In several countries, some macro-economic variables are not observed frequently (e.g. quarterly) and economic authorities need estimates of these high-frequency ®gures to make econometric analyses or to follow closely the country's economic growth. Two problems are involved in this context. The ®rst is to make these estimates after observing low-frequency values and some related indicators, and the second is to obtain predictions using just the observed indicators, i.e. before observing a new low-frequency ®gure. This paper gives a new optimal solution to the ®rst problem, and solves the second using a recursive optimal approach. In the second situation, additionally, statistical tests are developed for detecting structural changes at current periods in the macro-economic variable involved.
In some fields, we are forced to work with missing data in multivariate time series, unfortunately the analysis in this context cannot be done as in the case of complete data. Bayesian analysis of multivariate thresholds autoregressive models(MTAR) with exogenous inputs and missing data is carried out. MCMC methods are used to obtain samples from the marginal posterior distributions, including threshold values and missing data. In order to identify autoregressive orders, we adapt the Bayesian variable selection method to the MTAR models. The number of regimes is estimated using marginal likelihood and product space strategies. The forecasting of the output vector is implemented finding its predictive distributions. Simulation experiments and real data examples are presented. Resumen: En algunos campos, nos vemos forzados a trabajar con datos faltantes en series de tiempo multivaridas, desafortunadamente el análisis en este contexto no puede ser hecho como en caso completo. El análisis de modelos multivaridos autoregresivos de umbrales(MTAR) con entradas exogenas y datos faltantes es llevado a cabo vía el enfoque Bayesiano. Los métodos MCMC son usados para obtener muestras de las distribuciones marginales aposteriori, incluyendo los valores de los umbrales y los datos faltantes. Con el objetivo de identificar losórdenes autoregresivos, el método Bayesiano de selección de varibales es adaptado para modelos MTAR. El número de regímenes es estimado usando la versimilitud marginal y las estrategias de espacio producto. El pronóstico para el vector de salida es implementado encontrando sus densidades predictivas. Experimentos de simulación y ejemplos con datos reales son presentados.
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