Functional spherical autocorrelation: A robust estimate of the autocorrelation of a functional time series

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 after having been projected onto unit sphere. This enjoys several complimentary advantages compared to existing measures data, since it both 1) describes notion “sign” or “direction” serial dependence in series, and 2) more robust outliers. The asymptotic properties estimators spherical are established, used construct confidence intervals portmanteau white noise tests. These tests shown be effective simulation experiments, demonstrated applications model selection daily electricity price curves, volatility densely observed asset data.