The Hodrick–Prescott filter
Marcel Boumans · 2004
Kydland and Prescott (1996) did not use the Kalman filter but the ‘Hodrick-Prescott filter’ (HP filter). Its application was motivated by objective (1), that is, taking a moving average of the observations to extract one of the components. To simplify the discussion, we focus on time series containing only growth and business cycle components: = +g ct t ty y y component. In the subsequent discussion, filtering is understood as a way of detrending by representing the growth component as a moving average of the observed y == g t yBGygy )( where B is the backshift operator with Bnx t = x moving average of y t : ( ) ( )1ct t ty G B y C B y = − ≡ In the language of filtering theory, both G(B) and C(B) are linear filters.