One-sided HP filter beginning of the sample


1.I have applied one-sided HP filter to log GDP per capita series and it produced first two observations of cycle component at technically zero (1E-07). It seems rather strange at that period economy was characterized by high unemployment and low GDP growth and so next few observations are negative. So is it a good idea to drop first observations when using one-sided HP filter ?

  1. I have only 56 observations, so mean of cyclical component after one-sided HP filtering is around -0.003. Is it proper to demean this series prior to using as observable in DSGE ?

Thanks for your reply.

  1. Any filter will introduce artifacts at the beginning/end of the sample. For a one-sided backward-looking filter, this will only happen at the beginning of the sample. For a two-sided filter, it will happen at the end as well. You could drop the first observations, but I am not sure that would solve the problem, because generally the Kalman filter is applied with the initial state being the steady state, i.e. 0.
  2. A small mean like that is nothing to worry about. It simply tells you that over the sample the shocks tended to have an on average negative effect.

Thank you for your advice. Best wishes !