options crt;
name pears 'Pear demand dataset and autocorrelation tests';
?
?  This dataset was published in Henshaw, Econometrica, July 1966,
?  p.652.  It is originally from Hoos and Shear (1942), and was
?  analyzed later by Hildreth and Lu (1960).  Note that the values
?  of X6 printed in Hildreth and Lu are incorrect.
load;
?
?  OLS estimates
?             Henshaw's   TSP 4.4
?              results    results
? coef of   C    .9423    .942271
? coef of   X4  -.0085   -.00851466
? coef of   X6  -.0191   -.019121
? coef of   X7   .0332    .033248
? coef of   T   -.0240   -.024001
? Durbin-Watson 1.1713   1.17134
? D-W P-value    .01+     .013611 
?    Henshaw computed .01 significance points for the Durbin-Watson
? using 2 accurate methods (Durbin-Watson approximation, and his
? own beta approximation), and the observed Durbin-Watson was
? slightly larger than the .01 significance points in both cases.
? So I have entered ".01+" as his P-value.
?    Note that the Durbin-Watson statistic value of 1.1713 is in
? the inconclusive region (between dL and dU) for both .05 and .01,
? so this is a case in which the exact P-value is needed for
? obtaining a conclusion from the test.
regopt(dwpval=exact);
olsq x1 c x4 x6 x7 t;
print @DW %DW;
regopt;
?
?  AR1 estimates  (conditional ML and exact ML)
?              Henshaw    TSP 4.4    TSP 4.4    TSP 4.4
?              cond.ML    cond.ML    cond.ML    exact ML
?              2 digits   2 digits   6+ digits  6+ digits
? coef of   C    .950     .950239    .948130    .823743
? coef of   X4  -.0109   -.010921   -.010912   -.00851314
? coef of   X6  -.0176   -.017567   -.017566   -.018966
? coef of   X7   .0352    .035182    .035201    .034309
? coef of   T2  -.0673   -.067279   -.067392   -.044404
? rho            .30      .30        .304833    .393054
? S.S.R.         .2437    .219269    .219262
? LogLikelihood         10.4072    10.4075     7.53161
t2 = t/2;  ? apparently the definition of T was changed for Table III
ar1(method=hilu,rstep=.01) x1 c x4 x6 x7 t2;
?
? -----------------------------------------------------------
? Compute conditional ML estimates to more significant digits
?
?  AR1 (conditional ML, iteration to 6+ digits)
ar1(method=corc,tol=1e-11,maxit=100) x1 c x4 x6 x7 t2;
?
?  AR1 (conditional ML, via nonlinear least squares)
form(param,varpref=b,resid,print) ear1;
lsq(tol=1e-11) ear1;
?
? ------------------
? exact ML estimates
?
?  AR1 (exact ML, iteration to 6+ digits)
ar1(tol=1e-11,maxit=100) x1 c x4 x6 x7 t2;
end;
noprint;
doc x1 'price of California Bartletts (dollars)';
doc x4 'supply of California Bartletts (1000 short tons)';
doc x6 'supply of Oregon and Washington pears (1000 short tons)';
doc x7 'non-agricultural income (1924-29=100)';
doc t  'time trend, in 6 months, origin 1932-33';
doc t2 'time trend, in years, origin 1932-33';
freq a;
smpl 1925,1940;
read x1 x4 x6 x7 t;
2.78  83 39  98 -15
2.65 105 48 100 -13
3.31  88 30 102 -11
2.86 101 63 105 -9
3.61  82 32 109 -7
2.31 120 52  97 -5
2.61  84 23  83 -3
1.94  66 20  64 -1
2.30  52 25  64  1
2.53  72 17  71  3
2.35  53 33  78  5
2.33  68 40  89  7
2.45  80 36  95  9
1.93  89 40  87 11
2.53  67 36  93 13
2.33  68 44  99 15