# A robust functional time series forecasting method

## TL;DR

This paper introduces a robust functional time series forecasting method that effectively handles outliers by combining robust principal component analysis with a robust vector autoregressive model, improving forecast accuracy for functional data.

## Contribution

It presents a novel robust approach for functional time series forecasting that enhances outlier resistance and forecast accuracy compared to existing methods.

## Key findings

- Outperforms traditional methods in forecast accuracy.
- Robust parameter estimation improves model reliability.
- Effective in real-world ozone concentration forecasting.

## Abstract

Univariate time series often take the form of a collection of curves observed sequentially over time. Examples of these include hourly ground-level ozone concentration curves. These curves can be viewed as a time series of functions observed at equally spaced intervals over a dense grid. Since functional time series may contain various types of outliers, we introduce a robust functional time series forecasting method to down-weigh the influence of outliers in forecasting. Through a robust principal component analysis based on projection pursuit, a time series of functions can be decomposed into a set of robust dynamic functional principal components and their associated scores. Conditioning on the estimated functional principal components, the crux of the curve-forecasting problem lies in modeling and forecasting principal component scores, through a robust vector autoregressive forecasting method. Via a simulation study and an empirical study on forecasting ground-level ozone concentration, the robust method demonstrates the superior forecast accuracy that dynamic functional principal component regression entails. The robust method also shows the superior estimation accuracy of the parameters in the vector autoregressive models for modeling and forecasting principal component scores, and thus improves curve forecast accuracy.