Lagged dependent variable as input to the model

[ArseneWenger]

I am trying to introduce AR1 term into my models (lag of dependent variable). It is easy to do for the for the historic period which is lag(y). But I am wondering how to create it for the forecast period (it would actually be the lag of the prediction).  Is ther any SAS procedure or autoreg can do this??  My data looks like:

Date                                    Y                            lag(y)                    X1           X2

…                                          .006                      ….                        12           7

Q1 2016                              .005                      .006                      1             3             

Q2 2016                              .004                      .005                      11           7

Q3 2016                              .003                      .004                      8             7

Q4 2016                              .004                      .003                      10           6

Q1 2017                              .                             .004                      12           5

Q2 2017                              .                             .                             11           4

Q3 2017                              .                             .                             10           3

Q4 2017                              .                             .                             11           4

….

How do I populate lag(Y) for qtr’s Q2 2017 & beyond so that I can use it in regression??

Thanks in advance.

[alexchien · Accepted solution]

Input Variables and Regression with ARMA Errors

You can use PROC ARIMA from SAS/ETS with p = 1 (AR1) along with x1 and x2 as input variables. 

   proc arima data=<yourdata>;
      identify var=y crosscorr=(x1 x2);
      estimate p=1 input=(x1 x2);
   run;

[mkeintz]

You want a one period lead for Y.  I like @alexchien's answer, but here is a way to get a one period lead:

data need;

  merge have

             have (firstobs=2 keep=y rename=(y=y_lead1));

run;