Functional Time Series Forecasting: Functional Singular Spectrum Analysis Approaches

TL;DR

This paper introduces two nonparametric functional time series forecasting methods based on singular spectrum analysis, demonstrating improved performance over standard algorithms for periodic stochastic processes.

Contribution

The paper presents novel functional singular spectrum analysis recurrent and vector forecasting methods, enhancing prediction accuracy for functional time-dependent data.

Findings

Our methods outperform the gold standard in simulations.

They perform better on periodic stochastic processes.

The approaches are nonparametric and data-driven.

Abstract

In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of functional singular spectrum analysis and past observations in order to predict future data points where recurrent forecasting predicts one function at a time and the vector forecasting makes predictions using functional vectors. We compare our forecasting methods to a gold standard algorithm used in the prediction of functional, time-dependent data by way of simulation and real data and we find our techniques do better for periodic stochastic processes.