  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.
