Misspecified prediction for time series

In Bong Choi, Masanobu Taniguchi*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


Let [Xt] be a stationary process with spectral density g(λ.).It is often that the true structure g(λ) is not completely specified. This paper discusses the problem of misspecified prediction when a conjectured spectral density fθ(λ), θ ε Θ, is fitted to g(λ). Then, constructing the best linear predictor based on fθ(λ), we can evaluate the prediction error M(θ) Since θ is unknown we estimate it by a quasi-MLE θQ. The second-order asymptotic approximation of M(θ̂Q)is given. This result is extended to the case when Xt contains some trend, i.e. a time series regression model. These results are very general. Furthermore we evaluate the second-order asymptotic approximation of M(θ̂Q) for a time series regression model having a long-memory residual process with the true spectral density g(λ). Since the general formulae of the approximated prediction error are complicated, we provide some numerical examples. Then we illuminate unexpected effects from the misspecification of spectra.

Original languageEnglish
Pages (from-to)543-564
Number of pages22
JournalJournal of Forecasting
Issue number8
Publication statusPublished - 2001 Dec
Externally publishedYes


  • Best linear predictor
  • Conjectured spectral density
  • Long-memory process
  • Misspecified prediction
  • Multistep prediction
  • Quasi-MLE
  • Spectral density
  • Stationary process
  • Time series regression model

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Science Applications
  • Strategy and Management
  • Statistics, Probability and Uncertainty
  • Management Science and Operations Research


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