Forecasting an Accumulated Series Based on Partial Accumulation: A Bayesian Method for Short Series with Seasonal Patterns

In this paper, the problem of forecasting a time series with only a small amount of data is addressed within the Bayesian framework. The quantity to be predicted is the accumulated value of a positive and continuous variable for which some partially accumulated data has been observed. These conditions appear in a natural way in the prediction of sales of style goods and coupon redemption among many other examples. A very simple model is proposed to describe the relation between the partial and the total value to be forecasted under the assumption of stable seasonality. Analytic results are obtained for both, the pointwise forecast and the entire posterior predictive distribution. The proposed technique does not involve any approximation. Moreover, 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. Some real examples are included. (Bayesian Statistics; Forecast; Stable Seasonality)