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

We present a Bayesian solution to forecasting a time series when few observations are available. The quantity to predict is the accumulated value of a positive, continuous variable when partially accumulated data are observed. These conditions appear naturally in predicting sales of style goods and coupon redemption. A simple model describes the relation between partial and total values, assuming stable seasonality. Exact analytic results are obtained for point forecasts and the posterior predictive distribution. Noninformative priors allow automatic implementation. The procedure works well when standard methods cannot be applied due to the reduced number of observations. Examples are provided.