Empirical Economics

, Volume 24, Issue 2, pp 271–301

Performance of periodic time series models in forecasting

  • Helmut Herwartz

DOI: 10.1007/s001810050055

Cite this article as:
Herwartz, H. Empirical Economics (1999) 24: 271. doi:10.1007/s001810050055


The paper provides a comparison of alternative univariate time series models that are advocated for the analysis of seasonal data. Consumption and income series from (West-) Germany, United Kingdom, Japan and Sweden are investigated. The performance of competing models in forecasting is used to assess the adequacy of a specific model. To account for nonstationarity first and annual differences of the series are investigated. In addition, time series models assuming periodic integration are evaluated. To describe the stationary dynamics (standard) time invariant parametrizations are compared with periodic time series models conditioning the data generating process on the season. Periodic models improve the in-sample fit considerably but in most cases under study this model class involves a loss in ex-ante forecasting relative to nonperiodic models. Inference on unit-roots indicates that the nonstationary characteristics of consumption and income data may differ. For German and Swedish data forecasting exercises yield a unique recommendation of unit roots in consumption and income data which is an important (initial) result for multivariate analysis. Time series models assuming periodic integration are parsimonious to specify but often involve correlated one-step-ahead forecast errors.

Key words: Forecastingperiodic modelsseasonalityunit roots
JEL Classification: C22C52C53

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Helmut Herwartz
    • 1
  1. 1.Institut für Statistik und Ökonometrie, Humboldt Universität zu Berlin, Spandauer Str. 1, D-10178 Berlin, Germany (e-mail: helmut@wiwi.hu-berlin.de)DE