Interpolation, outliers and inverse autocorrelations

The paper addresses the problem of estimating missing observations in linear, possibly nonstationary, stochastic processes when the model is known. The general case of any possible distribution of missing observations in the time series is considered, and analytical expressions for the optimal estimators and their associated mean squared errors are obtained. These expressions involve solely the elements of the inverse or dual autocorrelation function of the series. This optimal estimator -the conditional expectation of the missing observations given the available ones-is equal oto the estimator that results from filling the missing values in the series with arbitrary numbers, treating these numbers as additive outliers, and removing the outlier effects from the invented numbers using intervention analysis

Missing observations and additive outliers in time series models

The paper deals with estimation of missing observations in possible nonstationary ARIMA models. First, the model is assumed known, and the structure of the interpolation filter is analyzed. 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; is 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

Interpolation, outliers and inverse autocorrelations.

The paper addresses the problem of estimating missing observations in linear, possibly nonstationary, stochastic processes when the model is known. The general case of any possible distribution of missing observations in the time series is considered, and analytical expressions for the optimal estimators and their associated mean squared errors are obtained. These expressions involve solely the elements of the inverse or dual autocorrelation function of the series. This optimal estimator -the conditional expectation of the missing observations given the available ones-is equal oto the estimator that results from filling the missing values in the series with arbitrary numbers, treating these numbers as additive outliers, and removing the outlier effects from the invented numbers using intervention analysis.Missing observations; Outliers; Intervention analysis; ARIMA models; Inverse autocorrelation function;

Missing observations and additive outliers in time series models.

The paper deals with estimation of missing observations in possible nonstationary ARIMA models. First, the model is assumed known, and the structure of the interpolation filter is analyzed. 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; is 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.ARIMA models; Interpolation; Inverse autocorrelations;

An application of TRAMO-SEATS : automatic procedure and sectoral aggregation : the Japanese foreign trade series

Se presenta una aplicacion de la metodologia TRAMO-SEATS a la desestacionalizacion y estimacion de la tendencia-ciclo de las series de exportaciones, importaciones y balanza comercial japonesas. Los programas utilizados de manera automatica producen resultados satisfactorios y se indica como el 'output' de SEATS puede ayudar a la hora de escoger un modelo final. Por ultimo, usando la relacion entre las tres series, se discute el problema de la estimacion directa frente a la indirecta. (am) (ad

On issues involved with the seasonal adjustment of time series

El documento analiza algunos aspectos relativos a la desestacionalizacion basada en modelos ARIMA. Estos se refieren a la justificacion de la desestacionalizacion, a la caracterizacion de los componentes, a los criterios utilizables para juzgar la sensatez de los resultados obtenidos, y, sobre todo, al problema de las revisiones

Computing missing values in time series

This work presents two algorithms to estimate missing values in time series. The first is the Kalman Filter, as developed by Kohn and Ansley (1986) and others. The second is the additive outlier approach, developed by Pefia, Ljung and Maravall. Both are exact and lead to the same results. However, the first is, in general, faster and the second more flexible

An application of the tramo-seats automatic procedure : direct versus indirect adjustment

En Maravall (2002) se ilustraba el uso y la interpretación de los resultados de la metodología basada en modelos ARIMA contenida en los programas TRAMO y SEATS, utilizados en forma automática sobre las series de comercio exterior japonesas. En el presente trabajo se completa la discusión del ejemplo. Se ilustran algunas mejoras en los resultados de la identificación automática de los modelos, y se analizan los modelos obtenidos para la serie ajustada de estacionalidad y su componente de tendencia-ciclo (en particular, su orden de integración). Se muestra de nuevo cómo los resultados de SEATS pueden ser de ayuda en la selección de modelos. Finalmente, se discute el importante problema práctico de seguir un procedimiento directo de ajuste de un agregado o indirecto (es decir, a través del ajuste de las series que lo componen). Se concluye que, debido a que la agregación afecta profundamente al perfil espectral del agregado, y a que la desestacionalización implica una transformación no-lineal de los datos, el ajuste directo es siempre preferible. Esta conclusión implica que las restricciones entre las series originales (debidas, por ejemplo, a identidades) no serán respetadas exactamente por las series desestacionalizadas

On structural time series models and the characterization of components

Se analizan los modelos estructurales de series temporales, recientemente propuestos, en los que se imponen estructuras especificas para los componentes no observados de una serie. Se obtiene que series para las cuales X11 es adecuado, o series con estructuras del tipo del modelo de las "lineas aereas" se ajustan al formato de los modelos estructurales. Sin embargo, la caracterizacion de los componentes es insatisfactoria, dado que la identificacion de sus modelos se consigue trasladando variacion del tipo ruido blanco del irregular a la tendencia y a la estacionalidad