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Bootstrap approximation to prediction MSE for state-space models with estimated parameters

Record type: Article

We propose simple parametric and nonparametric bootstrap methods for estimating the prediction mean square error (PMSE) of state vector predictors that use estimated model parameters. As is well known, substituting the model parameters by their estimates in the theoretical PMSE expression that assumes known parameter values results in underestimation of the true PMSE. The parametric method consists of generating parametrically a large number of bootstrap series from the model fitted to the original series, re-estimating the model parameters for each series using the same method as used for the original series and then estimating the separate components of the PMSE.
The nonparametric method generates the series by bootstrapping the standardized innovations estimated for the original series. The bootstrap methods are compared with other methods considered in the literature in a simulation study that also examines the robustness of the various methods to non-normality of the model error terms. Application of the bootstrap method to a model fitted to employment ratios in the USA that contains 18 unknown parameters, estimated by a three-step procedure yields unbiased PMSE estimators.

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Citation

Pfeffermann, Danny and Tiller, Richard (2005) Bootstrap approximation to prediction MSE for state-space models with estimated parameters Journal of Time Series Analysis, 26, (6), pp. 893-916. (doi:10.1111/j.1467-9892.2005.00448.x).

More information

Published date: November 2005
Keywords: hyper-parameters, kalman filter, mle, order of bias, reml

Identifiers

Local EPrints ID: 39064
URI: http://eprints.soton.ac.uk/id/eprint/39064
PURE UUID: 114ab3b4-6b53-4e5c-9a18-a9111efef700

Catalogue record

Date deposited: 19 Jun 2006
Last modified: 17 Jul 2017 15:37

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