An alternative approach to estimating the parameters of a generalised Grey Verhulst model: An application to steel intensity of use in the UK

• A more reliable method for estimating the parameters of GM(n,m) models.
• A diagnostic for deciding whether a chosen GM(n,m) is data compatible.
• A generalisation of the Grey–Verhulst offering greater flexibility for data fitting.
• Derivation of short to medium term predictions of steel intensity of use in the UK.

Being able to forecast time series accurately has been quite a popular subject for researchers both in the past and at present. However, researchers have resorted to various forecasting models that have different mathematical backgrounds, such as statistical time series models, causal econometric models, artificial neural networks, fuzzy predictors, evolutionary and genetic algorithms. In this paper, a brief review of a relatively new approach, known as grey system theory is provided. The paper offers an alternative approach to estimating the unknown parameters of the well know GM(1,1) and it is shown that this alternative procedure provides more reliable parameter estimates together with a simple visual framework for assessing whether the properties of the chosen GM(1,1) model are consistent with the actual data. In this paper a flexible generalisation of the Grey–Verhulst model is put forward which when applied to UK steel intensity of use produces very reliable multi step ahead predictions.