论文标题
功能球形自相关：功能时间序列的自相关的稳健估计值
Functional Spherical Autocorrelation: A Robust Estimate of the Autocorrelation of a Functional Time Series
论文作者
论文摘要
我们为功能时间序列提出了一个新的自相关度量，我们称为球形自相关。它基于测量被投影到单位球上后滞后串联对之间的平均角度。与现有功能数据的现有自相关措施相比，这一新措施具有几个免费的优势，因为它既有1）描述了该系列中串行依赖的符号或方向的概念，而2）对于离群值来说更强大。建立了球形自相关估计值的渐近性能，并用于构建置信区间和Portmanteau白噪声测试。这些置信区间和测试被证明在模拟实验中有效，并在应用于每日电价曲线的选择中证明，并测量密集观察到的资产价格数据的波动性。
We propose a new autocorrelation measure for functional time series that we term spherical autocorrelation. It is based on measuring the average angle between lagged pairs of series after having been projected onto the unit sphere. This new measure enjoys several complimentary advantages compared to existing autocorrelation measures for functional data, since it both 1) describes a notion of sign or direction of serial dependence in the series, and 2) is more robust to outliers. The asymptotic properties of estimators of the spherical autocorrelation are established, and are used to construct confidence intervals and portmanteau white noise tests. These confidence intervals and tests are shown to be effective in simulation experiments, and demonstrated in applications to model selection for daily electricity price curves, and measuring the volatility in densely observed asset price data.
