Uncertainty in model-based seasonal adjustment procedures and construction of minimax filters

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Abstract

Unobserved component autoregressive integrated moving average models are often the cornerstone of model-based seasonal adjustment procedures. Unfortunately these models are inherently underidentified and ad hoc assumptions must be made prior to the analysis. This article investigates the effect of seasonal adjustment filters on a class of observationally equivalent models. Bounds on the mean squared error (MSE) associated with arbitrary linear filters are derived. The article also derives robust seasonal adjustment filters. The filters are robust in the sense that they minimize the maximum MSE from the set of observationally equivalent models. The article shows that the minimax and minimum extraction filters are equivalent for a certain class of models. Empirical results for a number of economic time series are presented.

Original languageEnglish (US)
Pages (from-to)395-408
Number of pages14
JournalJournal of the American Statistical Association
Volume82
Issue number398
DOIs
StatePublished - Jun 1987
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Keywords

  • Minimax estimates
  • Signal extraction
  • Unobserved components model

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