The quarterly national accounts trend-cycle filter versus model-based filters

In this paper, we first review the Spanish Quarterly National Accounts (Sqna) trend-cycle filter and give a formula to compute the first component of the filter that corrects an error in the expression that has been used in the Sqna System so far. Then, the results obtained with this last filter are compared to the ones obtained using the Tramo andSeats programs, which apply a model-based methodology. It is concluded that the {\sc Sqna} filter presents some problems, such us the generation of spurious cycles, a phase delay, non-efficient initial conditions and larger estimation errors, which can be avoided if model-based filters are used. A Hodrick-Prescott filter with a suitable smoothing parameter is proposed to smooth trend-cycle series that are somewhat volatile and have been obtained with model-based filters. In this way, smooth signals can be obtained that are free of spurious cycles.