Hodrick-Prescott Filter Comparison

[PG007]

Dear All,

I'm looking into different ways of applying the Hodrick-Prescott Filter and I'm getting different results between the procedures below. I have not been able to understand these differences based on the online documentation and was hoping you might have some insight.

The first approach uses proc expand:

proc expand data=Int_qtr_l out=filter_data_out

method=none;

id Year_quarter2;

Convert ODR_l=ODR_l_hpt/transformout=(hp_t 1600);

Convert ODR_l=ODR_l_hpc/transformout=(hp_c 1600);

run;

While the 2nd uses proc UCM:

proc ucm data=Int_qtr_l ;

id Year_quarter2 interval=qtr;

model ODR_l;

irregular plot=smooth print=smooth;

level var=0 noest plot=smooth print=filter;

slope var=0.000625 noest print=filter;

estimate PROFILE;

forecast plot=(decomp);

run;

I was expecting the smoothed irregular component from proc ucm to match the cyclical HP series from proc expand, but there seems to be fairly large differences.

Any ideas?

Thanks 

[PG007]

Dear All,

I'm looking into different ways of applying the Hodrick-Prescott Filter and I'm getting different results between the procedures below. I have not been able to understand these differences based on the online documentation and was hoping you might have some insight.

The first approach uses proc expand:

proc expand data=Int_qtr_l out=filter_data_out

method=none;

id Year_quarter2;

Convert ODR_l=ODR_l_hpt/transformout=(hp_t 1600);

Convert ODR_l=ODR_l_hpc/transformout=(hp_c 1600);

run;

While the 2nd uses proc UCM:

proc ucm data=Int_qtr_l ;

id Year_quarter2 interval=qtr;

model ODR_l;

irregular plot=smooth print=smooth;

level var=0 noest plot=smooth print=filter;

slope var=0.000625 noest print=filter;

estimate PROFILE;

forecast plot=(decomp);

run;

I was expecting the smoothed irregular component from proc ucm to match the cyclical HP series from proc expand, but there seems to be fairly large differences.

Any ideas?

Thanks 

[Ksharp]

It is time series analysis, Plz post it at Forecast Forum .

[rselukar · Accepted solution]

Your expectation is reasonable.  Even if UCM and EXPAND use quite different algorithms (UCM is based on Kalman Filtering/Smoothing, while EXPAND computes HP filter by inverting a suitable matrix) the results should be close.  In my test case (shown below) this indeed happens.  Of course, numerical difference can arise for a variety of reasons when different algorithms are used.  Anyway, here is the test case (your program with a SASHEL data set).  In this case the differences are of the order 10^(-10):

proc ucm data=sashelp.gnp;

id date interval=qtr;

model gnp;

irregular ;

level var=0 noest ;

slope var=0.000625 noest;

estimate PROFILE;

forecast outfor=fucm lead=0;

run;

proc expand data=sashelp.gnp(keep=date gnp) out=fexp

method=none;

id date;

Convert gnp=hpt/transformout=(hp_t 1600);

Convert gnp=hpc/transformout=(hp_c 1600);

run;

data out;

merge fexp fucm(keep=date gnp s_irreg s_level);

by date;

label hpt = "HP_Trend";

label hpc = "HP_Cycle";

hptMucmt = hpt-s_level;

hpcMucmc = hpc-s_irreg;

run;

proc print data=out;

var date hptMucmt hpcMucmc;

run;

[PG007]

Thanks for the help! 

In case this helps anyone else, I believe the differences were due to a single missing value in the series I hadn't noticed 🙂