Temporal Aggregation of Economic Time Series 1 Temporal Aggregation of Economic Time

We call temporal aggregation the situation in which a variable that evolves through time can not be observed at all dates. This phenomenon arises frequently in economics, where it is very expensive to collect data on certain variables, and there is no reason to believe that economic time series are collected at the frequency required to fully capture the movements of the economy. For example, we only have quarterly observations on GNP, but it is reasonable to believe that the behavior of GNP within a quarter carries relevant information about the structure of the economy. In order to give a mathematical structure to this problem, we assume that there is an underlying stochastic process in continuous time that is observed only at discrete intervals. This structure has been used (1971) and Geweke (1978) to describe the effects of temporal ion in the distributed lag model. will be concerned with the issues that arise in the study of linear edictions of future values of the variables given all information up to e present. In other words, if we have a vector of n variables y, we try to predict y;(t + 1) using a function of the form CEO p i y(t k). Since the fundamental moving average representation (henceforth AR) of a stochastic process (or Wold decomposition) is a good sumof the properties of those predictions, we will describe what is the onship between the Wold decomposition of the unobserved wntintime process and the Wold decomposition of the discrete sampled