Statistics and Its Interface最新文献_第3页

Rank-R matrix autoregressive models for modeling spatio-temporal data 用于时空数据建模的 Rank-R 矩阵自回归模型

IF 0.8 4区数学

Statistics and Its Interface Pub Date : 2024-02-01 DOI: 10.4310/23-sii812

Nan-Jung Hsu, Hsin-Cheng Huang, Ruey S. Tsay, Tzu-Chieh Kao

{"title":"Rank-R matrix autoregressive models for modeling spatio-temporal data","authors":"Nan-Jung Hsu, Hsin-Cheng Huang, Ruey S. Tsay, Tzu-Chieh Kao","doi":"10.4310/23-sii812","DOIUrl":"https://doi.org/10.4310/23-sii812","url":null,"abstract":"We develop a matrix-variate autoregressive (MAR) model to analyze spatio-temporal data organized on a regular grid in space. The model is an extension of the bilinear MAR spatial model of Hsu, Huang and Tsay $href{ https://doi.org/10.1080/10618600.2021.1938587 }{[10]}$ by increasing its flexibility and applicability in empirical applications. Specifically, we propose to model each autoregressive (AR) coefficient matrix of the MAR model by $R$ bilinear terms, thereby establishing a rank‑R model. The extension can be interpreted as decomposing the AR dynamics of the data into $R$ bilinear MAR components. We further incorporate a banded neighborhood structure for AR coefficient matrices and utilize a flexible nonstationary low-rank covariance model for the spatial innovation process, leading to a parsimonious model without sacrificing its flexibility. We estimate all parameters of the model by the maximum likelihood method and develop a computationally efficient alternating direction method of multipliers algorithm, involving only closed-form expressions in all steps. Applications to a wind-speed dataset and an employment dataset, as well as two simulation experiments, demonstrate the effectiveness of the proposed method in estimation, model selection, and prediction.","PeriodicalId":51230,"journal":{"name":"Statistics and Its Interface","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139659193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}