An Ad Hoc Method for Forecasting Series with Zero Values

Abstract

When forecasting the demand for a product, it is sometimes necessary to model time series which are a mixture of zeros (i.e., no demand) and values much larger than zero. An ad hoc method is presented which consists of decomposing the original series into two series, one of which consists only of non-zero values, while the other is modeled as a Markov chain with states zero and one. The non-zero values are modeled as an ARIMA process. The Markov chain is classified using a statistical method due to Tong. These two series can then be used to generate an ensemble of forecasts for a given lead time, each with a specified probability of occurrence. Two illustrations of the method are made to series which represent market demand for steel.