Biquadratic functions: stationarity and invertibility in estimated time-series models
- Autores: D. S. G. Pollock
- Localización: Questiió: Quaderns d'Estadística, Sistemes, Informatica i Investigació Operativa, ISSN 0210-8054, Vol. 13, Nº. 1-3, 1989, págs. 13-30
- Idioma: inglés
- Títulos paralelos:
- Funciones bicuadráticas: estacionalidad e invertibilidad en modelos de series temporales estimadas
- Enlaces
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Resumen
It is important that the estimates of the parameters of an autoregressive moving-average (ARMA) model should satisfy the conditions of stationarity and invertibility. It can be shown that the unconditional maximum-likelihood estimates are bound to fill these conditions regardless of the size of the sample from which they are derived; and, in some quarters, it has been argued that they should be used in preference to any other estimates when the size of he sample is small. However, the maximum-likelihood estimates are difficult to obtain; and, in practice, estimates are usually derived from a least-squares criterion. In this paper we show that, if an appropriate form of least-squares criterion is adopted, then we can likewise guarantee that the conditions of stationarity and invertibility will be fulfilled. We also re-examine several of the alternative procedures for estimating ARMA models to see whether the criterion functions from which they are derived have the appropriate form.
