The Effect of Overlapping Aggregation on Time Series Models: An Application to the Unemployment Rate in Brazil

Abstract

The unemployment rate of SEADE/DIEESE, Brazil, is reported as a weighted average of the last three months. If xt denotes the original series observed at a certain time interval, the published series, yt, is roughly constructed as a weighted average of the last observations, i.e., (...) for (...), ... with the restrictions that (...) and (...) for every i and t. This problem is a special case of the overlapping aggregation or the use of moving-average filters in time serie models. This paper studies the effect of using moving-average filters in time series models, assuming that the original series could be characterized by an ARIMA process. It is also studied the effect of this kind of aggregation on identification, estimation, prediction and on the seasonal and trend components of time series models as well as detecting turning points and on the dynamic relationship between variables.