Bootstrapping Periodic State-Space Models |
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Authors: | Hafida Guerbyenne |
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Institution: | Faculty of Mathematics, USTHB, El Alia, Bab Ezzouar, Algiers, Algeria |
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Abstract: | This article is concerned with how the bootstrap can be applied to study conditional forecast error distributions and construct prediction regions for future observations in periodic time-varying state-space models. We derive, first, an algorithm for assessing the precision of quasi-maximum likelihood estimates of the parameters. As a result, the derived algorithm is exploited for numerically evaluating the conditional forecast accuracy of a periodic time series model expressed in state space form. We propose a method which requires the backward, or reverse-time, representation of the model for assessing conditional forecast errors. Finally, the small sample properties of the proposed procedures will be investigated by some simulation studies. Furthermore, we illustrate the results by applying the proposed method to a real time series. |
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Keywords: | Backward representation Bootstrap Finite sample distributions Forecasting Periodic Chandrasekhar filter Periodic state-space models PVARMA models prediction region |
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