High-dimensional and banded integer-valued autoregressive processes

IF 1.6 3区 数学 Q3 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
Nuo Xu, Kai Yang
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引用次数: 0

Abstract

The modeling of high-dimensional time series has always been an appealing and challenging problem. The main difficulties of modeling high-dimensional time series lie in the curse of dimensionality and complex cross dependence between adjacent components. To solve these problems for high-dimensional time series of counts, a class of high-dimensional and banded integer-valued autoregressive processes without assuming the innovation's distribution is proposed. A banded thinning structure is constructed to diminish the parameters' dimension. The componentwise conditional least squares and weighted conditional least squares methods are developed to estimate the banded autoregressive coefficient matrices. The bandwidth parameter is identified via a marginal Bayesian information criterion method. Some numerical results are provided to show the good performance of the estimators. Finally, the superiority of the proposed model is shown by an application to an air quality data set of different cities.
高维带整数值自回归过程
高维时间序列的建模一直是一个具有吸引力和挑战性的问题。高维时间序列建模的主要困难在于维度的诅咒和相邻分量之间复杂的交叉依赖。为了解决高维计数时间序列的这些问题,提出了一类不假设创新分布的高维带状整值自回归过程。采用带状减薄结构减小参数尺寸。提出了组合条件最小二乘法和加权条件最小二乘法来估计带状自回归系数矩阵。利用边际贝叶斯信息准则识别带宽参数。数值结果表明了该估计器的良好性能。最后,通过对不同城市空气质量数据集的应用,证明了该模型的优越性。
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来源期刊
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis 数学-计算机:跨学科应用
CiteScore
3.70
自引率
5.60%
发文量
167
审稿时长
60 days
期刊介绍: Computational Statistics and Data Analysis (CSDA), an Official Publication of the network Computational and Methodological Statistics (CMStatistics) and of the International Association for Statistical Computing (IASC), is an international journal dedicated to the dissemination of methodological research and applications in the areas of computational statistics and data analysis. The journal consists of four refereed sections which are divided into the following subject areas: I) Computational Statistics - Manuscripts dealing with: 1) the explicit impact of computers on statistical methodology (e.g., Bayesian computing, bioinformatics,computer graphics, computer intensive inferential methods, data exploration, data mining, expert systems, heuristics, knowledge based systems, machine learning, neural networks, numerical and optimization methods, parallel computing, statistical databases, statistical systems), and 2) the development, evaluation and validation of statistical software and algorithms. Software and algorithms can be submitted with manuscripts and will be stored together with the online article. II) Statistical Methodology for Data Analysis - Manuscripts dealing with novel and original data analytical strategies and methodologies applied in biostatistics (design and analytic methods for clinical trials, epidemiological studies, statistical genetics, or genetic/environmental interactions), chemometrics, classification, data exploration, density estimation, design of experiments, environmetrics, education, image analysis, marketing, model free data exploration, pattern recognition, psychometrics, statistical physics, image processing, robust procedures. [...] III) Special Applications - [...] IV) Annals of Statistical Data Science [...]
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