有序时间序列的软裁剪自回归模型

IF 1.3 4区 数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Christian H. Weiß, Osama Swidan
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引用次数: 0

摘要

线性自回归模型是时间序列分析实践中最常用的模型之一,这也促使人们将其应用于有序时间序列。我们对有序时间序列数据建模的起点是用潜变量方法定义广义线性模型。然而,这种方法通常会导致过去观测值与当前条件累积分布函数(cdf)之间的非线性关系。为了克服这一问题,我们使用软剪辑链接获得近似线性模型结构,并提出了一类广泛而灵活的软剪辑自回归(scAR)模型。施加在模型参数上的约束使我们能够识别scAR模型族的相关特殊情况。我们研究了转移概率的计算以及CDF的近似公式。通过数值算例和仿真实验说明了我们的建议,分析了最大似然估计和模型选择的性能。该模型族成功地应用于现实世界的金融有序时间序列。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Soft-Clipping Autoregressive Models for Ordinal Time Series

Soft-Clipping Autoregressive Models for Ordinal Time Series

The linear autoregressive models are among the most popular models in the practice of time series analysis, which constitutes an incentive to adapt them to ordinal time series as well. Our starting point for modeling ordinal time series data is the latent variable approach to define a generalized linear model. This method, however, typically leads to a non-linear relationship between the past observations and the current conditional cumulative distribution function (cdf). To overcome this problem, we use the soft-clipping link to obtain an approximately linear model structure and propose a wide and flexible class of soft-clipping autoregressive (scAR) models. The constraints imposed on the model parameters allow us to identify relevant special cases of the scAR model family. We study the calculation of transition probabilities as well as approximate formulae for the CDF. Our proposals are illustrated by numerical examples and simulation experiments, where the performance of maximum likelihood estimation as well as model selection is analyzed. The novel model family is successfully applied to a real-world ordinal time series from finance.

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来源期刊
CiteScore
2.70
自引率
0.00%
发文量
67
审稿时长
>12 weeks
期刊介绍: ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.
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