A depth-based method for functional time series forecasting

An approach is presented for making predictions about functional time series. The method is applied to data coming from periodically correlated processes and electricity demand, obtaining accurate point forecasts and narrow prediction bands that cover high proportions of the forecasted functional datum, for a given confidence level. The method is computationally efficient and substantially different to other functional time series methods, offering a new insight for the analysis of these data structures

A Study of Functional Depths

Functional depth is used for ranking functional observations from most outlying to most typical. The ranks produced by functional depth have been proposed as the basis for functional classifiers, rank tests, and data visualization procedures. Many of the proposed functional depths are invariant to domain permutation, an unusual property for a functional data analysis procedure. Essentially these depths treat functional data as if it were multivariate data. In this work, we compare the performance of several existing functional depths to a simple adaptation of an existing multivariate depth notion, $L^\infty$ depth ($L^{\infty}D$). On simulated and real data, we show $L^{\infty}D$ has performance comparable or superior to several existing notions of functional depth. In addition, we review how depth functions are evaluated and propose some improvements. In particular, we show that empirical depth function asymptotics can be mis--leading and instead propose a new method, the rank--rank plot, for evaluating empirical depth rank stability.Comment: 25 pages, 13 figure