Bayesian forecasts following a major level change in exponential smoothing

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Abstract
Exponential smoothing techniques enjoy a wide range of applications to problems in signal detection, inventory and production control, financial planning, and many other areas of business and engineering. One of the most useful models used to explain the theoretical structure of the process is a changing levels model, in which the underlying level of the stochastic process is assumed to undergo random changes in each time period. The observation is modelled as a noisy disturbance of this level. Occasionally a major intervention or level change occurs that is much larger than the typical period‐to‐period fluctuation in the random level. Using a Bayesian approach it is the purpose of this paper to show how the distribution of the major level change can be detected, estimated and then incorporated in forecasts. Updating equations are obtained for the posterior mean and variance of the major level change as well as the new level.

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