Resources

Dynamic Factor Modeling

/*--------------------------------------------------------------
                    SAS Sample Library

       Name: ssmex07.sas
       Description: Example program from SAS/ETS User's Guide,
              The SSM Procedure
       Title: Dynamic Factor Modeling
       Product: SAS/ETS Software
        Keys: Dynamic Factor Modeling
        PROC: SSM
        Notes:

--------------------------------------------------------------*/

 title;

data Dns;
input date : date. yield maturity mtype;
format date date.;
datalines;
1-Jan-70    8.019    3    1
1-Jan-70    8.091    6    2
1-Jan-70    8.108    9    3
1-Jan-70    8.01     12   4
1-Jan-70    7.836   15    5
1-Jan-70    7.888   18    6
1-Jan-70    7.896    21    7
1-Jan-70    7.989    24    8
1-Jan-70    8.058    30    9
1-Jan-70    8.065    36  10
1-Jan-70    8.088    48  11
1-Jan-70    8.067    60  12
1-Jan-70    7.815    72  13
1-Jan-70    7.515    84  14
1-Jan-70    7.515    96  15
1-Jan-70    7.515  108  16
1-Jan-70    7.515  120  17
1-Feb-70    6.983     3    1
1-Feb-70    6.987    6    2
1-Feb-70    6.97    9    3
1-Feb-70    6.922    12    4
1-Feb-70    6.938    15    5
1-Feb-70    6.965    18    6
1-Feb-70    6.957    21    7
1-Feb-70    7.024    24    8
1-Feb-70    7.057    30    9
1-Feb-70    7.03    36    10
1-Feb-70    7.162    48    11
1-Feb-70    7.145    60    12
1-Feb-70    7.043    72    13
1-Feb-70    7.02    84    14
1-Feb-70    7.02    96    15
1-Feb-70    7.02    108    16
1-Feb-70    7.02    120    17
1-Mar-70    6.495    3    1
1-Mar-70    6.648    6    2
1-Mar-70    6.473    9    3
1-Mar-70    6.611    12    4
1-Mar-70    6.756    15    5
1-Mar-70    6.735    18    6
1-Mar-70    6.806    21    7
1-Mar-70    6.911    24    8
1-Mar-70    6.87    30    9
1-Mar-70    6.862    36    10
1-Mar-70    7.135    48    11
1-Mar-70    7.052    60    12
1-Mar-70    6.956    72    13
1-Mar-70    7.163    84    14
1-Mar-70    7.163    96    15
1-Mar-70    7.163    108    16
1-Mar-70    7.163    120    17
1-Apr-70    7.052    3    1
1-Apr-70    7.368    6    2
1-Apr-70    7.435    9    3
1-Apr-70    7.492    12    4
1-Apr-70    7.552    15    5
1-Apr-70    7.489    18    6
1-Apr-70    7.55    21    7
1-Apr-70    7.581    24    8
1-Apr-70    7.673    30    9
1-Apr-70    7.736    36    10
1-Apr-70    7.815    48    11
1-Apr-70    7.742    60    12
1-Apr-70    7.771    72    13
1-Apr-70    7.812    84    14
1-Apr-70    7.812    96    15
1-Apr-70    7.812    108    16
1-Apr-70    7.812    120    17
1-May-70    7.079    3    1
1-May-70    7.268    6    2
1-May-70    7.429    9    3
1-May-70    7.441    12    4
1-May-70    7.519    15    5
1-May-70    7.571    18    6
1-May-70    7.665    21    7
1-May-70    7.745    24    8
1-May-70    7.655    30    9
1-May-70    7.604    36    10
1-May-70    7.675    48    11
1-May-70    7.606    60    12
1-May-70    7.65    72    13
1-May-70    7.628    84    14
1-May-70    7.628    96    15
1-May-70    7.628    108    16
1-May-70    7.628    120    17
1-Jun-70    6.585    3    1
1-Jun-70    6.677    6    2
1-Jun-70    7.136    9    3
1-Jun-70    7.192    12    4
1-Jun-70    7.262    15    5
1-Jun-70    7.367    18    6
1-Jun-70    7.411    21    7
1-Jun-70    7.453    24    8
1-Jun-70    7.529    30    9
1-Jun-70    7.571    36    10
1-Jun-70    7.629    48    11
1-Jun-70    7.543    60    12
1-Jun-70    7.501    72    13
1-Jun-70    7.746    84    14
1-Jun-70    7.746    96    15
1-Jun-70    7.746    108    16
1-Jun-70    7.746    120    17
1-Jul-70    6.466    3    1
1-Jul-70    6.643    6    2
1-Jul-70    6.87    9    3
1-Jul-70    6.811    12    4
1-Jul-70    6.989    15    5
1-Jul-70    7.102    18    6
1-Jul-70    7.154    21    7
1-Jul-70    7.186    24    8
1-Jul-70    7.276    30    9
1-Jul-70    7.318    36    10
1-Jul-70    7.485    48    11
1-Jul-70    7.373    60    12
1-Jul-70    7.369    72    13
1-Jul-70    7.466    84    14
1-Jul-70    7.466    96    15
1-Jul-70    7.466    108    16
1-Jul-70    7.466    120    17
1-Aug-70    6.396    3    1
1-Aug-70    6.717    6    2
1-Aug-70    6.864    9    3
1-Aug-70    6.8    12    4
1-Aug-70    6.833    15    5
1-Aug-70    6.962    18    6
1-Aug-70    7.036    21    7
1-Aug-70    7.012    24    8
1-Aug-70    7.072    30    9
1-Aug-70    7.191    36    10
1-Aug-70    7.363    48    11
1-Aug-70    7.255    60    12
1-Aug-70    7.239    72    13
1-Aug-70    7.512    84    14
1-Aug-70    7.512    96    15
1-Aug-70    7.512    108    16
1-Aug-70    7.512    120    17
1-Sep-70    5.923    3    1
1-Sep-70    6.586    6    2
1-Sep-70    6.555    9    3
1-Sep-70    6.594    12    4
1-Sep-70    6.541    15    5
1-Sep-70    6.648    18    6
1-Sep-70    6.584    21    7
1-Sep-70    6.555    24    8
1-Sep-70    6.687    30    9
1-Sep-70    6.829    36    10
1-Sep-70    6.978    48    11
1-Sep-70    7.05    60    12
1-Sep-70    7.07    72    13
1-Sep-70    7.266    84    14
1-Sep-70    7.266    96    15
1-Sep-70    7.266    108    16
1-Sep-70    7.266    120    17
1-Oct-70    5.938    3    1
1-Oct-70    6.16    6    2
1-Oct-70    6.353    9    3
1-Oct-70    6.324    12    4
1-Oct-70    6.351    15    5
1-Oct-70    6.479    18    6
1-Oct-70    6.517    21    7
1-Oct-70    6.511    24    8
1-Oct-70    6.492    30    9
1-Oct-70    6.703    36    10
1-Oct-70    6.852    48    11
1-Oct-70    6.877    60    12
1-Oct-70    7.027    72    13
1-Oct-70    7.096    84    14
1-Oct-70    7.096    96    15
1-Oct-70    7.096    108    16
1-Oct-70    7.096    120    17
1-Nov-70    5.09    3    1
1-Nov-70    5.038    6    2
1-Nov-70    5.093    9    3
1-Nov-70    5.099    12    4
1-Nov-70    5.175    15    5
1-Nov-70    5.162    18    6
1-Nov-70    5.193    21    7
1-Nov-70    5.313    24    8
1-Nov-70    5.473    30    9
1-Nov-70    5.635    36    10
1-Nov-70    5.824    48    11
1-Nov-70    5.906    60    12
1-Nov-70    6.288    72    13
1-Nov-70    6.308    84    14
1-Nov-70    6.308    96    15
1-Nov-70    6.308    108    16
1-Nov-70    6.308    120    17
1-Dec-70    4.915    3    1
1-Dec-70    4.956    6    2
1-Dec-70    4.95    9    3
1-Dec-70    4.886    12    4
1-Dec-70    5.141    15    5
1-Dec-70    5.236    18    6
1-Dec-70    5.339    21    7
1-Dec-70    5.403    24    8
1-Dec-70    5.537    30    9
1-Dec-70    5.768    36    10
1-Dec-70    5.813    48    11
1-Dec-70    5.922    60    12
1-Dec-70    6.131    72    13
1-Dec-70    6.142    84    14
1-Dec-70    6.142    96    15
1-Dec-70    6.142    108    16
1-Dec-70    6.142    120    17
1-Jan-71    4.194    3    1
1-Jan-71    4.261    6    2
1-Jan-71    4.303    9    3
1-Jan-71    4.31    12    4
1-Jan-71    4.255    15    5
1-Jan-71    4.385    18    6
1-Jan-71    4.528    21    7
1-Jan-71    4.643    24    8
1-Jan-71    4.955    30    9
1-Jan-71    5.234    36    10
1-Jan-71    5.602    48    11
1-Jan-71    5.655    60    12
1-Jan-71    6.1    72    13
1-Jan-71    6.068    84    14
1-Jan-71    6.068    96    15
1-Jan-71    6.068    108    16
1-Jan-71    6.068    120    17
1-Feb-71    3.437    3    1
1-Feb-71    3.616    6    2
1-Feb-71    3.745    9    3
1-Feb-71    3.772    12    4
1-Feb-71    3.77    15    5
1-Feb-71    3.933    18    6
1-Feb-71    4.131    21    7
1-Feb-71    4.278    24    8
1-Feb-71    4.543    30    9
1-Feb-71    4.836    36    10
1-Feb-71    5.154    48    11
1-Feb-71    5.304    60    12
1-Feb-71    5.849    72    13
1-Feb-71    5.786    84    14
1-Feb-71    5.786    96    15
1-Feb-71    5.786    108    16
1-Feb-71    5.786    120    17
1-Mar-71    3.629    3    1
1-Mar-71    3.741    6    2
1-Mar-71    3.718    9    3
1-Mar-71    3.758    12    4
1-Mar-71    3.904    15    5
1-Mar-71    3.978    18    6
1-Mar-71    4.075    21    7
1-Mar-71    4.147    24    8
1-Mar-71    4.273    30    9
1-Mar-71    4.514    36    10
1-Mar-71    4.818    48    11
1-Mar-71    4.977    60    12
1-Mar-71    5.435    72    13
1-Mar-71    5.313    84    14
1-Mar-71    5.313    96    15
1-Mar-71    5.313    108    16
1-Mar-71    5.313    120    17
1-Apr-71    3.961    3    1
1-Apr-71    4.282    6    2
1-Apr-71    4.522    9    3
1-Apr-71    4.552    12    4
1-Apr-71    4.701    15    5
1-Apr-71    4.9    18    6
1-Apr-71    5.081    21    7
1-Apr-71    5.216    24    8
1-Apr-71    5.491    30    9
1-Apr-71    5.708    36    10
1-Apr-71    5.799    48    11
1-Apr-71    5.973    60    12
1-Apr-71    6.217    72    13
1-Apr-71    6.055    84    14
1-Apr-71    6.055    96    15
1-Apr-71    6.055    108    16
1-Apr-71    6.055    120    17
1-May-71    4.378    3    1
1-May-71    4.618    6    2
1-May-71    4.747    9    3
1-May-71    4.886    12    4
1-May-71    5.141    15    5
1-May-71    5.252    18    6
1-May-71    5.331    21    7
1-May-71    5.406    24    8
1-May-71    5.713    30    9
1-May-71    5.854    36    10
1-May-71    5.84    48    11
1-May-71    6.206    60    12
1-May-71    6.407    72    13
1-May-71    6.243    84    14
1-May-71    6.243    96    15
1-May-71    6.243    108    16
1-May-71    6.243    120    17
1-Jun-71    5.271    3    1
1-Jun-71    5.516    6    2
1-Jun-71    5.9    9    3
1-Jun-71    6.057    12    4
1-Jun-71    6.14    15    5
1-Jun-71    6.144    18    6
1-Jun-71    6.151    21    7
1-Jun-71    6.267    24    8
1-Jun-71    6.535    30    9
1-Jun-71    6.677    36    10
1-Jun-71    6.614    48    11
1-Jun-71    6.783    60    12
1-Jun-71    6.946    72    13
1-Jun-71    6.792    84    14
1-Jun-71    6.792    96    15
1-Jun-71    6.792    108    16
1-Jun-71    6.792    120    17
1-Jul-71    5.369    3    1
1-Jul-71    5.822    6    2
1-Jul-71    6.035    9    3
1-Jul-71    6.109    12    4
1-Jul-71    6.118    15    5
1-Jul-71    6.216    18    6
1-Jul-71    6.28    21    7
1-Jul-71    6.315    24    8
1-Jul-71    6.631    30    9
1-Jul-71    6.731    36    10
1-Jul-71    6.827    48    11
1-Jul-71    6.891    60    12
1-Jul-71    6.954    72    13
1-Jul-71    6.889    84    14
1-Jul-71    6.889    96    15
1-Jul-71    6.889    108    16
1-Jul-71    6.889    120    17
1-Aug-71    4.477    3    1
1-Aug-71    4.823    6    2
1-Aug-71    5.181    9    3
1-Aug-71    5.27    12    4
1-Aug-71    5.417    15    5
1-Aug-71    5.446    18    6
1-Aug-71    5.286    21    7
1-Aug-71    5.447    24    8
1-Aug-71    5.641    30    9
1-Aug-71    5.711    36    10
1-Aug-71    5.803    48    11
1-Aug-71    6.024    60    12
1-Aug-71    6.174    72    13
1-Aug-71    6.113    84    14
1-Aug-71    6.183    96    15
1-Aug-71    6.237    108    16
1-Aug-71    6.279    120    17
1-Sep-71    4.653    3    1
1-Sep-71    5.003    6    2
1-Sep-71    5.193    9    3
1-Sep-71    5.271    12    4
1-Sep-71    5.345    15    5
1-Sep-71    5.399    18    6
1-Sep-71    5.35    21    7
1-Sep-71    5.399    24    8
1-Sep-71    5.603    30    9
1-Sep-71    5.651    36    10
1-Sep-71    5.77    48    11
1-Sep-71    5.965    60    12
1-Sep-71    6.056    72    13
1-Sep-71    5.97    84    14
1-Sep-71    5.941    96    15
1-Sep-71    5.918    108    16
1-Sep-71    5.902    120    17
1-Oct-71    4.352    3    1
1-Oct-71    4.514    6    2
1-Oct-71    4.57    9    3
1-Oct-71    4.589    12    4
1-Oct-71    4.681    15    5
1-Oct-71    4.769    18    6
1-Oct-71    4.814    21    7
1-Oct-71    4.956    24    8
1-Oct-71    5.14    30    9
1-Oct-71    5.209    36    10
1-Oct-71    5.43    48    11
1-Oct-71    5.66    60    12
1-Oct-71    5.835    72    13
1-Oct-71    5.824    84    14
1-Oct-71    5.814    96    15
1-Oct-71    5.805    108    16
1-Oct-71    5.8    120    17
1-Nov-71    4.377    3    1
1-Nov-71    4.502    6    2
1-Nov-71    4.699    9    3
1-Nov-71    4.743    12    4
1-Nov-71    4.793    15    5
1-Nov-71    4.693    18    6
1-Nov-71    4.906    21    7
1-Nov-71    5.059    24    8
1-Nov-71    5.224    30    9
1-Nov-71    5.285    36    10
1-Nov-71    5.496    48    11
1-Nov-71    5.722    60    12
1-Nov-71    5.985    72    13
1-Nov-71    6.085    84    14
1-Nov-71    6.126    96    15
1-Nov-71    6.157    108    16
1-Nov-71    6.182    120    17
1-Dec-71    3.714    3    1
1-Dec-71    4.078    6    2
1-Dec-71    4.152    9    3
1-Dec-71    4.181    12    4
1-Dec-71    4.439    15    5
1-Dec-71    4.531    18    6
1-Dec-71    4.704    21    7
1-Dec-71    4.828    24    8
1-Dec-71    4.98    30    9
1-Dec-71    5.079    36    10
1-Dec-71    5.204    48    11
1-Dec-71    5.426    60    12
1-Dec-71    5.762    72    13
1-Dec-71    5.841    84    14
1-Dec-71    5.834    96    15
1-Dec-71    5.83    108    16
1-Dec-71    5.869    120    17
1-Jan-72    3.382    3    1
1-Jan-72    3.782    6    2
1-Jan-72    3.995    9    3
1-Jan-72    4.12    12    4
1-Jan-72    4.442    15    5
1-Jan-72    4.595    18    6
1-Jan-72    4.714    21    7
1-Jan-72    4.804    24    8
1-Jan-72    5.1    30    9
1-Jan-72    5.331    36    10
1-Jan-72    5.479    48    11
1-Jan-72    5.718    60    12
1-Jan-72    5.971    72    13
1-Jan-72    6.007    84    14
1-Jan-72    6.026    96    15
1-Jan-72    6.041    108    16
1-Jan-72    6.088    120    17
1-Feb-72    3.47    3    1
1-Feb-72    3.831    6    2
1-Feb-72    3.983    9    3
1-Feb-72    4.291    12    4
1-Feb-72    4.391    15    5
1-Feb-72    4.443    18    6
1-Feb-72    4.626    21    7
1-Feb-72    4.769    24    8
1-Feb-72    5.04    30    9
1-Feb-72    5.246    36    10
1-Feb-72    5.443    48    11
1-Feb-72    5.665    60    12
1-Feb-72    5.897    72    13
1-Feb-72    5.96    84    14
1-Feb-72    6.028    96    15
1-Feb-72    6.082    108    16
1-Feb-72    6.283    120    17
1-Mar-72    3.874    3    1
1-Mar-72    4.463    6    2
1-Mar-72    4.663    9    3
1-Mar-72    4.937    12    4
1-Mar-72    5.141    15    5
1-Mar-72    5.317    18    6
1-Mar-72    5.466    21    7
1-Mar-72    5.528    24    8
1-Mar-72    5.59    30    9
1-Mar-72    5.774    36    10
1-Mar-72    5.875    48    11
1-Mar-72    5.999    60    12
1-Mar-72    6.119    72    13
1-Mar-72    6.11    84    14
1-Mar-72    6.096    96    15
1-Mar-72    6.084    108    16
1-Mar-72    6.269    120    17
1-Apr-72    3.648    3    1
1-Apr-72    4.113    6    2
1-Apr-72    4.355    9    3
1-Apr-72    4.527    12    4
1-Apr-72    4.568    15    5
1-Apr-72    4.78    18    6
1-Apr-72    4.969    21    7
1-Apr-72    5.109    24    8
1-Apr-72    5.354    30    9
1-Apr-72    5.526    36    10
1-Apr-72    5.644    48    11
1-Apr-72    5.798    60    12
1-Apr-72    5.941    72    13
1-Apr-72    5.98    84    14
1-Apr-72    6.063    96    15
1-Apr-72    6.128    108    16
1-Apr-72    6.24    120    17
1-May-72    3.835    3    1
1-May-72    4.232    6    2
1-May-72    4.446    9    3
1-May-72    4.631    12    4
1-May-72    4.63    15    5
1-May-72    4.76    18    6
1-May-72    4.855    21    7
1-May-72    4.947    24    8
1-May-72    5.178    30    9
1-May-72    5.382    36    10
1-May-72    5.563    48    11
1-May-72    5.715    60    12
1-May-72    5.894    72    13
1-May-72    5.937    84    14
1-May-72    5.996    96    15
1-May-72    6.042    108    16
1-May-72    6.249    120    17
1-Jun-72    4.101    3    1
1-Jun-72    4.664    6    2
1-Jun-72    5.054    9    3
1-Jun-72    5.254    12    4
1-Jun-72    5.182    15    5
1-Jun-72    5.311    18    6
1-Jun-72    5.382    21    7
1-Jun-72    5.438    24    8
1-Jun-72    5.556    30    9
1-Jun-72    5.702    36    10
1-Jun-72    5.855    48    11
1-Jun-72    5.909    60    12
1-Jun-72    6.057    72    13
1-Jun-72    6.019    84    14
1-Jun-72    5.999    96    15
1-Jun-72    5.984    108    16
1-Jun-72    6.301    120    17
1-Jul-72    3.857    3    1
1-Jul-72    4.409    6    2
1-Jul-72    4.75    9    3
1-Jul-72    4.95    12    4
1-Jul-72    5.012    15    5
1-Jul-72    5.053    18    6
1-Jul-72    5.151    21    7
1-Jul-72    5.248    24    8
1-Jul-72    5.428    30    9
1-Jul-72    5.667    36    10
1-Jul-72    5.862    48    11
1-Jul-72    5.891    60    12
1-Jul-72    6.017    72    13
1-Jul-72    6.024    84    14
1-Jul-72    6.045    96    15
1-Jul-72    6.06    108    16
1-Jul-72    6.329    120    17
1-Aug-72    4.607    3    1
1-Aug-72    5.065    6    2
1-Aug-72    5.245    9    3
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1-Oct-01    .    30    9
1-Oct-01    .    36    10
1-Oct-01    .    48    11
1-Oct-01    .    60    12
1-Oct-01    .    72    13
1-Oct-01    .    84    14
1-Oct-01    .    96    15
1-Oct-01    .    108    16
1-Oct-01    .    120    17
1-Nov-01    .    3    1
1-Nov-01    .    6    2
1-Nov-01    .    9    3
1-Nov-01    .    12    4
1-Nov-01    .    15    5
1-Nov-01    .    18    6
1-Nov-01    .    21    7
1-Nov-01    .    24    8
1-Nov-01    .    30    9
1-Nov-01    .    36    10
1-Nov-01    .    48    11
1-Nov-01    .    60    12
1-Nov-01    .    72    13
1-Nov-01    .    84    14
1-Nov-01    .    96    15
1-Nov-01    .    108    16
1-Nov-01    .    120    17
1-Dec-01    .    3    1
1-Dec-01    .    6    2
1-Dec-01    .    9    3
1-Dec-01    .    12    4
1-Dec-01    .    15    5
1-Dec-01    .    18    6
1-Dec-01    .    21    7
1-Dec-01    .    24    8
1-Dec-01    .    30    9
1-Dec-01    .    36    10
1-Dec-01    .    48    11
1-Dec-01    .    60    12
1-Dec-01    .    72    13
1-Dec-01    .    84    14
1-Dec-01    .    96    15
1-Dec-01    .    108    16
1-Dec-01    .    120    17
1-Jan-02    .    3    1
1-Jan-02    .    6    2
1-Jan-02    .    9    3
1-Jan-02    .    12    4
1-Jan-02    .    15    5
1-Jan-02    .    18    6
1-Jan-02    .    21    7
1-Jan-02    .    24    8
1-Jan-02    .    30    9
1-Jan-02    .    36    10
1-Jan-02    .    48    11
1-Jan-02    .    60    12
1-Jan-02    .    72    13
1-Jan-02    .    84    14
1-Jan-02    .    96    15
1-Jan-02    .    108    16
1-Jan-02    .    120    17
1-Feb-02    .    3    1
1-Feb-02    .    6    2
1-Feb-02    .    9    3
1-Feb-02    .    12    4
1-Feb-02    .    15    5
1-Feb-02    .    18    6
1-Feb-02    .    21    7
1-Feb-02    .    24    8
1-Feb-02    .    30    9
1-Feb-02    .    36    10
1-Feb-02    .    48    11
1-Feb-02    .    60    12
1-Feb-02    .    72    13
1-Feb-02    .    84    14
1-Feb-02    .    96    15
1-Feb-02    .    108    16
1-Feb-02    .    120    17
1-Mar-02    .    3    1
1-Mar-02    .    6    2
1-Mar-02    .    9    3
1-Mar-02    .    12    4
1-Mar-02    .    15    5
1-Mar-02    .    18    6
1-Mar-02    .    21    7
1-Mar-02    .    24    8
1-Mar-02    .    30    9
1-Mar-02    .    36    10
1-Mar-02    .    48    11
1-Mar-02    .    60    12
1-Mar-02    .    72    13
1-Mar-02    .    84    14
1-Mar-02    .    96    15
1-Mar-02    .    108    16
1-Mar-02    .    120    17
1-Apr-02    .    3    1
1-Apr-02    .    6    2
1-Apr-02    .    9    3
1-Apr-02    .    12    4
1-Apr-02    .    15    5
1-Apr-02    .    18    6
1-Apr-02    .    21    7
1-Apr-02    .    24    8
1-Apr-02    .    30    9
1-Apr-02    .    36    10
1-Apr-02    .    48    11
1-Apr-02    .    60    12
1-Apr-02    .    72    13
1-Apr-02    .    84    14
1-Apr-02    .    96    15
1-Apr-02    .    108    16
1-Apr-02    .    120    17
1-May-02    .    3    1
1-May-02    .    6    2
1-May-02    .    9    3
1-May-02    .    12    4
1-May-02    .    15    5
1-May-02    .    18    6
1-May-02    .    21    7
1-May-02    .    24    8
1-May-02    .    30    9
1-May-02    .    36    10
1-May-02    .    48    11
1-May-02    .    60    12
1-May-02    .    72    13
1-May-02    .    84    14
1-May-02    .    96    15
1-May-02    .    108    16
1-May-02    .    120    17
1-Jun-02    .    3    1
1-Jun-02    .    6    2
1-Jun-02    .    9    3
1-Jun-02    .    12    4
1-Jun-02    .    15    5
1-Jun-02    .    18    6
1-Jun-02    .    21    7
1-Jun-02    .    24    8
1-Jun-02    .    30    9
1-Jun-02    .    36    10
1-Jun-02    .    48    11
1-Jun-02    .    60    12
1-Jun-02    .    72    13
1-Jun-02    .    84    14
1-Jun-02    .    96    15
1-Jun-02    .    108    16
1-Jun-02    .    120    17
1-Jul-02    .    3    1
1-Jul-02    .    6    2
1-Jul-02    .    9    3
1-Jul-02    .    12    4
1-Jul-02    .    15    5
1-Jul-02    .    18    6
1-Jul-02    .    21    7
1-Jul-02    .    24    8
1-Jul-02    .    30    9
1-Jul-02    .    36    10
1-Jul-02    .    48    11
1-Jul-02    .    60    12
1-Jul-02    .    72    13
1-Jul-02    .    84    14
1-Jul-02    .    96    15
1-Jul-02    .    108    16
1-Jul-02    .    120    17
1-Aug-02    .    3    1
1-Aug-02    .    6    2
1-Aug-02    .    9    3
1-Aug-02    .    12    4
1-Aug-02    .    15    5
1-Aug-02    .    18    6
1-Aug-02    .    21    7
1-Aug-02    .    24    8
1-Aug-02    .    30    9
1-Aug-02    .    36    10
1-Aug-02    .    48    11
1-Aug-02    .    60    12
1-Aug-02    .    72    13
1-Aug-02    .    84    14
1-Aug-02    .    96    15
1-Aug-02    .    108    16
1-Aug-02    .    120    17
1-Sep-02    .    3    1
1-Sep-02    .    6    2
1-Sep-02    .    9    3
1-Sep-02    .    12    4
1-Sep-02    .    15    5
1-Sep-02    .    18    6
1-Sep-02    .    21    7
1-Sep-02    .    24    8
1-Sep-02    .    30    9
1-Sep-02    .    36    10
1-Sep-02    .    48    11
1-Sep-02    .    60    12
1-Sep-02    .    72    13
1-Sep-02    .    84    14
1-Sep-02    .    96    15
1-Sep-02    .    108    16
1-Sep-02    .    120    17
1-Oct-02    .    3    1
1-Oct-02    .    6    2
1-Oct-02    .    9    3
1-Oct-02    .    12    4
1-Oct-02    .    15    5
1-Oct-02    .    18    6
1-Oct-02    .    21    7
1-Oct-02    .    24    8
1-Oct-02    .    30    9
1-Oct-02    .    36    10
1-Oct-02    .    48    11
1-Oct-02    .    60    12
1-Oct-02    .    72    13
1-Oct-02    .    84    14
1-Oct-02    .    96    15
1-Oct-02    .    108    16
1-Oct-02    .    120    17
1-Nov-02    .    3    1
1-Nov-02    .    6    2
1-Nov-02    .    9    3
1-Nov-02    .    12    4
1-Nov-02    .    15    5
1-Nov-02    .    18    6
1-Nov-02    .    21    7
1-Nov-02    .    24    8
1-Nov-02    .    30    9
1-Nov-02    .    36    10
1-Nov-02    .    48    11
1-Nov-02    .    60    12
1-Nov-02    .    72    13
1-Nov-02    .    84    14
1-Nov-02    .    96    15
1-Nov-02    .    108    16
1-Nov-02    .    120    17
1-Dec-02    .    3    1
1-Dec-02    .    6    2
1-Dec-02    .    9    3
1-Dec-02    .    12    4
1-Dec-02    .    15    5
1-Dec-02    .    18    6
1-Dec-02    .    21    7
1-Dec-02    .    24    8
1-Dec-02    .    30    9
1-Dec-02    .    36    10
1-Dec-02    .    48    11
1-Dec-02    .    60    12
1-Dec-02    .    72    13
1-Dec-02    .    84    14
1-Dec-02    .    96    15
1-Dec-02    .    108    16
1-Dec-02    .    120    17
;

 proc iml;
    use dns;
    read all var {date} into x;
    bsp = bspline(x, 2, ., 4);
    create spline var{c1 c2 c3 c4 c5 c6 c7};
    append from bsp;
 quit;
 data dns;
    merge dns spline;
 run;

  proc ssm data=Dns optimizer(technique=dbldog maxiter=400);
       id date interval=month;

      /* Time varying parameter lambda */
      parms v1-v7;
      lambda = exp(v1*c1 + v2*c2 + v3*c3 + v4*c4
           + v5*c5 + v6*c6 + v7*c7);

      /*Observation equation white noise -- separate variance for each maturity */
      parms sigma1-sigma17 / lower=1.e-4;
      array s_array(17) sigma1-sigma17;
       do i=1 to 17;
          if (mtype=i) then sigma = s_array[i];
       end;
       irregular wn variance=sigma;

       /* Variables Z1, Z2, Z3 needed in the observation equation */
       Z1= 1.0;
       tmp = lambda*maturity;
       Z2 = (1-exp(-tmp))/tmp;
       Z3 = ( 1-exp(-tmp)-tmp*exp(-tmp) )/tmp;

        /* Zero-mean VAR(1) factor zeta and the associated component */
       state zeta(3) type=VARMA(p(d)=1) cov(g) print=(cov ar);
       comp zetaComp = (Z1-Z3)*zeta;

       /* Constant mean vector mu and the associated component */
        state mu(3) type=rw;
        comp muComp = (Z1-Z3)*mu;

        /* Observation equation */
        model yield = muComp zetaComp wn;

        /* Various components defined only for the output purposes  */
        eval yieldSurface = muComp + zetaComp;

        comp zeta1 = zeta[1];
        comp zeta2 = zeta[2];
        comp zeta3 = zeta[3];
        comp mu1 = mu[1];
        comp mu2 = mu[2];
        comp mu3 = mu[3];

        comp z2zeta = (Z2)*zeta[2];
        comp z3zeta = (Z3)*zeta[3];
        comp z2Mu =  (Z2)*mu[2];
        comp z3Mu =  (Z3)*mu[3];

        eval beta1 = mu1 + zeta1;
        eval beta2 = mu2 + zeta2;
        eval beta3 = mu3 + zeta3;

        eval shortTem = z2zeta + z2Mu;
        eval medTerm = z3zeta + z3Mu;

        /* output the component estimates and the forecasts */
        output out=dnsFor pdv;
    run;


 proc sgplot data= dnsFor;
     title "The Estimated Yield Surface and the Observed Yields ";
     where maturity in (3 60 120) and date >= '31dec1990'd;
     series x=date y=smoothed_yieldSurface / group=maturity;
     scatter x=date y=yield / group=maturity;
     refline '31dec2000'd / axis=x lineattrs=GraphReference(pattern = Dash)
         name="RefLine"   label="Start of multistep forecasts";
 run;

 proc sgplot data=dnsFor;
    title "Long-Term Bond Yields Over Time ";
    series x=date y=smoothed_beta1 ;
    refline '31dec2000'd / axis=x lineattrs=GraphReference(pattern = Dash)
         name="RefLine"   label="Start of multistep forecasts";
 run;

 proc sgplot data=dnsFor;
   title "The Correction Term for the Short-Term Yields ";
   where maturity in (3 120);
   series x=date y=smoothed_shortTem / group=maturity;
   refline '31dec2000'd / axis=x lineattrs=GraphReference(pattern = Dash)
         name="RefLine"   label="Start of multistep forecasts";
 run;

 title;