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Fitting time series models by minimising multistep-ahead errors: a frequency domain approach.

Haywood, J. and Tunnicliffe Wilson, G. (1997) Fitting time series models by minimising multistep-ahead errors: a frequency domain approach. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 59 (1). pp. 237-254. ISSN 1369-7412

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Abstract

This paper brings together two topics in the estimation of time series forecasting models: the use of the multistep-ahead error sum of squares as a criterion to be minimized and frequency domain methods for carrying out this minimization. The methods are developed for the wide class of time series models having a spectrum which is linear in unknown coefficients. This includes the IMA(1, 1) model for which the common exponentially weigh-ted moving average predictor is optimal, besides more general structural models for series exhibiting trends and seasonality. The method is extended to include the Box–Jenkins `air line' model. The value of the multistep criterion is that it provides protection against using an incorrectly specified model. The value of frequency domain estimation is that the iteratively reweighted least squares scheme for fitting generalized linear models is readily extended to construct the parameter estimates and their standard errors. It also yields insight into the loss of efficiency when the model is correct and the robustness of the criterion against an incorrect model. A simple example is used to illustrate the method, and a real example demonstrates the extension to seasonal models. The discussion considers a diagnostic test statistic for indicating an incorrect model.

Item Type: Article
Journal or Publication Title: Journal of the Royal Statistical Society: Series B (Statistical Methodology)
Uncontrolled Keywords: diagnostic test • frequency domain estimation • iterative reweighting • multistep errors • time series forecasting
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 19499
Deposited By: ep_ss_importer
Deposited On: 14 Nov 2008 14:28
Refereed?: Yes
Published?: Published
Last Modified: 23 Oct 2014 16:12
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19499

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