It is often the case that decision makers are presented with multiple forecasts for the same variable, produced perhaps from different forecasting models or experts. While attempting to identify a single ‘best forecast’ does offer a valid approach, favourable performance is often achieved through combining the N available forecasts in some way. As such, forecast combination presents a ubiquitous problem for decision makers in a wide array of fields, and provides the first focus of this thesis.

Although perhaps a seemingly simple problem, the combination of forecasts can prove difficult due to issues such as correlation between forecasts, and changing statistical properties of forecasters throughout time. In order to account for such nonstationary behaviour, it is necessary to combine the forecasts dynamically. In this thesis, we propose a dynamic linear model based procedure for combining point forecasts. This combination procedure works by creating a linearly weighted combination of forecasts, where the weights are allowed to evolve temporally in response to observed data. Following this, we consider the problem when one or more of the N forecasters fails to
provide a prediction at time t. We discuss how this can also be interpreted as a sudden change in forecaster quality, and provide adaptive methods for dealing with this.

As the second focus of this thesis, we examine another problem in nonstationary
time series, pertaining to the autoregressive process of order 1 (AR(1)). From two
bivariate AR(1) processes, we construct a nonstationary oscillating stochastic process, for which we derive key theoretical properties.