Functional Spherical Autocorrelation: A Robust Estimate of the Autocorrelation of a Functional Time Series

TL;DR

This paper introduces spherical autocorrelation, a new robust measure for functional time series that captures directional dependence and is resistant to outliers, with proven asymptotic properties and practical applications.

Contribution

It proposes a novel spherical autocorrelation measure for functional data, including its theoretical properties and practical utility in model selection and volatility measurement.

Findings

Effective in simulation experiments

Useful for model selection in electricity prices

Robust to outliers in asset price data

Abstract

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.