A class of periodic trend models for seasonal time series

Tommaso Proietti*, Martyna Marczak, Gianluigi Mazzi

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


Trend and seasonality are the most prominent features of economic time series that are observed at the subannual frequency. Modeling these components serves a variety of analytical purposes, including seasonal adjustment and forecasting. In this paper we introduce unobserved components models for which both the trend and seasonal components arise from systematically sampling a multivariate transition equation, according to which each season evolves as a random walk with a drift. By modeling the disturbance covariance matrix we can encompass traditional models for seasonal time series, like the basic structural model, and can formulate more elaborate ones, dealing with season specific features, such as seasonal heterogeneity and correlation, along with the different role of the nonstationary cycles defined at the fundamental and the harmonic frequencies in determining the shape of the seasonal pattern.

Original languageEnglish
JournalJournal of Forecasting
Pages (from-to)106-121
Number of pages16
Publication statusPublished - 2019


  • circular correlation
  • seasonal cycles
  • seasonal heterogeneity
  • unobserved components


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