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.
翻译:我们为功能时间序列提出了一个新的自动关系测量标准,我们用这个标准来表示球体自动关系,它基于在被投射到单位球体后对序列的滞后方之间的平均角度的测量,与功能数据的现有自动关系测量标准相比,这一新标准具有若干互补的优势,因为新标准(1)描述了系列中序列依赖性标志或方向的概念,2)对外部线来说更加有力。球体自动关系测量员的无症状特性已经建立,并被用于构建信任间隔和港门托白噪声测试。这些信任间隔和测试在模拟实验中是有效的,在模型选择每日电价曲线和测量观察到的密集资产价格数据波动的应用程序中都证明了这些信任间隔和测试是有效的。