The effect of temporal aggregation on the estimation accuracy of time series models

In time series analysis, Autoregressive Moving Average (ARMA) models play a central role. Because of the importance of parameter estimation in ARMA modeling and since it is based on aggregate time series so often, we analyze the effect of temporal aggregation on estimation accuracy. We derive the relationships between the aggregate and the basic parameters and compute the actual values of the former from those of the latter in order to measure and compare their estimation accuracy. We run a simulation experiment that shows that aggregation seriously worsens estimation accuracy and that the impact increases with the order of aggregation.