Modeling data with multiple time dimensions

A large class of problems in time series analysis can be represented by a set of overlapping time series with different starting times. These time series may be treated as different probes of the same underlying process. Such probes may follow a characteristic lifecycle as a function of the time since the series began. They may also be subject to environmental shocks according to calendar time. In addition, the calibration of each probe may be unknown such that each series may show a different magnitude of response to the underlying lifecycles and environmental impacts. This paper describes an approach to analyzing these multiple time series as a single set such that the underlying lifecycles and calendar-based shocks may be measured. Simultaneously, the individual calibrations of the time series are also measured. This technique is referred to as dual-time dynamics, and it applies to many important business problems. Applications to tree ring analysis, the SETI@home project, and retail loan portfolio forecasting are provided. Other areas of possible application include digital media services, insurance, human resource management, health care, and biological systems to name a few. (c) 2007 Elsevier B.V. All rights reserved.