Continuous Time Models to Extract a Signal in Presence of Irregular Surveys

A typical statistical problem arises when a time series consists of observations collected using two different timing intervals. This is often the case in Statistical Offices, when the frequency of their surveys changes. In such cases the classical tools to deal with signal extraction, such as the Hodrick-Prescott filter, are used on the most recent homogeneous span, losing information deriving from the previous period; alternative solutions are to aggregate or disaggregate the series to obtain the same frequency. To use all the available information we exploit the fact that the Hodrick-Prescott filter has a state-space representation in a continuous time support, which provides the possibility to deal with different spans. In this paper we investigate the advantages of the continuous time models in extracting a trend from a time series with respect to the Hodrick-Prescott filter in the presence of irregular surveys. The flexibility of this model will be highlighted through examples of Monte Carlo experiments and an application on real data.

Keywords: Hodrick-Prescott filter, smoothing parameter, cubic spline, state-space model.