论文标题
功能时间序列中的非参数趋势估计，适用于年死亡率
Nonparametric Trend Estimation in Functional Time Series with Application to Annual Mortality Rates
论文作者
论文摘要
在这里，我们解决了功能时间序列的趋势估计问题。现有的贡献要么涉及检测功能趋势或假设一个简单的模型。他们既不考虑对一般功能趋势的估计，也不考虑具有功能趋势成分的功能时间序列的分析。与单变量时间序列相似，我们提出了一种替代方法来分析功能时间序列，考虑到功能趋势组件。我们建议通过使用易于实现，解释并允许控制估算器的平滑度的张量产品表面来估计功能趋势。通过一项蒙特卡洛研究，我们模拟了功能过程的不同情况，以表明我们的估计器准确地识别了功能趋势成分。我们还表明，估计的固定时间序列成分的依赖性结构不受功能趋势分量的误差近似的显着影响。我们将方法应用于法国的年度死亡率。
Here, we address the problem of trend estimation for functional time series. Existing contributions either deal with detecting a functional trend or assuming a simple model. They consider neither the estimation of a general functional trend nor the analysis of functional time series with a functional trend component. Similarly to univariate time series, we propose an alternative methodology to analyze functional time series, taking into account a functional trend component. We propose to estimate the functional trend by using a tensor product surface that is easy to implement, to interpret, and allows to control the smoothness properties of the estimator. Through a Monte Carlo study, we simulate different scenarios of functional processes to show that our estimator accurately identifies the functional trend component. We also show that the dependency structure of the estimated stationary time series component is not significantly affected by the error approximation of the functional trend component. We apply our methodology to annual mortality rates in France.
