High-dimensional and banded integer-valued autoregressive processes

Nuo Xu and Kai Yang

Computational Statistics & Data Analysis, 2025, vol. 212, issue C

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.

Keywords: High-dimensional time series; Integer-valued autoregressive model; Banded coefficient matrices; Bayesian information criterion; Forecasting (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:212:y:2025:i:c:s0167947325001197

DOI: 10.1016/j.csda.2025.108243

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