/*
okun.def

 g  u

  Obs: 98, quarterly (1985Q2 - 2009Q3)  

	g = percentage change in U.S. Gross Domestic Product, seasonally adjusted.

        u = U.S. Civilian Unemployment Rate  (Seasonally adjusted)

	The variable DU used in Chapter 9 is defined as U(t)-U(t-1).

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
           g |        98    1.276531    .6469279       -1.4        2.5
           u |        98    5.704082    1.132638        3.9        9.6


Data Source:  Federal Reserve Bank of St Louis
*/

data Okun;
input g	u;
datalines;
1.4	7.3
2	7.2
1.4	7
1.5	7
0.9	7.2
1.5	7
1.2	6.8
1.5	6.6
1.6	6.3
1.7	6
2.5	5.8
1.3	5.7
2.2	5.5
1.7	5.5
2.1	5.3
2.1	5.2
1.7	5.2
1.5	5.2
0.9	5.4
2.3	5.3
1.6	5.3
0.9	5.7
-0.1	6.1
0.6	6.6
1.4	6.8
1.2	6.9
1	7.1
1.6	7.4
1.7	7.6
1.5	7.6
1.6	7.4
0.8	7.1
1.2	7.1
1	6.8
1.9	6.6
1.5	6.6
1.9	6.2
1.2	6
1.6	5.6
0.8	5.5
0.7	5.7
1.3	5.7
1.2	5.6
1.3	5.5
2.1	5.5
1.2	5.3
1.7	5.3
1.4	5.2
1.7	5
1.6	4.9
1.1	4.7
1.1	4.6
1.1	4.4
1.7	4.5
2	4.4
1.3	4.3
1.1	4.3
1.6	4.2
2.2	4.1
1.1	4
2.5	3.9
0.7	4
1.1	3.9
0.3	4.2
1.3	4.4
0	4.8
0.7	5.5
1.2	5.7
1	5.8
0.9	5.7
0.6	5.9
1.1	5.9
1.1	6.1
2.2	6.1
1.4	5.8
1.6	5.7
1.6	5.6
1.5	5.4
1.6	5.4
1.9	5.3
1.1	5.1
1.8	5
1.4	4.9
2.1	4.7
1.2	4.7
0.8	4.6
1.2	4.4
1.4	4.5
1.5	4.5
1.3	4.7
1.1	4.8
0.3	4.9
0.9	5.4
0.3	6.1
-1.4	6.9
-1.2	8.1
-0.2	9.3
0.8	9.6
;

data okun;
  set okun;
  difu = u - lag(u);
  time = _n_;
run;

symbol1 interpol=join
        value=dot;

title 'Plot of nonstationary time series U';
title2 'Times Series is slow-turning';
title3 'Data needs to be differenced'; 
proc gplot data = okun;
   plot u*time;
run;

title 'Getting the autocorrelation function for U';
title2 'It appears to be slowly damping and thus U is nonstationary';
proc arima data = okun;
  identify var = u;
run;

title 'Difference in Unemployment versus Time';
title2 'Data is now in stationary form';
proc gplot data = okun;
   plot difu*time;
run;

title 'Autocorrelation Function of difu series';
title2 'The ACF of difu is quickly damping';
proc arima data = okun;
   identify var = difu;
run;

title 'Growth versus Time';
title2 'Data is quickly turning and therefore stationary';
proc gplot data = okun;
   plot g*time;
run;

title 'Autocorrelation Function of g series';
title2 'The ACF of g is quickly damping';
proc arima data = okun;
   identify var = g;
run;

/*  Both the difu and g series appear to be ergotic (stationary) because their ACF's are quickly damping.
    Let's proceed with our analysis. */

/* Now we are going to use formal tests of whether a time series needs to be differenced
   to make it stationary.  The battery of tests are called the Augmented Dickey-Fuller
   Unit Root tests.  The major drawback of the SAS version of the ADF tests is that
   there is no choice of optimal number of augminting terms to use. */ 

title 'Unit Root Test for U';
proc arima data=okun;
    identify var=u stationarity=(adf=6);
run;

title 'Unit Root Test for U(1)';
proc arima data=okun;
	identify var=u(1) stationarity=(adf=6);
run;

title 'Unit Root Test for f';
proc arima data=okun;
    identify var=g stationary=(adf=6);
run;