1          OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 55         
 56         /* Lynch1.sas */
 57         title 'Hovland and Sears Lynching data';
 58         
 59         data lynch;
 60              infile '/folders/myfolders/Lynch.data.txt' firstobs=7;
 61                                           /* Skipping the header */
 62              input Year Ayres Cotton1 Cotton2 Blynch Totlynch;
 63              label ayres = 'Ayres'' composite economic index'
 64                    cotton1 = 'Per-acre value of cotton'
 65                    cotton2 = 'Farm value of cotton'
 66                    blynch  = 'Negro lynchings'
 67                    totlynch = 'Total lynchings';
 68              olynch = totlynch-blynch;
 69              label olynch = 'Non-Black lynchings';
 70              one=1; /* Used below -- one "subject." */
 71         
 
 NOTE: The infile '/folders/myfolders/Lynch.data.txt' is:
       Filename=/folders/myfolders/Lynch.data.txt,
       Owner Name=root,Group Name=vboxsf,
       Access Permission=-rwxrwx---,
       Last Modified=22Mar2016:13:25:43,
       File Size (bytes)=3083
 
 NOTE: 48 records were read from the infile '/folders/myfolders/Lynch.data.txt'.
       The minimum record length was 54.
       The maximum record length was 55.
 NOTE: The data set WORK.LYNCH has 48 observations and 8 variables.
 NOTE: DATA statement used (Total process time):
       real time           0.01 seconds
       cpu time            0.00 seconds
       
 72         proc sgplot;
 
 73              title2 'Lynchings and Cotton Prices over Time';
 74              series x=year y=cotton2;
 75              series x=year y=totlynch / y2axis;
 76         
 
 77         proc means;
 NOTE: PROCEDURE SGPLOT used (Total process time):
       real time           0.49 seconds
       cpu time            0.12 seconds
       
 NOTE: There were 48 observations read from the data set WORK.LYNCH.
 
 78              var ayres -- olynch;
 
 NOTE: There were 48 observations read from the data set WORK.LYNCH.
 NOTE: PROCEDURE MEANS used (Total process time):
       real time           0.06 seconds
       cpu time            0.06 seconds
       
 79         proc corr;
 
 80              var year -- olynch;
 81         
 82         
 
 NOTE: PROCEDURE CORR used (Total process time):
       real time           0.09 seconds
       cpu time            0.09 seconds
       
 83         proc reg plots=none;
 
 84              title2 'Naive regression, but request Durbin-Watson statistic';
 85              title3 'Lower Durbin-Watson critical value = 1.5';
 86              model totlynch = year cotton2 / dw;
 87              output out = Dixie  residual = epsilonhat; /* Save residuals */
 88         
 
 NOTE: The data set WORK.DIXIE has 48 observations and 9 variables.
 NOTE: PROCEDURE REG used (Total process time):
       real time           0.06 seconds
       cpu time            0.06 seconds
       
 89         proc arima;
 
 90              title2 'Autocorrelations and partial autocorrelations';
 91              identify var = epsilonhat;
 92         
 93         /* That looks like an AR(1) */
 94         
 95         /* Apparently SAS university Edition does not include proc autoreg,
 96            so this does not work.
 97         
 98         *********************************************************
 99         proc autoreg;
 100             title2 'Fit AR(1) with proc autoreg';
 101             model totlynch = year cotton2 /  nlag=1 method=ml;
 102        *********************************************************/
 103        
 
 NOTE: PROCEDURE ARIMA used (Total process time):
       real time           0.60 seconds
       cpu time            0.13 seconds
       
 104        proc mixed;
 
 105             title2 'Fit AR(1) with proc mixed';
 106             model  totlynch = year cotton2 / solution;
 107             repeated / type=ar(1) subject=one;
 108        
 109        /* Test for difference between AR(1) and ARMA(1,1), using
 110           a likelihood ratio chi-squared test. AR(1) is the
 111           reduced model. Fit the models with maximum likelihood. */
 112        
 
 NOTE: Convergence criteria met.
 NOTE: PROCEDURE MIXED used (Total process time):
       real time           0.11 seconds
       cpu time            0.09 seconds
       
 113        proc mixed method=ml;
 
 114             title2 'Reduced model is AR(1)';
 115             model  totlynch = year cotton2 / solution;
 116             repeated / type=ar(1) subject=one;
 117        
 
 NOTE: Convergence criteria met.
 NOTE: PROCEDURE MIXED used (Total process time):
       real time           0.08 seconds
       cpu time            0.08 seconds
       
 118        proc mixed method=ml;
 
 119             title2 'Full model is Autoregressive Moving Average: ARMA(1,1)';
 120             model  totlynch = year cotton2 / solution;
 121             repeated / type=arma(1,1) subject=one;
 122        
 
 NOTE: Convergence criteria met.
 NOTE: PROCEDURE MIXED used (Total process time):
       real time           0.09 seconds
       cpu time            0.08 seconds
       
 123        proc iml;
 
 NOTE: IML Ready
 124             title2 'Difference between -2 Log Likelihood values is chi-squared';
 125             Chisquare = 443.7-441.5;
 125      !                               df=1;
 125      !                                     pvalue = 1-probchi(Chisquare,df);
 126             print Chisquare df pvalue;
 127        
 128        
 129        
 130        OPTIONS NONOTES NOSTIMER NOSOURCE NOSYNTAXCHECK;
 142