Trend-Cycle Decomposition of GDP: A Flexible Filter

The measurement of the Trend or long-term GDP is of vital importance for the characterization of macroeconomic scenarios. However, the usual filters are in some cases unstable when adding new data points and quite rigid in terms of their specification, which makes it difficult to calculate. This is especially relevant in contexts of greater uncertainty, where different shocks of varying magnitude can affect the aggregate economy. These filters are quite popular, although they could be unstable in very long series and with potential structural breaks. In this work a so-called 'flexible filter' is proposed, which is of the Cycle-Trend type, but which considers shocks with varying variances over time (Stochastic Volatility). The aforementioned filter is applied to quarterly data from the United States, Canada and Peru. In general, the consideration of a stochastic volatility component is a safe strategy against structural changes. Finally, the methodology also makes it possible to quantify the uncertainty associated with these estimates.