An investigation of aggregate variable time series forecast strategies with specific subaggregate time series statistical correlation

In order to meet demand for family-based forecasting systems, firms such as IBM and American Software, Inc. offer software packages capable of forecasting demand for individual items and families of items. These systems, sometimes referred to as constrained or hierarchical forecasting (HF), are based upon a user defined strategy for aggregating items into families. HF systems are for determining forecasts for items and their respective families following either a direct strategy, which utilizes the contemporaneous demand values to compute a forecast, or a derived strategy, which determines forecasts for items by proportioning a parent family forecast. The objectives of HF systems include improved forecast performance and a reduction in the overall forecasting burden. HF strategies rely upon the premise that forecasts for families of items are more accurate than forecasts for individual items. Research literature indicates that HF system forecast performance is dependent upon the statistical nature of the items comprising the aggregated family. This literature further suggests that families be formed such that important information (demand patterns) exhibited within the item-level time series does not get lost when summing these series to define the aggregated group time series. Therefore, families of HF systems would logically be defined to provide a high degree of homogeneity, or positive correlation among family members. This strategy suggests that a group of homogeneous items will tend to result in an aggregate time series which exhibits (or at least does not obscure) data patterns present in time series of the component items comprising the family. This study is an examination of strategies and guidelines for specifying aggregated families within HF systems. In particular, simulation is used as the vehicle to measure forecast performance at the aggregate (family) level. Varying degrees of systematically controlled, statistical correlation between subaggregate (item) time series comprising the forecast families is investigated using all four combinations of two forecast smoothing techniques and two forecast strategies. The results of this study support the research literature conclusion that higher positive correlation does indeed lead to improved forecast performance at the aggregate level. However, the results also indicate that higher negative correlation also leads to improved forecast performance at the aggregate level. An additional observation suggests that direct forecasts of an aggregate variable are more accurate than derived forecasts.