Functional time series forecasting: Functional singular spectrum analysis approaches

Abstract

We introduce two novel nonparametric forecasting methods designed for functional time series (FTS), namely, functional singular spectrum analysis (FSSA) recurrent and vector forecasting. Our algorithms rely on extracted signals obtained from the FSSA method and innovative recurrence relations to make predictions. These techniques are model‐free, capable of predicting nonstationary FTS and utilize a computational approach for parameter selection. We also employ a bootstrap algorithm to assess the goodness‐of‐prediction. Through comprehensive evaluations on both simulated and real‐world climate data, we showcase the effectiveness of our techniques compared to various parametric and nonparametric approaches for forecasting nonstationary stochastic processes. Furthermore, we have implemented these methods in the Rfssa R package and developed a shiny web application for interactive exploration of the results.

A journey from univariate to multivariate functional time series: A comprehensive review

“…Once the decomposition is obtained, the forecasted functions for each component can be generated separately (using recurrent‐FSSA, and vector‐FSSA prediction procedures), and then combined to obtain the final forecast for the original FTS. For more details about FSSA forecasting see Trinka (2021) and Trinka et al (2023).…”