# Forecasting functional time series using weighted likelihood methodology

## TL;DR

This paper introduces a robust weighted likelihood approach for forecasting functional time series, effectively handling outliers to improve prediction accuracy, demonstrated through simulations and real data.

## Contribution

The paper proposes a novel weighted likelihood methodology for robust forecasting of functional time series, addressing outlier sensitivity in existing models.

## Key findings

- Proposed method outperforms existing forecasting techniques in simulations.
- Numerical results show improved accuracy in real-data applications.
- Method provides reliable point and interval forecasts despite outliers.

## Abstract

Functional time series whose sample elements are recorded sequentially over time are frequently encountered with increasing technology. Recent studies have shown that analyzing and forecasting of functional time series can be performed easily using functional principal component analysis and existing univariate/multivariate time series models. However, the forecasting performance of such functional time series models may be affected by the presence of outlying observations which are very common in many scientific fields. Outliers may distort the functional time series model structure, and thus, the underlying model may produce high forecast errors. We introduce a robust forecasting technique based on weighted likelihood methodology to obtain point and interval forecasts in functional time series in the presence of outliers. The finite sample performance of the proposed method is illustrated by Monte Carlo simulations and four real-data examples. Numerical results reveal that the proposed method exhibits superior performance compared with the existing method(s).