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Publisher: Elsevier.

Issued date: 2001-01

Citation: International Journal of Forecasting, Jan.–Mar. 2001,171 , 83–103

ISSN: 0169-2070

DOI: 10.1016-S0169-20700000069-8

Sponsor: Acknowledgements The authors are very grateful to the referees for comments that helped to improve the paper. Also, we are grateful to Lory A. Thombs for her comments, to Eva Senra for providing the Italian IPI data and to Regina Kaiser for helping us to clean the series of outliers. Financial support was provided by the European Union project ERBCHRXCT 940514 and by projects CICYT PB95-0299, DGICYT PB96-0111 from the Spanish Government and Cátedra de Calidad BBV.

Publisher version: http:-dx.doi.org-10.1016-S0169-20700000069-8

Keywords: Forecasting , Least absolute deviations , Non normal distributions , Ordinary least squares

Abstract:We use abootstrap procedure to study the impact of parameterestimation on predictiondensities, focusing on seasonal ARIMA processes with possibly non normal innovations. We compare predictiondensities obtained using the Box and Jenkins approach with bootstrapdWe use abootstrap procedure to study the impact of parameterestimation on predictiondensities, focusing on seasonal ARIMA processes with possibly non normal innovations. We compare predictiondensities obtained using the Box and Jenkins approach with bootstrapdensities which may be constructed either taking into account parameterestimation variability or using parameter estimates as if they were known parameters. By means of Monte Carlo experiments, we show that the average coverage of the intervals is closer to the nominal value when intervals are constructed incorporating parameter uncertainty. The effects of parameterestimation are particularly important for small sample sizes and when the error distribution is not Gaussian. We also analyze the effect of the estimation method on the shape of predictiondensities comparing predictiondensities constructed when the parameters are estimated by Ordinary Least Squares OLS and by Least Absolute Deviations LAD. We show how, when the error distribution is not Gaussian, the average coverage and length of intervals based on LAD estimates are closer to nominal values than those based on OLS estimates. Finally, the performance of the bootstrap intervals is illustrated with two empirical examples.+-





Author: Pascual, Lorenzo; Romo Urroz, Juan; Ruiz, Esther

Source: http://e-archivo.uc3m.es


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Universidad Carlos III de Madrid Repositorio institucional e-Archivo http:--e-archivo.uc3m.es Departamento de Estadística DES - Artículos de Revistas 2001-01 Effects of parameter estimation on prediction densities: a bootstrap approach. Pascual, Lorenzo Elsevier. þÿInternational Journal of Forecasting, ( Jan.
Mar.
2001),17(1) , 83 103 http:--hdl.handle.net-10016-14845 Descargado de e-Archivo, repositorio institucional de la Universidad Carlos III de Madrid Effects of parameter estimation on prediction densities: a bootstrap approach Lorenzo Pascual, Juan Romo, Esther Ruiz* Departamento de Estadı stica y Econometrı ,aUniversidad Carlos III de Madrid, C -Madrid, 126, 28903 Getafe, Madrid, Spain Abstract We use a bootstrap procedure to study the impact of parameter estimation on prediction densities, focusing on seasonal ARIMA processes with possibly non normal innovations.
We compare prediction densities obtained using the Box and Jenkins approach with bootstrap densities which may be constructed either taking into account parameter estimation variability or using parameter estimates as if they were known parameters.
By means of Monte Carlo experiments, we show that the average coverage of the intervals is closer to the nominal value when intervals are constructed incorporating parameter uncertainty.
The effects of parameter estimation are particularly important for small sample sizes and when the error distribution is not Gaussian.
We also analyze the effect of the estimation method on the shape of prediction densities comparing prediction densities constructed when the parameters are estimated by Ordinary Least Squares (OLS) and by Least Absolute Deviations (LAD).
We show how, when the error distribution is not Gaussian, the average coverage and length of intervals based on LAD estimates are closer to nominal values than those based on OLS estimates.
Finally, the performance of the bootstrap intervals is illustrated with two empirical examples. Keyword...





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