Modelling an Forecasting Time series Sampled at Different Frequencies

This paper discusses how to specify an observable high-frequency model for a vector of time series sampled at high and low frequencies. To this end we first study how aggregation over time affects both, the dynamic components of a time series and their observability, in a multivariate linear framework. We find that the basic dynamic components remain unchanged but some of them, mainly those related to the seasonal structure, become unobservable. Building on these results, we propose a structured specification method built on the idea that the models relating the variables in high and low sampling frequencies should be mutually consistent. After specifying a consistent and observable high-frequency model, standard state-space techniques provide an adequate framework for estimation, diagnostic checking, data interpolation and forecasting. Our method has three main uses. First, it is useful to disaggregate a vector of low-frequency time series into high-frequency estimates coherent with both, the sample information and its statistical properties. Second, it may improve forecasting of the low-frequency variables, as the forecasts conditional to high-frequency indicators have in general smaller error variances than those derived from the corresponding low-frequency values. Third, the resulting forecasts can be updated as new high-frequency values become available, thus providing an effective tool to assess the effect of new information over medium term expectations. An example using national accounting data illustrates the practical application of this method.