阶数未知的ARMA模型Bootstrap预测区间构造
发布时间：2018-07-31 05:17
【摘要】：在进行建模处理预测问题时,会遇到很多模型细节未知的情形。本文主要讨论在ARMA模型假设下,当模型阶数未知时,预测区间的构造算法。关于ARMA模型阶数的选择已经有很多成熟的工作,并且在回归和AR(p)模型下预测区间的构建,也已有相关成熟的Bootstrap算法。本文首先介绍了阶数选择最常用的AIC准则以及相关的Bootstrap算法。然后,本文给出在ARM[A模型下,一致的预测区间Bootstrap算法,并且证明了该算法可同时捕捉到模型估计误差和随机误差。对于阶数未知的ARMA模型,通常做法是先确定阶数p,q,再对ARMA(p,q)模型构建预测区间,本文最后将提出一种基于阶数p,q条件分布的预测区间Bootstrap算法,较之前的做法具有更好的覆盖率和鲁棒性,并证明了相关的渐近性质。在数据模拟部分,通过随机生成4种ARMA模型的数据,将本文提出的基于条件分布+预测根(predictive roots)的Bootstrap算法与其他三种算法进行比较。从实验结果看到,本文提出的基于条件分布+预测根(predictive roots)的Bootstrap算法较其他算法明显提高了预测区间关于真实数值的覆盖率,且在数据小、p,q无法准确估计时拥有更好的鲁棒性。
[Abstract]:When modeling is used to deal with prediction problems, there are many cases in which the details of the model are unknown. This paper mainly discusses the algorithm of constructing prediction interval under the assumption of ARMA model when the order of the model is unknown. There has been a lot of mature work on how to select the order of ARMA model, and there are some mature Bootstrap algorithms in regression and AR (p) model. This paper first introduces the most commonly used order selection AIC criterion and related Bootstrap algorithm. Then, in this paper, we give a consistent prediction interval Bootstrap algorithm under ARM [A] model, and prove that the algorithm can capture both model estimation errors and random errors. For the ARMA model with unknown order, the usual method is to determine the order pQ first, then to construct the prediction interval for ARMA (PQ) model. In the end, this paper proposes a prediction interval Bootstrap algorithm based on the distribution of order pnq condition. It has better coverage and robustness than the previous approach, and proves the asymptotic properties. In the part of data simulation, the Bootstrap algorithm based on conditional distribution prediction root (predictive roots) is compared with the other three algorithms by randomly generating the data of four kinds of ARMA models. The experimental results show that the proposed Bootstrap algorithm based on conditional distribution predictive root (predictive roots) improves the coverage of the real value of the prediction interval obviously compared with other algorithms, and has better robustness when the data can not be accurately estimated.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224
，
本文编号：2154533
[Abstract]:When modeling is used to deal with prediction problems, there are many cases in which the details of the model are unknown. This paper mainly discusses the algorithm of constructing prediction interval under the assumption of ARMA model when the order of the model is unknown. There has been a lot of mature work on how to select the order of ARMA model, and there are some mature Bootstrap algorithms in regression and AR (p) model. This paper first introduces the most commonly used order selection AIC criterion and related Bootstrap algorithm. Then, in this paper, we give a consistent prediction interval Bootstrap algorithm under ARM [A] model, and prove that the algorithm can capture both model estimation errors and random errors. For the ARMA model with unknown order, the usual method is to determine the order pQ first, then to construct the prediction interval for ARMA (PQ) model. In the end, this paper proposes a prediction interval Bootstrap algorithm based on the distribution of order pnq condition. It has better coverage and robustness than the previous approach, and proves the asymptotic properties. In the part of data simulation, the Bootstrap algorithm based on conditional distribution prediction root (predictive roots) is compared with the other three algorithms by randomly generating the data of four kinds of ARMA models. The experimental results show that the proposed Bootstrap algorithm based on conditional distribution predictive root (predictive roots) improves the coverage of the real value of the prediction interval obviously compared with other algorithms, and has better robustness when the data can not be accurately estimated.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224
，
本文编号：2154533
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