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Fathoming the Theta Method for a Unit Root Process

Thomakos, D.D. and Nikolopoulos, K. (2012) Fathoming the Theta Method for a Unit Root Process. IMA Journal of Management Mathematics, 25 (1). pp. 105-124. DOI: 10.1093/imaman/dps030

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Abstract

In this paper, building on earlier work by Assimakopoulos and Nikolopoulos ([2000. The theta model: a decomposition approach to forecasting. Int. J. Forecast., 16, 521�530], hereafter A&N) and Hyndman and Billah ([2003. Unmasking the theta method. Int. J. Forecast., 19, 287�290], hereafter H&B) on the properties and performance of the theta method, we derive new results for a unit root data generating process. In particular, (a) we investigate the theoretical underpinnings of the method when a single �theta line� is used, rather than a combination of two �theta lines� as in A&N and H&B, and we provide an optimal value for the theta parameter that coincides with the first-order autocorrelation of the innovations; (b) we demonstrate that the optimal forecast function for the model examined in A&N is identical with that of ARIMA(1,1,0) and (c) we provide formulae for optimal weights when combining two �theta lines� as in the model used by A&N in M3 competition�rather than an optimal value for the drift as in H&B. The paper concludes with a series of simulations as well as empirical investigations on the M3 yearly data.

Item Type: Article
Subjects: Research Publications
Departments: College of Business, Law, Education and Social Sciences > Bangor Business School
Date Deposited: 09 Dec 2014 16:47
Last Modified: 23 Sep 2015 03:10
ISSN: 1471-678X
URI: http://e.bangor.ac.uk/id/eprint/1083
Identification Number: DOI: 10.1093/imaman/dps030
Publisher: Oxford University Press
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