A robust functional time series forecasting method

Han Lin Shang*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 modelling 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 modelling and forecasting principal component scores, and thus improves curve forecast accuracy.
Original languageEnglish
Pages (from-to)795-814
Number of pages20
JournalJournal of Statistical Computation and Simulation
Issue number5
Publication statusPublished - 24 Mar 2019
Externally publishedYes


  • Robust functional principal component regression
  • projection pursuit
  • multivariate least trimmed squares estimators
  • vector autoregressive model
  • ground-level ozone concentration
  • 62G08
  • 62J05
  • 62P12
  • 62G35

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