Working Papers 1999 – Abstracts

1/99
Forecasting Models And Prediction Intervals For The Multiplicative Holt- Winters Method
Anne B. Koehler, Ralph D. Snyder, J. Keith Ord

A new class of models for data showing trend and multiplicative seasonality is presented. The models allow the forecast error variance to depend on the trend and/ or the seasonality. It can be shown that each of these models has the same updating equations and forecast functions as the multiplicative HoltWinters method, regardless of whether the error variation in the model is constant or not. While the point forecasts from the different models are identical, the prediction intervals will, of course, depend on the structure of the error variance and so it is essential to be able to choose the most appropriate form of model. Two methods for making this choice are presented and examined by simulation.

2/99
Generalized Additive Modelling Of Mixed Distribution Markov Models With Application To Melbourne's Rainfall.
Rob J. Hyndman and Gary K. Grunwald

We consider modelling time series using a generalized additive model with first- order Markov structure and mixed transition density having a discrete component at zero and a continuous component with positive sample space. Such models have application, for example, in modelling daily occurrence and intensity of rainfall, and in modelling the number and size of insurance claims. We show how these methods extend the usual sinusoidal seasonal assumption in standard chain- dependent models by assuming a general smooth pattern of occurrence and intensity over time. These models can be fitted using standard statistical software. The methods of Grunwald and Jones (1998) can be used to combine these separate occurrence and intensity models into a single model for amount. We use 36 years of rainfall data from Melbourne, Australia, as a vehicle of illustration, and use the models to investigate the effect of the El Niño phenomenon on Melbourne's rainfall.

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