options double crt nwidth=20,signif=10 nodate;
?
?  AR(1) model with multiple optima (conditional ML), without
?  a lagged dependent variable.  Data are from:
?  Dufour, J., Gaudry, M.J.I., Liem, T.C., "The Cochrane-Orcutt
?  Procedure Numerical Examples of Multiple Admissible Minima,"
?  Economic Letters, (1980), pp.43-47.
?     Additional numerical results from:
?  Lovell, M.C. and Selover, D.D., "Econometric Software Accidents,"
?  The Economic Journal, 104, (1994), pp.713-726.
?     Note:  default convergence criteria were used for the
?  Lovell-Selover results listed here, so they are only accurate to
?  a few digits at best.  Most of the TSP results should be accurate to
?  roughly 10 digits, due to the special convergence criterion used.
?  The global optimum conditional ML results are only accurate to
?  7-8 digits.
?  
load;

title 'AR(1) conditional ML - local optimum';
?              TSP       Lovell-Selover   L-S        L-S       Dufour
?  C     -229251.31455      MicroFit     RATS       Shazam
? (s.e.)  (84878.375624)      C-O       C-O,H-L      DROP
?  X2      2.9800902553      2.9802     2.9801      2.9807
? (s.e.)  (3.0586145327)
?  X3     -660.48454300
? (s.e.)  (16889.061088)
?  X4      25423.042926
? (s.e.)  (18654.766424)
?  X5      2.9586236967
? (s.e.)  (4.9031908844)
?  rho     .32888123637     .32883      .3289       .32867      .3289
? (s.e.)  (.21116783992)
?  SSR      31644512460.   3.16e+10  316644512460  3.1645e+10  3.16e+10
?  LogL   -240.19975380
ar1(method=corc,tol=1e-11,maxit=100) yee c x2 x3 x4 x5;

title 'AR(1) conditional ML - global optimum';
?               TSP       Lovell-Selover   Dufour-Gaudry-Liem
?  C       534114.58201       Shazam
? (s.e.)  (359433.21576)     GS DROP
?  X2     -2.8527903125      -2.8334
? (s.e.)  (3.3906736496)
?  X3     -12065.619763
? (s.e.)  (14586.038716)
?  X4      18161.171798
? (s.e.)  (16908.015761)
?  X5     -5.2060324726
? (s.e.)  (4.9899718122)
?  rho     .93187031452        .93            .9318
? (s.e.)  (.08112265926)
?  SSR      31124698199.    3.1126e+10       3.11e+10
?  LogL   -240.03412287
ar1(method=corc,rstart=.9,tol=1e-11,maxit=100) yee c x2 x3 x4 x5;

? Estimate conditional ML directly via nonlinear least squares,
? after explicitly dropping first observation.
? From the non-convergence warning message, we can see that the
? TSP results are accurate to 7-8 digits, not 10-11 as was hoped for.
smpl 1901,1920;
form(param,varpref=b) ar1;
lsq(tol=1e-11,maxsqz=25) ar1;

title 'AR(1) exact ML - only one optimum';
?              TSP       Lovell-Selover   L-S      L-S
?  C     -225488.67731      MicroFit     RATS     Shazam
? (s.e.)  (72724.053866)     Exact        B-M       ML
?  X2      3.0562664848     3.0562      3.0563    3.0566
? (s.e.)  (2.9368181062)
?  X3      -1851.3618057
? (s.e.)  (12893.309076)
?  X4      26097.620409
? (s.e.)  (16608.225127)
?  X5      2.8057272628
? (s.e.)  (4.4982772910)
?  rho     .31660006021      .31661      .3166     .31649
? (s.e.)  (.23827283644)
?  LogL   -251.76161355
smpl 1900,1920;
ar1(tol=1e-11,maxit=100) yee c x2 x3 x4 x5;

? Can also verify that grid search detects the global optimum
? for conditional ML
ar1(method=hilu,rstep=.05) yee c x2 x3 x4 x5;
end;
noprint;
freq a;
smpl 1900 1920;
load yee x2 x3 x4 x5;
 41257.19 31029.69  5.28  6.81    63.77
 44865.40 32583.78  6.06  6.87    85.57
 22923.50 36650.81  8.87  7.32    88.46
 32965.03 36891.94  9.47  7.08   386.20
 54792.10 42317.09  9.22  7.30   290.85
 33108.06 40589.08  9.83  7.36   393.46
 39056.50 41118.95 10.22  7.34   765.05
172234.73 40704.33  9.92  8.36   442.37
156048.66 47811.32 10.16  8.47   913.72
119613.33 46579.47  9.10  7.28  2750.65
101615.00 52399.32  9.20  7.51   730.62
140263.66 52394.25  9.22  7.51  5598.61
157970.33 53433.06  8.92  8.12 11172.30
153197.00 57034.16 10.10  8.10 11231.01
220405.33 63357.77 13.04  9.10  1998.53
221200.00 62331.26 12.92 11.14  1840.21
149608.33 65005.41 13.83 11.51  1527.44
230434.33 65754.51 13.63 11.34  1829.89
250505.66 69541.05 14.04 10.83  2691.17
294424.66 60494.35 13.24 10.22  3225.85
281281.66 63381.69 12.67 10.36  3980.40