CMMSE: A Time-Varying Approach to Linear Mixed Models

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-02-19 DOI:10.1002/mma.10819

Dário Ferreira, Sandra Ferreira

引用次数: 0

Abstract

Linear mixed models (LMMs) are widely utilized for their ability to handle both fixed and random effects, making them versatile tools in statistical analysis. However, traditional LMMs assume constant random effects over time, a limitation when dealing with data where variances and structures change. On the other hand, time series models like ARIMA and GARCH are great at capturing time-related patterns and volatility but cannot handle random effects. In this study, we propose a time-varying linear mixed model (TVLMM) that integrates the strengths of ARIMA, GARCH, and LMMs, allowing for dynamic random effects over time. This novel framework offers a more flexible and realistic approach to modeling data, particularly in contexts where underlying processes evolve, such as in finance, economics, and social sciences. We demonstrate the efficacy of TVLMM through a simulated dataset, highlighting its potential for more accurate and reliable forecasting.

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线性混合模型的时变方法

线性混合模型（lmm）因其处理固定和随机效应的能力而被广泛应用，使其成为统计分析中的通用工具。然而，传统的lmm假设随着时间的推移产生恒定的随机效应，这在处理方差和结构变化的数据时是一个限制。另一方面，像ARIMA和GARCH这样的时间序列模型可以很好地捕捉与时间相关的模式和波动性，但不能处理随机效应。在这项研究中，我们提出了一个时变线性混合模型（TVLMM），它集成了ARIMA， GARCH和lmm的优势，允许随时间的动态随机效应。这种新颖的框架为数据建模提供了一种更加灵活和现实的方法，特别是在底层过程不断发展的环境中，例如在金融、经济和社会科学中。我们通过模拟数据集证明了TVLMM的有效性，强调了其在更准确和可靠的预测方面的潜力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.