Statistical Modelling

Statistical models provide an alternative approach to using dynamical models in seasonal climate forecasting. In statistical models relationships between one set of data, the predictors, and a second set, the predictands, are sought. Common predictands include seasonal mean temperatures and accumulated precipitation, and are typically predicted using antecedent sea surface temperatures primarily within the tropical oceans. Predictions are made on the assumption that historically observed relationships are expected to apply in the future. There are many conditions for such an assumption to be valid, including the need for high-quality datasets to ensure that the historical relationships are robustly measured, and the need for relationships to have a sound theoretical basis. Because of the possibility of identifying spurious relationships between the predictors and the predictands, the statistical model should be tested carefully on independent data. Most statistical models are based on linear regression, which provides a “best guess” forecast under the assumption that a given change in the value of a predictor results in a constant change in the expected value of the predictand regardless of the value of the predictor. Modifications to the linear model can be made or alternative statistical procedures used when there is good reason to expect a relationship to be nonlinear. However, other weaknesses of linear regression may also require these alternatives to be considered seriously. The primary problems with linear regression are multiplicity, multicolinearity, and non-normality of the predictands. Multiplicity refers to the effects of having a large number of candidate predictors: the danger of finding a spurious relationship increases. Multicolinearity arises when more than one predictor is used in the model and there are strong relationships between the predictors which can result in large errors in calculating the parameters of the model. Finally, a linear regression model may not be adequately constructed if the data being predicted have a strongly skewed or otherwise non-Gaussian distribution; seasonally accumulated precipitation often exhibits such problems. Alternative forms of linear and non-linear statistical models can be applied to address such distributional problems.