Gain of the one-sided HP Filter

Hello everyone,

I’m working on the one-sided version HP filter, and i’m trying to use the analytical formula (gain) of this last one to try and approximate (adjuste) the lambda parameter to converge to a two-sided HP filter. Do anyone have some papers that have a analytical formula for the gain of the one-sided HP Filter, or is it a lost cause ?

Did you check


Yeah, i checked it but on this article they’re computing weights to use it as a moving average, while i’m trying to see if it’s possible to have an analytical formula like this one : lambda_ * (4 * (1 - np.cos(omega)))**2) / (1 + lambda_ * (4 * (1 - np.cos(omega)))**2 (this is the formula for the two sided hp filter)

I haven’t seen anything like that.

okey, that should answer my question. Thank you for you time