具有时间函数方差噪声的 ARMA 模型的渐近推论

IF 0.8 4区数学 Q3 STATISTICS & PROBABILITY

Scandinavian Journal of Statistics Pub Date : 2024-02-05 DOI:10.1111/sjos.12708

Bibi Cai, Enwen Zhu, Shiqing Ling

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引用次数: 0

摘要

本文研究具有时间函数方差（TFV）噪声的自回归移动平均（ARMA）模型，称为 ARMA-TFV 模型。我们首先建立了其最小二乘估计器（LSE）的一致性和渐近正态性。根据变量选择和模型检验理论，构建了 Wald 检验和 portmanteau 检验。为了评估我们的方法在有限样本中的性能，我们进行了模拟研究，并给出了两个实际例子。需要指出的是，ARMA-TFV 模型产生的过程不是静态的，本文中的技术是非标准的，可能会为该领域的未来研究提供启示。

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Asymptotic inference of the ARMA model with time-functional variance noises

This paper studies the autoregressive and moving average (ARMA) model with time-functional variance (TFV) noises, called the ARMA-TFV model. We first establish the consistency and asymptotic normality of its least squares estimator (LSE). The Wald tests and portmanteau tests are constructed based on the theory for variable selection and model checking. A simulation study is carried out to assess the performance of our approach in finite samples, and two real examples are given. It should be mentioned that the process generated from the ARMA-TFV model is not stationary, and the technique in this paper is nonstandard and may provide insights for future research in this area.

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来源期刊

Scandinavian Journal of Statistics 数学-统计学与概率论

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The Scandinavian Journal of Statistics is internationally recognised as one of the leading statistical journals in the world. It was founded in 1974 by four Scandinavian statistical societies. Today more than eighty per cent of the manuscripts are submitted from outside Scandinavia. It is an international journal devoted to reporting significant and innovative original contributions to statistical methodology, both theory and applications. The journal specializes in statistical modelling showing particular appreciation of the underlying substantive research problems. The emergence of specialized methods for analysing longitudinal and spatial data is just one example of an area of important methodological development in which the Scandinavian Journal of Statistics has a particular niche.