High-dimensional functional time series forecasting: An application to age-specific mortality rates
High-dimensional functional time series forecasting: An application to age-specific mortality rates
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DOI：
10.1016/j.jmva.2018.10.003
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发表时间：
2019-03-01
影响因子：
1.6
通讯作者：
Yang, Yanrong
中科院分区：
文献类型：
--
作者：
Gao, Yuan;Shang, Han Lin;Yang, Yanrong
我们通过两次降维的方法来解决高维函数时间序列的预测问题。高维函数时间序列预测的困难在于维度灾难。在本文中，我们提出了一种新的方法来解决这个问题。首先应用动态泛函主成分分析将每个函数时间序列归结为一个向量。然后，我们使用因子模型作为进一步的降维技术，以便只保留少量的潜在因子。可以使用经典的时间序列模型来预测因素，并可以构造函数的条件预测。建立了逼近函数的渐近性质，包括估计误差和预测误差。该方法易于实现，特别是当函数时间序列的维度较大时。我们通过模拟研究和对日本特定年龄死亡率的应用展示了我们方法的优越性。(C)2018 Elsevier Inc.保留所有权利。
We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement, especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates. (C) 2018 Elsevier Inc. All rights reserved.