Temporal Aggregation in Dynamic Linear Models

Abstract

One important aspect concerning the analysis and forecasting of time series that is sometimes neglected is the relationship between a model and the sampling interval, in particular, when the observation is cumulative over the sampling period. This paper intends to study the temporal aggregation in Bayesian dynamic linear models (DLM). Suppose that a time series Yt is observed at time units t and the observations of the process are aggregated over r units of time, defining a new time series Zk=Σri=1Yrk+i. The relevant factors explaining the variation of Zk can, and in general will, be different, depending on how the sampling interval r is chosen. It is shown that if Yt follows certain dynamic linear models, then the aggregated series can also be described by possibly different DLM. In the examples, the industrial production of Brazil is analysed under various aggregation periods and the results are compared. © 1997 John Wiley & Sons, Ltd.