Missing observations and additive outliers in time series models
- Autores: Agustín Maravall, Daniel Peña Sánchez de Rivera
- Localización: Documentos de trabajo - Banco de España, ISSN 0213-2710, Nº 12, 1996, págs. 5-51
- Idioma: inglés
- Enlaces
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Resumen
The papers deals with estimation of missing observations in possibly nonstationary ARIMA 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 extemes 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 autoco'i'relation 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.
