Exponential smoothing and non-negative data


15 June 2008


ISF 2008, Nice, France


Abstract: The most common forecasting methods in business are based on exponential smoothing and the most common time series in business are inherently non-negative. Therefore it is of interest to consider the properties of the potential stochastic models underlying exponential smoothing when applied to non-negative data. We explore nonlinear exponential smoothing state space models for non-negative data under various assumptions about the innovations, or error, process.

We discuss three problems with exponential smoothing state space models for non-negative data:

  1. The forecasts and prediction intervals can be negative
  2. The forecast distributions can have infinite variance
  3. The processes can converge to zero almost surely.

We propose a new model with similar properties to exponential smoothing, but which does not have these problems, and we develop some distributional properties for our new model.

Download pdf