Hodrick-Prescott filter (see Hodrick and Prescott (1997)) is a popular tool in macroeconomics for fitting smooth trend to time series. In SAS, we can use PROC UCM to realize the HP filter. The dataset considered in this example consists of quarterly real GDP for the United States from 1947-2016 (b illions of chained 2009 dollars , seasonally adjusted annual rate ). The data can be download from this link https://fred.stlouisfed.org/series/GDPC1 %macro hp(input= ,date= ,int= ,var= ,par= ,out= ); proc ucm data=&input; id &date interval=∫ model &var; irregular plot=smooth; level var= 0 noest plot=smooth; slope var=&par noest; estimate PROFILE; forecast plot=(decomp) outfor=&out; run; %mend ; % hp (input=gdp,date=year,int=qtr,var=gdp,par= 0.000625 ,out=result); I use SAS MACROS to define a function for HP filter. "input" is the data file you use, "date" is the variable for time, "int...