Article ID: | iaor201412 |
Volume: | 25 |
Issue: | 1 |
Start Page Number: | 105 |
End Page Number: | 124 |
Publication Date: | Jan 2014 |
Journal: | IMA Journal of Management Mathematics |
Authors: | Nikolopoulos K, Thomakos D |
Keywords: | forecasting: applications, simulation: applications |
In this paper, building on earlier work by Assimakopoulos and Nikolopoulos (2000) and Hyndman and Billah (2003) 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.