Functional spherical autocorrelation: robust autocorrelation estimation of a functional time series

Abstract

Measuring the serial dependence across time is critical in model identification and diagnosis in time series (TS) analysis. In classic TS analysis, the autocorrelation function is perhaps the most widely used method to examine the temporal relationship of the scalar or vector-valued observations. In functional TS (FTS), which refers to TS of functional data, their dependence is best summarised by an autocovariance operator. Evaluating the size and information contained in such an object can be difficult. Existing methods are relatively constrained and unable to capture certain characteristics contained in the FTS objects, such as the "direction" of dependence. We develop a new method to address this problem by projecting lagged pairs unit sphere and computing the angle between them, which we refer to as spherical autocorrelation. We establish the asymptotic properties of the empirical spherical autocorrelation, and we study its use in an application to European electricity data.

This is a joint work with Gregory Rice and Joel A. Dubin.

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