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The application of a methodology that proposes the use of spectral methods to inform the development of statistical forecasting models for cholera case data is explored in this paper. The seasonal behaviour of the target variable (cholera cases) is analysed using singular spectrum analysis followed by spectrum estimation using the maximum entropy method. This seasonal behaviour is compared to that of environmental variables (rainfall and temperature). The spectral analysis is refined by means of a cross-wavelet technique, which is used to compute lead times for co-varying variables, and suggests transformations that enhance co-varying behaviour. Several statistical modelling techniques, including generalised linear models, ARIMA time series modelling, and dynamic regression are investigated for the purpose of developing a cholera cases forecast model fed by environmental variables. The analyses are demonstrated on data collected from Beira, Mozambique. Dynamic regression was found to be the preferred forecasting method for this data set. Keywords:Cholera, modelling, signal processing, dynamic regression, negative binomial regression, wavelet analysis, cross-wavelet analysis.ORiON Vol. 24 (1) 2008: pp. 17-36

In every country the prosecution of criminal cases is governed by different laws, policies and processes. In South Africa, the National Prosecuting Authority (NPA) has the responsibility of planning and managing all prosecution functions. The NPA has certain unique characteristics that make it different from other similar organisations internationally. The development of a planning tool that the NPA could use to plan their future resource requirements over the short to medium term required extensive modelling, and its final form included features which, to the best knowledge of the development team, make it unique both locally and internationally. Model design was largely influenced by the challenges emanating from the special requirements and context of the problem. Resources were not forecasted directly, but were derived with the help of simulation models that traced docket flows through various resource-driven processes. Docket flows were derived as a proportion of reported crimes, and these were forecasted using a multivariate statistical model which could take into account explanatory variables as well as the correlations between the patterns observed within different crime categories. The simulation consisted of a number of smaller models which could be run independently, and not of one overarching model. This approach was found to make the best use of available data, and compensated for the fact that certain parameters, linking different courts and court types, were not available. In addition, it simplified scenario testing and sensitivity analysis. The various components of the planning tool, including inputs and outputs of the simulation models and the linkages between the forecasts and the simulation models, were implemented in a set of spreadsheets. By using spreadsheets as a common user interface, the planning tool could be used by prosecutors and managers who may not have extensive mathematical or modelling experience.