Approximate Factor Models for Functional Time Series

TL;DR

This paper introduces a new approximate factor model for functional time series data, enabling better structural understanding and forecasting of curve data like mortality and yield curves.

Contribution

The paper presents a novel factor model for functional time series that uses autocovariance structures for component identification and improves forecasting over traditional PCA methods.

Findings

Model provides parsimonious representations of dynamics.

Outperforms functional PCA in forecast accuracy.

Applicable to mortality and yield curve data.

Abstract

We propose a novel approximate factor model tailored for analyzing time-dependent curve data. Our model decomposes such data into two distinct components: a low-dimensional predictable factor component and an unpredictable error term. These components are identified through the autocovariance structure of the underlying functional time series. The model parameters are consistently estimated using the eigencomponents of a cumulative autocovariance operator and an information criterion is proposed to determine the appropriate number of factors. Applications to mortality and yield curve modeling illustrate key advantages of our approach over the widely used functional principal component analysis, as it offers parsimonious structural representations of the underlying dynamics along with gains in out-of-sample forecast performance.