这有可能导致过高地估计指数,甚至导致研究者产生误判,在备择假设下,拒绝率随着均值跳跃幅度增大以及指数跳跃幅度的增大而增大,并趋于无穷,均值的影响相对较大。通过蒙特卡罗模拟验证理论的合理性与正当性。综上所述,对以上两种长记忆回归模型,均能利用ratio检验统计量有效检验长记忆指数变点,同样地,数值模拟也能验证理论的合理性与正当性。
[Abstract]:Since 1980s, the theory of long memory time series has been developing rapidly in the field of econometrics, and has been widely used in the fields of economics, finance and so on. Nowadays, more and more financial data show long memory characteristics, and structural change points often appear in financial time series. It is very important to study the problem of exponential change point test of long memory sequence. The innovation of this paper is as follows: firstly, the regression model of long memory sequence with exponential change point is established. Based on the exponential change point of the ratio test statistic test sequence, it is found that the ratio test statistic converges to a fractional Brownian bridge under the original hypothesis, and the ratio test statistic is divergent under the alternative hypothesis. The data simulation results show that: under the original hypothesis, the ratio test statistic is divergent. The rejection rate increases with the increase of the sample size and is close to 5. Under the alternative assumption, the rejection rate increases with the increase of the sample size and the jump amplitude of the index, and the highest value is 66.3%. The estimation of the change point depends on different long memory time series and sample size. More accurately, with the increase of the jump amplitude of the index, the estimation of the change point will be more accurate. Close to the real value. Monte Carlo simulation shows that the theory is consistent with the experimental simulation. Secondly, a long memory sequence regression model with mean and exponential change points is established. Based on the exponential change point of the ratio test statistics, it is found that the ratio test statistics diverge at the rate of 0.21 dT- under the original hypothesis, and the statistics of the ratio test tend to infinity under the alternative hypothesis. The data simulation results show that: under the original hypothesis, the ratio test statistics tend to be infinite. The rejection rate increases with the increase of the mean jump amplitude and decreases with the increase of the long memory index, and the mean value plays a decisive role, which may lead to overestimation of the index, and even lead to the misjudgment of the researcher. The rejection rate increases with the increase of the mean jump amplitude and the exponential jump amplitude, and tends to infinity. The influence of the mean value is relatively large. The validity and rationality of the theory are verified by Monte Carlo simulation. For the above two kinds of long memory regression models, the ratio test statistics can be used to test the long memory index variation points effectively. Similarly, numerical simulation can also verify the rationality and legitimacy of the theory.
【学位授予单位】：西安科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

【参考文献】