Predicting a Multitude of Time Series

Abstract

Principles for constructing estimators of the Stein type (shrinkage estimators) are discussed in general terms, with emphasis on underlying assumptions. The problem of parameter estimation and prediction for multiple time series is examined with these principles in mind, particularly for the case in which the number of time series is large and the number of observations from each series is small. Our results are applied to the problem of demand estimation in an inventory control setting.

Key Words:

• Multiple time series
• Stein estimators
• Shrinkage estimators