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A prototypical seasonal adjustment model. (English) Zbl 0608.62115
The paper analyzes unobserved-components modelling and estimation for the simplest ARIMA process that accepts a full decomposition into trend, seasonal and irregular components. This prototypical model exemplifies many features of and issues arising in model-based seasonal adjustment that are less transparent in more complex seasonal time series models.
In particular the analysis illuminates the major issues surrounding the specification of the component models and the identification of a unique structure for them. In so doing, the relationship between reduced- and structural-form approaches to unobserved components estimation is illustrated within an ARIMA-modelling framework. Finally, the properties of the minimum mean-squared-error estimators of the unobserved components are examined and the two main types of estimation error, revisions in the preliminary estimator and error in the final estimator, are analyzed.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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