Forecasting functional time series using weighted likelihood methodology

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).

Keywords:

• Bootstrap
• functional principal components
• functional time series
• weighted likelihood

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62G35
• 62M10
• 62P12

Acknowledgments

We thank the anonymous referee and AE for their careful reading of our manuscript and valuable suggestions and comments, which have helped us produce a significantly better paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ufuk Beyaztas  http://orcid.org/0000-0002-5208-4950

Han Lin Shang  http://orcid.org/0000-0003-1769-6430

Additional information

Funding

The second author also acknowledges the financial support from a research grant at the College of Business and Economics at the Australian National University.