  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).

Methodology