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


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), 893-916. (doi:10.1111/j.1467-9892.2005.00448.x).

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Description/Abstract

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.

Item Type: Article
ISSNs: 0143-9782 (print)
Related URLs:
Keywords: hyper-parameters, kalman filter, mle, order of bias, reml
Subjects: H Social Sciences > HA Statistics
Q Science > QA Mathematics > QA76 Computer software
Divisions: University Structure - Pre August 2011 > Southampton Statistical Sciences Research Institute
ePrint ID: 39064
Date Deposited: 19 Jun 2006
Last Modified: 27 Mar 2014 18:24
Contact Email Address: D.Pfeffermann@soton.ac.uk
URI: http://eprints.soton.ac.uk/id/eprint/39064

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