Modeling Functional Time Series and Mixed-Type Predictors With Partially Functional Autoregressions

Xiaofei Xu, Ying Chen*, Ge Zhang, Thorsten Koch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In many business and economics studies, researchers have sought to measure the dynamic dependence of curves with high-dimensional mixed-type predictors. We propose a partially functional autoregressive model (pFAR) where the serial dependence of curves is controlled by coefficient operators that are defined on a two-dimensional surface, and the individual and group effects of mixed-type predictors are estimated with a two-layer regularization. We develop an efficient estimation with the proven asymptotic properties of consistency and sparsity. We show how to choose the sieve and tuning parameters in regularization based on a forward-looking criterion. In addition to the asymptotic properties, numerical validation suggests that the dependence structure is accurately detected. The implementation of the pFAR within a real-world analysis of dependence in German daily natural gas flow curves, with seven lagged curves and 85 scalar predictors, produces superior forecast accuracy and an insightful understanding of the dynamics of natural gas supply and demand for the municipal, industry, and border nodes, respectively.

Original languageEnglish
Pages (from-to)349-366
Number of pages18
JournalJournal of Business and Economic Statistics
Issue number2
Publication statusPublished - 2024


  • Energy forecasting
  • Functional time series
  • High dimensionality
  • Mixed-type covariates
  • Two-layer sparsity

ASJC Scopus subject areas

  • Statistics and Probability
  • Social Sciences (miscellaneous)
  • Economics and Econometrics
  • Statistics, Probability and Uncertainty


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