Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series

Bootstrap prediction mean squared errors of unobserved states based on the Kalman filter with estimated parameters

Prediction intervals in State Space models can be obtained by assuming Gaussian innovations and using the prediction equations of the Kalman filter, where the true parameters are substituted by consistent estimates. This approach has two limitations. First, it does not incorporate the uncertainty due to parameter estimation. Second, the Gaussianity assumption of future innovations may be inaccurate. To overcome these drawbacks, Wall and Stoffer (2002) propose to obtain prediction intervals by using a bootstrap procedure that requires the backward representation of the model. Obtaining this representation increases the complexity of the procedure and limits its implementation to models for which it exists. The bootstrap procedure proposed by Wall and Stoffer (2002) is further complicated by fact that the intervals are obtained for the prediction errors instead of for the observations. In this paper, we propose a bootstrap procedure for constructing prediction intervals in State Space models that does not need the backward representation of the model and is based on obtaining the intervals directly for the observations. Therefore, its application is much simpler, without loosing the good behavior of bootstrap prediction intervals. We study its finite sample properties and compare them with those of the standard and the Wall and Stoffer (2002) procedures for the Local Level Model. Finally, we illustrate the results by implementing the new procedure to obtain prediction intervals for future values of a real time series.NAIRU, Output gap, Parameter uncertainty, Prediction Intervals, State Space Models

A POWERFUL TEST FOR CONDITIONAL HETEROSCEDASTICITY FOR FINANCIAL TIME SERIES WITH HIGHLY PERSISTENT VOLATILITIES.

Traditional tests for conditional heteroscedasticity are based on testing for significant autocorrelations of squared or absolute observations. In the context of high frequency time series of financial returns, these autocorrelations are often positive and very persistent, although their magnitude is usually very small. Moreover, the sample autocorrelations are severely biased towards zero, specially if the volatility is highly persistent. Consequently, the power of the traditional tests is often very low. In this paper, we propose a new test that takes into account not only the magnitude of the sample autocorrelations but also possible patterns among them. This aditional information makes the test more powerful in situations of empirical interest. The asymptotic distribution of the new statistic is derived and its finite sample properties are analized by means of Monte Carlo experiments. The performance of the new test is compared with other alternative tests. Finally, we illustrate the results analysing several real time series of financial returns.

GARCH models with leverage effect : differences and similarities

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage e?ect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH speci cation is the most exible while the GJR model may have important limitations when restricted to have nite kurtosis. On the other hand, we show empirically that the conditional standard deviations estimated by the TGARCH and EGARCH models are almost identical and very similar to those estimated by the APARCH model. However, the estimates of the QGARCH and GJR models di?er among them and with respect to the other three speci cations

GARCH models with leverage effect : differences and similarities

In this paper, we compare the statistical properties of some of the most popular GARCH models with leverage effect when their parameters satisfy the positivity, stationarity and nite fourth order moment restrictions. We show that the EGARCH specication is the most exible while the GJR model may have important limitations when restricted to have nite kurtosis. On the other hand, we show empirically that the conditional standard deviations estimated by the TGARCH and EGARCH models are almost identical and very similar to those estimated by the APARCH model. However, the estimates of the QGARCH and GJR models differ among them and with respect to the other three specications.EGARCH, GJR, QGARCH, TGARCH, APARCH

Propuesta de un sistema de información documental para las televisiones locales

It is carried out a proposal of organization of the documental information in local televisions in the mark of the systemic theory of the information, taking like reference the concept of Information Management System like method of organizing the administration in the managerial structure. For it, and describing the structures of Televisión Española and Antena 3 Televisión, they are defined the subsystems of administration of audiovisual, sound, write and photographic documentation

Un sistema económico heredado: ¿El Guadiana como espejo de Tarteso?

Trabajo presentado a las IV Jornadas de Investigación en Historia Antigua, celebradas en Madrid del 21 al 23 de noviembre de 2014.Este trabajo se inscribe en el marco del Proyecto “Estudio arqueológico comparativo entre los territorios periféricas de Tartesos: los valles del Guadiana y del Tajo” (HAR2012-33985) dentro de la Unidad Asociada ANTA entre la UAM y el Instituto de Arqueología del CSIC.Peer Reviewe

Ferrer Albelda, E. y Cantillo Duarte, J. J. (coords.) (2017): Arqueología en Vejer. De la Prehistoria al Período Andalusí [Reseña]

Reseña de: Ferrer Albelda, E. y Cantillo Duarte, J. J. (coords.) (2017): Arqueología en Vejer. De la Prehistoria al Período Andalusí, Sevilla, Editorial Universidad de Sevilla y Ayuntamiento de Vejer de la Frontera, 361 pp. ISBN: 978-84-472-1844-8