PROC UCM: Forecast

[Yamani]

Hello all,

I want to run out-of-sample forecasts with rolling regressions for N countries from September 2008 to August 2017 *************;

********************************************************* Data Set *****************************************

* My dataset is panel monthly data with 10 countries

* Sample period: From December 1996 to August 2017.

Here is an example to show my data set.

Date                  Country     Y       X      Number      Observation

12/31/1996       Australia                           1                   1

01/31/1997      Australia                            1                   2

......

.....

.....

08/31/2017     Australia                              1                   250

12/31/1996     Canada                               2                   1

........

.......

08/31/2017     Australia                              2                  250

......

.....

......

12/31/1996     UK                                      10                   1

.......

......

......

08/31/2017     UK                                      10                   250

****************** Modified Data set ********************************************

I modified the above data set by creating a new date variable called 'Rankdate' that shows the ending date in each rolling regression, as follows:

    Rankdate                     Date             Country     Y       X       Number      Observations

 August 2008             12/31/1996       Australia                            1                   1

 August 2008              01/31/1997      Australia                            1                   2

......

August 2008               08/31/2008      Australia                           1                 

September 2008         01/31/1997       Australia                          1                

.....

September 2008         09/30/2008     Australia                              1                 

...................

.....................

August 2017                  12/31/2005       Australia                          1 

............

August 2017                  08/30/2017       Australia                          1               

August 2008                  12/31/1996        Canada                             2                   

........

.......

......

.....

......

August 2017            08/31/2017                   UK                            10

************************************ Goal: Run Recursive Regression ************************************

* I want to run several recursive regressions for EACH country (i.e. keeps the starting date (i.e., December 1996) fixed,

and then adding an observation to the end of the sample with every run of the regression).
More specifically, I run the following sas code:

PROC UCM DATA = ma.developingrank(where=(country='CZ')); BY rankdate;
ID DATE INTERVAL=MONTH;
MODEL RETURN = MA;
IRREGULAR;
level var=0;
estimate back=1 outest=ma.OOSRollEst1;*The default is BACK=0,
which means that the forecast starts at the end of the available data;
FORECAST back=1 LEAD=1 outfor=ma.OOSRollRes1 plot=forecasts;
*forecast span;*This reports the one-step ahead out-of-sample forecast;
RUN;

My problem, however, is that the above code gives me forecast for each rolling window, and I don't know which model to report in my paper, and HOW?

Thanks for your help in advance.  

[rselukar]

Your question has many parts.  I am going to answer the part about the computation of rolling forecasts.  What to do with these rolling forecasts is up to you.

Currently there is no option in the UCM procedure to produce rolling forecasts.  Until such an option becomes available, one must resort to repeated calls to UCM (quite inefficient and tedious).  I am going to illustrate one such way.

First some notation.  Suppose we have N measurements on a response variable y: y_1, y_2, ..., y_N.  For h >= 1, let F(t,h) denote the h-step-ahead forecast of y_(t+h) using data y_1, y_2, ..., y_t.  When (t+h) <= N, let E(t,h) = y_(t+h) - F(t,h) denote the (in-sample) h-step-ahead residual.  The UCM procedure provides one-step-ahead (h=1) forecasts and residuals, F(t,1) and E(t,1), for many time instances t within the historical period by default.  However, the in-sample multi-step-ahead forecasts and residuals
(F(t,h) and E(t,h) for h > 1) are NOT provided for different time instances.  The computation of rolling forecasts (and residuals) involves computation of F(t,h) and E(t,h) for various t and h combinations where (t+h) <= N.  Unfortunately, at the moment there is no simple option to output all possible rolling forecasts in a single UCM call.    On the other hand, you can make repeated UCM calls with different holdout periods (BACK= option in the FORECAST statement) to get the necessary rolling forecasts.  When you use BACK=k, you get F(N-k, h) and E(N-k,h) for h=1, 2,..,k.  Of course, this is not a very efficient way to get the rolling forecasts.  But at the moment this is the simplest way I can think of.  The "roll" macro given below provides an illustration.  The "roll" macro makes repeated calls to UCM to create a large data set--finalFor--that contains the rolling forecasts.  Actually, finalFor must be processed further to extract the rolling forecasts.  For example, the last k values of for k column in finalFor correspond to F(N-k, h) for h=1, 2, ..,k.  You can then rearrange these numbers: for example, collect all 3-step ahead forecasts in a new data set.  It does get tedious but the necessary numbers are in the output table finalFor. 

/*------- illustration ---------*/

/* estimate model parameters */
proc ucm data=sashelp.air;
   id date interval=month;
   model air;
   irregular;
   level;
   slope variance=0 noest;
run;

%let start = 5;
%let end = 6;
%macro roll;
%do k=&start %to &end; /* different values of BACK= option */
    /* model parameters from the earlier call */
 proc ucm data=sashelp.air;* noprint;
    id date interval=month;
    model air;
    irregular variance=0.00027444 noest;
    level variance=1139.35114 noest;
    slope variance=0 noest;
    forecast back=&k lead=&k outfor=for;
 run;
 data rfor;
    set for(keep=date air forecast residual std);
    for_&k = forecast;
    std_&k = std;
    residual_&k = residual;
 run;
 %if &k = 5 %then %do;
    data finalFor;
       set rfor;
    run;
 %end;
 %else %do;
    data finalFor;
       merge rfor finalFor;
    run;
 %end;
%end;
%mend;

%roll;
run;