變數校正函數型自我迴歸模型

Abstract

函數型自我迴歸模型是在函數型時間序列數據分析中被廣泛使用的技術，用於捕捉函數型數據之間的時間相關結構。現有的大多數函數型自我迴歸模型並未考慮額外變數對函數型觀測值的影響。在本文中，我們引入了基本函數型自我迴歸模型的擴展，稱為變數校正函數型自我迴歸模型，該模型結合了過去的觀測值和一組額外變數資訊，以更好地描述函數型時間序列數據中的潛在過程。我們通過在簡易設置下進行模擬研究，以及對法國年齡別死亡率曲線的時間序列數據進行分析，評估了所提出的變數校正函數型自我迴歸模型的性能，並與現有的函數型自我迴歸模型進行比較。結果表明，納入額外變數資訊可以提高模型的有效性。

Functional autoregressive (FAR) models are a widely used technique in functional time series data analysis, which have been proposed to capture the temporal dependence structure among functional data. Most of the existing FAR models do not consider the influence of additional covariates on functional observations. In this paper, we introduce an extension of the FAR model, called the covariate-adjusted FAR (cFAR) model, which incorporates both past observations and a set of covariates to better describe the underlying processes in functional time series data. We evaluated the performance of the proposed covariate-adjusted functional autoregressive model through a simulation study under a simplified setting and by analyzing time series data of age-specific mortality curves in France. The model was compared with the existing functional autoregressive method. The results demonstrate that incorporating additional covariate information significantly enhances the model's effectiveness.