Autori
Maravall, Augustin
Daniel, Pena

Titolo
Missing observations and additive outliers in time series models
Periodico
European University Institute of Badia Fiesolana (Fi). Department of Economics - Working papers
Anno: 1992 - Fascicolo: 97 - Pagina iniziale: 1 - Pagina finale: 41

The paper deals with estimation of missing observations in possibly nonstationary A rima models. First, the model is assumed known, and the structure of the interpolation filter is analysed. Using the inverse or dual autocorrelation function it is seen how estimation of a missing observation is analogous to the removal of an outlier effect; both problems are closely related with the signal plus noise decomposition of the series. The results are extended to cover, first, the case of a missing observation near the two extremes of the series; then to the case of a sequence of missing observations, and finally to the general case of any number of sequences of any length of missing observations. The optimal estimator can always be expressed, in a compact way, in terms of the dual autocorrelation function or a truncation thereof; its mean squared error is equal to the inverse of the (appropriately chosen) dual autocovariance matrix. The last part of the paper illustrates a point of applied interest: When the model is unknown, the additive outlier approach may provide a convenient and efficient alternative to the standard Kalman filter-fixed point smoother approach for missing observations estimation.




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