Forecasting an accumulated series based on partial accumulation II: A new Bayesian method for short series with stable seasonal patterns

The problem of forecasting a time series with only a small amount of data is addressed within a Bayesian framework. The quantity to be predicted is the accumulated value of a positive and continuous variable for which partially accumulated data are available. These conditions appear in a natural way in many situations. A simple model is proposed to describe the relationship between the partial and total values of the variable to be forecasted assuming stable seasonality, which is specified in stochastic terms. Analytical results are obtained for both the point forecast and the entire posterior predictive distribution. The proposed technique does not involve approximations. It allows the use of non-informative priors so that implementation may be automatic. The procedure works well when standard methods cannot be applied due to the reduced number of observations. It also improves on previous results published by the authors. Some real examples are included.