Estimating Trends with Percentage of Smoothness Chosen by the User

This work presents a method for estimating trends of economic time series that allows the user to fix at the outset the desired percentage of smoothness for the trend. The calculations are based on the Hodrick-Prescott (HP) filter usually employed in business cycle analysis. The situation considered here is not related to that kind of analysis, but with describing the dynamic behaviour of the series by way of a smooth curve. To apply the filter, the user has to specify a smoothing constant that determines the dynamic behaviour of the trend. A new method that formalizes the concept of trend smoothness is proposed here to choose that constant. Smoothness of the trend is measured in percentage terms with the aid of an index related to the underlying statistical model of the HP filter. Empirical illustrations are provided using data on Mexico's GDP.