FAQ: how do I extract the output gap?

I study potentials and gaps, permanent and transitory fluctuations in macroeconomic variables using the Smets and Wouter (2007) model. Model-based gaps display low frequency variations; possess more than business cycle fluctuations; have similar frequency representation as potentials, and are correlated with them. Permanent and transitory fluctuations display similar features, but are uncorrelated. I use a number of filters to extract trends and cycles using simulated data. Gaps are best approximated with a polynomial filter; transitory fluctuations with a differencing approach, but distortions are large. Explanations for the results are given. I propose a filter which reduces the biases of existing procedures.