Count Series Forecasting

Many organizations need to forecast large numbers of time series that are discretely valued. These series, called count series, fall approximately between continuously valued time series, for which there are many forecasting techniques (ARIMA, UCM, ESM, and others), and intermittent time series, for which there are few forecasting techniques (Croston’s method and others). This paper proposes a technique for large-scale automatic count series forecasting and uses SAS Forecast Server and SAS/ETS software to demonstrate this technique. INTRODUCTION Most traditional time series analysis techniques assume that the time series values are continuously distributed. For example, autoregressive integrated moving average (ARIMA) models assume that the time series values are generated by continuous white noise passing through various types of filters. When a time series takes on small, discrete values (0, 1, 2, 3, and so on), this assumption of continuity is unrealistic. By using discrete probability distributions, count series analysis can better predict future values and, most importantly, more realistic confidence intervals. In addition, count series often contain many zero values (a characteristic that is called zero-inflation). Any realistic distribution must account for the “extra” zeros. Count series analysis includes in the following analyses:  Forecasting count series: From the historical count series values, you can predict its future values and generate confidence intervals that are discretely valued. Count series forecasting is important for inventory replenishment where unit demand is very low. For example, the demand for spare parts in a particular week is small and discretely valued.  Monitoring count series: You can monitor recent values of a count series to detect anomalous values from its historical values. Count series monitoring is important for monitoring processes that generate count data. For example, the number of failures in an industrial process and the many devices in the new world of the Internet of Things generate counts over time (count series data). The paper combines proven traditional time series analysis techniques with proven discrete probability distribution analysis techniques to propose a novel technique for forecasting and monitoring count series. MOTIVATION AND SCOPE Many real-world time series data are not continuously valued. Sometimes these time series values are small and discretely valued. This situation is true for many inventory control problems that are related to “slow moving items.” Figures 1 through 4 illustrate the issues of concern. Figure 1. Time Series Plot Figure 2. Seasonal Component