Temporal Aggregation of an Econometric Equation

Abstract

: Structural breaks in an economy may make the time period available for estimation of an econometric equation exceedingly short. To use the existing information efficiently, it may be profitable to use high-frequency data, say monthly data, for estimation of a particular equation, even if the rest of the model is expressed in terms of data of lower frequency, say quarterly or half-yearly. In order to be included in the model, this equation has to be transformed to the same data frequency as the rest of the model. If the variables are of different types, or if some of the variables are lagged, exact transformations to equations that produce equivalent predicted values of the dependent variable are not possible. This note gives approximations and estimates for the various terms of the equations. Linear interpolation estimates as well as estimates that are optimal in a certain sense are given for the case of aggregation of monthly variables to semi-annual ones. It turns out that in the exchange rate equation in the KOSMOS model, the approximations do not increase the equation error substantially. Keywords: Short time series, structural breaks, temporal aggregation. Acknowledgement: The research reported in this paper was sponsored by the National Institute of Economic Research. The author wants to thank Alek Markowski and Lars-Erik ller for fruitful suggestions and Jan Alsterlind for important help. 2 1.