Part I Replication of Hepworth and West whitening equations ============================================================ LS // Dependent Variable is LYNBLK1 Date: 12/05/97 Time: 16:10 Sample: 1882 1930 Included observations: 49 Convergence achieved after 8 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 1.945060 0.036470 53.33286 0.0000 YR -0.013771 0.001705 -8.078459 0.0000 YR2 -0.000844 0.000135 -6.258297 0.0000 MA(1) 0.551306 0.145606 3.786290 0.0005 ============================================================ R-squared 0.861341 Mean dependent var 1.773035 Adjusted R-squared 0.852097 S.D. dependent var 0.286114 S.E. of regression 0.110034 Akaike info criter-4.335823 Sum squared resid 0.544837 Schwarz criterion -4.181389 Log likelihood 40.69968 F-statistic 93.17894 Durbin-Watson stat 1.701977 Prob(F-statistic) 0.000000 ============================================================ Inverted MA Roots -.55 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:42 Sample: 1882 1930 Included observations: 49 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1 0.061 0.061 0.1912 . |*. | . |*. | 2 0.070 0.066 0.4501 0.502 . | . | . | . | 3-0.026-0.034 0.4861 0.784 . |*. | . |*. | 4 0.150 0.150 1.7290 0.631 .*| . | .*| . | 5-0.130-0.149 2.6958 0.610 .*| . | .*| . | 6-0.149-0.156 3.9786 0.552 .*| . | .*| . | 7-0.141-0.100 5.1630 0.523 . | . | . | . | 8-0.020-0.020 5.1872 0.637 .*| . | .*| . | 9-0.115-0.071 6.0206 0.645 .*| . | .*| . | 10-0.101-0.073 6.6757 0.671 . | . | . |*. | 11 0.051 0.075 6.8495 0.740 . | . | . | . | 12 0.051 0.004 7.0267 0.797 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 6.022074 Probability 0.001540 Obs*R-squared 14.03675 Probability 0.002856 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:42 Sample: 1882 1930 Included observations: 49 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.008120 0.003723 2.181184 0.0344 YR 0.000424 0.000140 3.024885 0.0041 YR^2 -1.95E-05 3.90E-05 -0.499956 0.6195 YR2^2 9.58E-08 7.27E-08 1.317718 0.1943 ============================================================ R-squared 0.286464 Mean dependent var 0.011119 Adjusted R-squared 0.238895 S.D. dependent var 0.015915 S.E. of regression 0.013884 Akaike info criter-8.475875 Sum squared resid 0.008675 Schwarz criterion -8.321440 Log likelihood 142.1309 F-statistic 6.022074 Durbin-Watson stat 1.158514 Prob(F-statistic) 0.001540 ============================================================ ============================================================ LS // Dependent Variable is LYNTOT1 Date: 12/05/97 Time: 16:10 Sample: 1882 1930 Included observations: 49 Convergence achieved after 6 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 1.991726 0.038764 51.38021 0.0000 YR -0.020408 0.001817 -11.23054 0.0000 YR2 -0.000498 0.000143 -3.488634 0.0011 MA(1) 0.641022 0.130584 4.908874 0.0000 ============================================================ R-squared 0.899066 Mean dependent var 1.889145 Adjusted R-squared 0.892337 S.D. dependent var 0.337275 S.E. of regression 0.110667 Akaike info criter-4.324354 Sum squared resid 0.551122 Schwarz criterion -4.169920 Log likelihood 40.41868 F-statistic 133.6113 Durbin-Watson stat 1.827106 Prob(F-statistic) 0.000000 ============================================================ Inverted MA Roots -.64 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:44 Sample: 1882 1930 Included observations: 49 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1 0.029 0.029 0.0428 . | . | . | . | 2 0.011 0.010 0.0493 0.824 . | . | . | . | 3-0.004-0.005 0.0502 0.975 . |*. | . |*. | 4 0.124 0.124 0.9035 0.825 .*| . | .*| . | 5-0.080-0.089 1.2694 0.867 **| . | **| . | 6-0.248-0.251 4.8554 0.434 . | . | . | . | 7-0.044-0.029 4.9684 0.548 . | . | . | . | 8-0.023-0.029 5.0014 0.660 .*| . | .*| . | 9-0.136-0.127 6.1615 0.629 .*| . | . | . | 10-0.079-0.021 6.5636 0.682 . |*. | . | . | 11 0.077 0.061 6.9541 0.730 . | . | . | . | 12 0.014-0.057 6.9669 0.802 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 5.824173 Probability 0.001885 Obs*R-squared 13.70448 Probability 0.003336 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:44 Sample: 1882 1930 Included observations: 49 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.007139 0.002982 2.393858 0.0209 YR 0.000372 0.000112 3.309812 0.0018 YR^2 1.57E-05 3.12E-05 0.504122 0.6166 YR2^2 1.34E-08 5.82E-08 0.229577 0.8195 ============================================================ R-squared 0.279683 Mean dependent var 0.011247 Adjusted R-squared 0.231662 S.D. dependent var 0.012689 S.E. of regression 0.011123 Akaike info criter-8.919456 Sum squared resid 0.005567 Schwarz criterion -8.765021 Log likelihood 152.9987 F-statistic 5.824173 Durbin-Watson stat 2.113373 Prob(F-statistic) 0.001885 ============================================================ ============================================================ LS // Dependent Variable is AYRES Date: 12/05/97 Time: 16:10 Sample: 1882 1930 Included observations: 49 Convergence achieved after 6 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.833336 0.617840 1.348788 0.1839 MA(5) -0.446770 0.134429 -3.323458 0.0017 ============================================================ R-squared 0.144085 Mean dependent var 0.748980 Adjusted R-squared 0.125874 S.D. dependent var 7.544731 S.E. of regression 7.053923 Akaike info criter 3.947128 Sum squared resid 2338.618 Schwarz criterion 4.024345 Log likelihood -164.2326 F-statistic 7.912010 Durbin-Watson stat 1.707723 Prob(F-statistic) 0.007145 ============================================================ Inverted MA Roots .8 .26 -.81 .26+.81i -.69+.50i -.69 -.50i ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:44 Sample: 1882 1930 Included observations: 49 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . |*. | . |*. | 1 0.104 0.104 0.5591 **| . | **| . | 2-0.223-0.236 3.1943 0.074 .*| . | .*| . | 3-0.136-0.088 4.1936 0.123 **| . | **| . | 4-0.201-0.246 6.4476 0.092 . | . | . | . | 5 0.047 0.043 6.5727 0.160 . | . | .*| . | 6 0.044-0.095 6.6876 0.245 .*| . | .*| . | 7-0.120-0.160 7.5478 0.273 .*| . | **| . | 8-0.136-0.198 8.6766 0.277 . | . | .*| . | 9-0.056-0.122 8.8748 0.353 . |*. | . | . | 10 0.132 0.011 9.9849 0.352 . |*. | . | . | 11 0.158-0.002 11.617 0.312 . | . | . | . | 12 0.022-0.047 11.648 0.391 ============================================================== ============================================================ ARCH Test: ============================================================ F-statistic 0.754102 Probability 0.389689 Obs*R-squared 0.774198 Probability 0.378922 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:44 Sample(adjusted): 1883 1930 Included observations: 48 after adjusting endpoints ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 54.12006 12.67248 4.270678 0.0001 RESID^2(-1) -0.131146 0.151022 -0.868391 0.3897 ============================================================ R-squared 0.016129 Mean dependent var 48.20821 Adjusted R-squared -0.005259 S.D. dependent var 73.85848 S.E. of regression 74.05245 Akaike info criter 8.650321 Sum squared resid 252253.2 Schwarz criterion 8.728288 Log likelihood -273.7168 F-statistic 0.754102 Durbin-Watson stat 1.911768 Prob(F-statistic) 0.389689 ============================================================ ============================================================ LS // Dependent Variable is LCOTTON Date: 12/05/97 Time: 16:10 Sample: 1882 1930 Included observations: 49 Convergence achieved after 7 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 1.275962 0.032383 39.40274 0.0000 YR 0.020499 0.003027 6.771608 0.0000 YR2 0.000809 0.000333 2.427941 0.0194 YR3 -3.28E-05 7.59E-06 -4.318883 0.0001 YR4 -1.44E-06 6.14E-07 -2.351740 0.0233 MA(1) 0.493611 0.143638 3.436480 0.0013 ============================================================ R-squared 0.800781 Mean dependent var 1.335003 Adjusted R-squared 0.777616 S.D. dependent var 0.172476 S.E. of regression 0.081335 Akaike info criter-4.904071 Sum squared resid 0.284464 Schwarz criterion -4.672420 Log likelihood 56.62176 F-statistic 34.56864 Durbin-Watson stat 1.891308 Prob(F-statistic) 0.000000 ============================================================ Inverted MA Roots -.49 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:45 Sample: 1882 1930 Included observations: 49 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1 0.020 0.020 0.0216 . | . | . | . | 2-0.010-0.010 0.0269 0.870 **| . | **| . | 3-0.232-0.231 2.9429 0.230 **| . | **| . | 4-0.191-0.193 4.9729 0.174 .*| . | .*| . | 5-0.061-0.073 5.1874 0.269 . |*. | . | . | 6 0.097 0.040 5.7316 0.333 . | . | .*| . | 7-0.030-0.128 5.7866 0.448 .*| . | .*| . | 8-0.096-0.187 6.3525 0.499 .*| . | .*| . | 9-0.131-0.165 7.4322 0.491 . |*. | . |*. | 10 0.186 0.177 9.6472 0.380 **| . | ***| . | 11-0.220-0.361 12.826 0.234 . |*. | .*| . | 12 0.080-0.099 13.258 0.277 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 2.293223 Probability 0.052717 Obs*R-squared 12.09138 Probability 0.059961 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:45 Sample: 1882 1930 Included observations: 49 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.000757 0.003433 0.220392 0.8266 YR 0.000528 0.000246 2.142850 0.0380 YR^2 0.000204 0.000114 1.787512 0.0811 YR2^2 -1.29E-06 9.29E-07 -1.393712 0.1707 YR3 -7.65E-07 6.27E-07 -1.220103 0.2292 YR3^2 2.67E-09 2.60E-09 1.025751 0.3109 YR4^2 -1.72E-12 2.32E-12 -0.740695 0.4630 ============================================================ R-squared 0.246763 Mean dependent var 0.005805 Adjusted R-squared 0.139158 S.D. dependent var 0.010494 S.E. of regression 0.009736 Akaike info criter-9.132266 Sum squared resid 0.003981 Schwarz criterion -8.862006 Log likelihood 161.2125 F-statistic 2.293223 Durbin-Watson stat 2.154291 Prob(F-statistic) 0.052717 ============================================================ Part II. Whitening Equations for Alternative Series (order of presentation follows the EVIEWS replication program) number of anti-black lynchings ============================================================ LS // Dependent Variable is LYNCHBLK Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1930 Included observations: 48 after adjusting endpoints Convergence achieved after 3 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 83.01649 10.16704 8.165259 0.0000 YR -1.913029 0.562995 -3.397950 0.0015 YR2 -0.051415 0.042995 -1.195834 0.2382 AR(1) 0.670122 0.111047 6.034592 0.0000 ============================================================ R-squared 0.813447 Mean dependent var 69.52083 Adjusted R-squared 0.800727 S.D. dependent var 35.49048 S.E. of regression 15.84294 Akaike info criter 5.605104 Sum squared resid 11043.95 Schwarz criterion 5.761037 Log likelihood -198.6315 F-statistic 63.95252 Durbin-Watson stat 1.963553 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .67 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:47 Sample: 1883 1930 Included observations: 48 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1-0.002-0.002 0.0002 .*| . | .*| . | 2-0.118-0.118 0.7237 0.395 . |*. | . |*. | 3 0.078 0.079 1.0498 0.592 . | . | . | . | 4-0.029-0.044 1.0962 0.778 **| . | **| . | 5-0.229-0.215 4.0243 0.403 . | . | . | . | 6-0.039-0.055 4.1116 0.533 . | . | .*| . | 7-0.022-0.072 4.1396 0.658 . |*. | . |*. | 8 0.086 0.111 4.5868 0.710 .*| . | .*| . | 9-0.113-0.145 5.3703 0.717 .*| . | .*| . | 10-0.084-0.121 5.8183 0.758 . |** | . |*. | 11 0.212 0.165 8.7258 0.558 . | . | .*| . | 12-0.034-0.065 8.8035 0.640 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 1.782250 Probability 0.164459 Obs*R-squared 5.200828 Probability 0.157669 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:47 Sample: 1883 1930 Included observations: 48 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 210.7936 90.70238 2.324014 0.0248 YR -6.465254 3.527867 -1.832624 0.0736 YR^2 0.775363 0.981993 0.789581 0.4340 YR2^2 -0.001901 0.001903 -0.998837 0.3233 ============================================================ R-squared 0.108351 Mean dependent var 230.0823 Adjusted R-squared 0.047556 S.D. dependent var 343.8742 S.E. of regression 335.5979 Akaike info criter 11.71148 Sum squared resid 4955543. Schwarz criterion 11.86742 Log likelihood -345.1846 F-statistic 1.782250 Durbin-Watson stat 1.607756 Prob(F-statistic) 0.164459 ============================================================ Number of anti-black lynchings, w/o deterministic trend ============================================================ LS // Dependent Variable is LYNCHBLK Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1930 Included observations: 48 after adjusting endpoints Convergence achieved after 3 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 64.27995 24.03969 2.673909 0.0103 AR(1) 0.896636 0.071001 12.62854 0.0000 ============================================================ R-squared 0.776134 Mean dependent var 69.52083 Adjusted R-squared 0.771267 S.D. dependent var 35.49048 S.E. of regression 16.97368 Akaike info criter 5.704102 Sum squared resid 13252.87 Schwarz criterion 5.782068 Log likelihood -203.0075 F-statistic 159.4799 Durbin-Watson stat 2.044553 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .90 ============================================================ ============================================================ ARCH Test: ============================================================ F-statistic 1.215508 Probability 0.276106 Obs*R-squared 1.236141 Probability 0.266216 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:48 Sample(adjusted): 1884 1930 Included observations: 47 after adjusting endpoints ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 236.4449 73.82807 3.202643 0.0025 RESID^2(-1) 0.161931 0.146876 1.102501 0.2761 ============================================================ R-squared 0.026301 Mean dependent var 281.9330 Adjusted R-squared 0.004663 S.D. dependent var 420.7071 S.E. of regression 419.7250 Akaike info criter 12.12082 Sum squared resid 7927610. Schwarz criterion 12.19955 Log likelihood -349.5294 F-statistic 1.215508 Durbin-Watson stat 1.960017 Prob(F-statistic) 0.276106 ============================================================ number of lynching events in 5 deep south states ============================================================ LS // Dependent Variable is BOOKBEVT Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1930 Included observations: 48 after adjusting endpoints Convergence achieved after 3 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 31.27459 1.885310 16.58857 0.0000 YR -0.404784 0.091420 -4.427714 0.0001 YR2 -0.033709 0.007381 -4.566963 0.0000 AR(1) 0.208123 0.149871 1.388682 0.1719 ============================================================ R-squared 0.630955 Mean dependent var 24.52083 Adjusted R-squared 0.605793 S.D. dependent var 10.98353 S.E. of regression 6.896108 Akaike info criter 3.941570 Sum squared resid 2092.478 Schwarz criterion 4.097503 Log likelihood -158.7067 F-statistic 25.07555 Durbin-Watson stat 2.008109 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .21 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:48 Sample: 1883 1930 Included observations: 48 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1-0.022-0.022 0.0243 . |*. | . |*. | 2 0.074 0.074 0.3111 0.577 . |*. | . |*. | 3 0.133 0.137 1.2567 0.533 .*| . | .*| . | 4-0.068-0.069 1.5112 0.680 **| . | **| . | 5-0.192-0.223 3.5782 0.466 . | . | . | . | 6-0.025-0.048 3.6144 0.606 .*| . | . | . | 7-0.090-0.038 4.0891 0.665 .*| . | . | . | 8-0.092-0.039 4.5970 0.709 . |*. | . |*. | 9 0.114 0.112 5.3963 0.715 . | . | . | . | 10-0.030-0.039 5.4540 0.793 . | . | . | . | 11 0.060 0.035 5.6877 0.841 .*| . | .*| . | 12-0.065-0.136 5.9706 0.875 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 0.593895 Probability 0.622328 Obs*R-squared 1.868014 Probability 0.600247 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:48 Sample: 1883 1930 Included observations: 48 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 28.16621 21.46620 1.312119 0.1963 YR -0.136021 0.834928 -0.162913 0.8713 YR^2 0.282664 0.232405 1.216259 0.2304 YR2^2 -0.000583 0.000450 -1.295507 0.2019 ============================================================ R-squared 0.038917 Mean dependent var 43.59328 Adjusted R-squared -0.026611 S.D. dependent var 78.38858 S.E. of regression 79.42475 Akaike info criter 8.829275 Sum squared resid 277564.8 Schwarz criterion 8.985209 Log likelihood -276.0117 F-statistic 0.593895 Durbin-Watson stat 2.456532 Prob(F-statistic) 0.622328 ============================================================ log of lynchings+1 through 1938 (data from Guzman [1952]) ============================================================ LS // Dependent Variable is LLYNBLK52 Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1938 Included observations: 56 after adjusting endpoints Convergence achieved after 8 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 1.909769 0.026734 71.43604 0.0000 YR -0.013776 0.001586 -8.685666 0.0000 YR2 -0.000638 9.63E-05 -6.629471 0.0000 AR(1) 0.323840 0.132758 2.439332 0.0182 MA(6) -0.341444 0.152958 -2.232273 0.0300 ============================================================ R-squared 0.888073 Mean dependent var 1.668114 Adjusted R-squared 0.879294 S.D. dependent var 0.365958 S.E. of regression 0.127144 Akaike info criter-4.039827 Sum squared resid 0.824443 Schwarz criterion -3.858992 Log likelihood 38.65461 F-statistic 101.1635 Durbin-Watson stat 2.021747 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .32 Inverted MA Roots .8 .42 -.72 .42+.72i -.42 -.72i -.42+.7 -.84 ============================================================ ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 3.725051 Probability 0.016804 Obs*R-squared 9.905929 Probability 0.019383 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:49 Sample: 1883 1938 Included observations: 56 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.002709 0.005722 0.473376 0.6379 YR 0.000515 0.000246 2.091507 0.0414 YR^2 8.08E-05 3.65E-05 2.212200 0.0314 YR2^2 -8.42E-08 4.26E-08 -1.973441 0.0538 ============================================================ R-squared 0.176892 Mean dependent var 0.014722 Adjusted R-squared 0.129405 S.D. dependent var 0.025879 S.E. of regression 0.024146 Akaike info criter-7.378492 Sum squared resid 0.030319 Schwarz criterion -7.233824 Log likelihood 131.1372 F-statistic 3.725051 Durbin-Watson stat 1.910449 Prob(F-statistic) 0.016804 ============================================================ number of anti-black lynchings through 1938 ============================================================ LS // Dependent Variable is LYNCHBLK52 Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1938 Included observations: 56 after adjusting endpoints Convergence achieved after 5 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 70.72253 8.279518 8.541866 0.0000 YR -2.018628 0.468807 -4.305882 0.0001 AR(1) 0.636081 0.100898 6.304177 0.0000 MA(3) 0.387926 0.130621 2.969869 0.0045 ============================================================ R-squared 0.844404 Mean dependent var 59.87500 Adjusted R-squared 0.835427 S.D. dependent var 36.96635 S.E. of regression 14.99634 Akaike info criter 5.484362 Sum squared resid 11694.30 Schwarz criterion 5.629030 Log likelihood -229.0227 F-statistic 94.06634 Durbin-Watson stat 2.096360 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .64 Inverted MA Roots .36+.6 .36 -.63 -.73 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:50 Sample: 1883 1938 Included observations: 56 Q-statistic probabilities adjusted for 2 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== .*| . | .*| . | 1-0.061-0.061 0.2213 . | . | . | . | 2-0.020-0.024 0.2457 . | . | . | . | 3-0.020-0.023 0.2703 0.603 **| . | **| . | 4-0.239-0.243 3.8254 0.148 . | . | .*| . | 5-0.028-0.065 3.8744 0.275 . | . | . | . | 6 0.052 0.034 4.0507 0.399 . | . | . | . | 7-0.001-0.012 4.0508 0.542 .*| . | .*| . | 8-0.062-0.131 4.3087 0.635 . | . | .*| . | 9-0.028-0.068 4.3644 0.737 .*| . | .*| . | 10-0.068-0.067 4.6955 0.790 . |*. | . |*. | 11 0.163 0.157 6.6090 0.678 . | . | . | . | 12 0.024-0.007 6.6506 0.758 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 2.700553 Probability 0.076410 Obs*R-squared 5.179044 Probability 0.075056 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:50 Sample: 1883 1938 Included observations: 56 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 247.5172 75.14064 3.294052 0.0018 YR -7.168602 3.741920 -1.915755 0.0608 YR^2 -0.022848 0.219809 -0.103946 0.9176 ============================================================ R-squared 0.092483 Mean dependent var 208.8267 Adjusted R-squared 0.058237 S.D. dependent var 395.8785 S.E. of regression 384.1782 Akaike info criter 11.95430 Sum squared resid 7822423. Schwarz criterion 12.06280 Log likelihood -411.1808 F-statistic 2.700553 Durbin-Watson stat 1.744271 Prob(F-statistic) 0.076410 ============================================================ ayres index through 1938, as reported in appendix to ayres volume ============================================================ LS // Dependent Variable is AYRES Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1938 Included observations: 56 after adjusting endpoints Convergence achieved after 10 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 4.616844 2.141041 2.156355 0.0358 YR -0.018997 0.143876 -0.132038 0.8955 YR2 -0.032230 0.008453 -3.812719 0.0004 AR(1) 0.515373 0.121073 4.256700 0.0001 MA(5) -0.417480 0.131456 -3.175813 0.0025 ============================================================ R-squared 0.649190 Mean dependent var-3.771964 Adjusted R-squared 0.621676 S.D. dependent var 13.35072 S.E. of regression 8.211769 Akaike info criter 4.296182 Sum squared resid 3439.091 Schwarz criterion 4.477017 Log likelihood -194.7537 F-statistic 23.59450 Durbin-Watson stat 1.865079 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .52 Inverted MA Roots .8 .26 -.80 .26+.80i -.68 -.49i -.68+.49i ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:50 Sample: 1883 1938 Included observations: 56 Q-statistic probabilities adjusted for 2 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1 0.050 0.050 0.1454 .*| . | .*| . | 2-0.087-0.090 0.6020 . | . | . | . | 3 0.004 0.013 0.6029 0.437 **| . | **| . | 4-0.197-0.208 3.0249 0.220 . | . | . |*. | 5 0.047 0.075 3.1652 0.367 . |*. | . | . | 6 0.087 0.041 3.6534 0.455 . | . | . | . | 7 0.028 0.040 3.7038 0.593 .*| . | .*| . | 8-0.082-0.124 4.1574 0.655 **| . | **| . | 9-0.243-0.217 8.2252 0.313 . |*. | . |*. | 10 0.077 0.120 8.6493 0.373 . |*. | . |*. | 11 0.159 0.137 10.485 0.313 . | . | .*| . | 12-0.048-0.095 10.653 0.385 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 2.835265 Probability 0.047015 Obs*R-squared 7.872378 Probability 0.048724 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:51 Sample: 1883 1938 Included observations: 56 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 42.29158 19.96646 2.118131 0.0390 YR 2.265753 0.858378 2.639575 0.0109 YR^2 0.183882 0.127404 1.443301 0.1549 YR2^2 -0.000276 0.000149 -1.857956 0.0688 ============================================================ R-squared 0.140578 Mean dependent var 61.41234 Adjusted R-squared 0.090996 S.D. dependent var 88.36791 S.E. of regression 84.25146 Akaike info criter 8.936361 Sum squared resid 369112.1 Schwarz criterion 9.081029 Log likelihood -325.6787 F-statistic 2.835265 Durbin-Watson stat 2.152097 Prob(F-statistic) 0.047015 ============================================================ log price of cotton through 1938 ============================================================ LS // Dependent Variable is LCOTTON Date: 12/05/97 Time: 16:10 Sample(adjusted): 1883 1938 Included observations: 56 after adjusting endpoints Convergence achieved after 3 iterations ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 1.360419 0.058928 23.08610 0.0000 YR 0.009766 0.003808 2.564511 0.0133 YR2 -0.000308 0.000186 -1.652993 0.1044 AR(1) 0.703196 0.094365 7.451840 0.0000 ============================================================ R-squared 0.703628 Mean dependent var 1.332469 Adjusted R-squared 0.686530 S.D. dependent var 0.166990 S.E. of regression 0.093495 Akaike info criter-4.670943 Sum squared resid 0.454549 Schwarz criterion -4.526275 Log likelihood 55.32585 F-statistic 41.15182 Durbin-Watson stat 1.760728 Prob(F-statistic) 0.000000 ============================================================ Inverted AR Roots .70 ============================================================ Correlogram of Residuals ============================================================== Date: 12/05/97 Time: 21:51 Sample: 1883 1938 Included observations: 56 Q-statistic probabilities adjusted for 1 ARMA term(s) ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . |*. | . |*. | 1 0.119 0.119 0.8308 .*| . | .*| . | 2-0.091-0.107 1.3325 0.248 .*| . | .*| . | 3-0.148-0.127 2.6774 0.262 .*| . | .*| . | 4-0.109-0.088 3.4201 0.331 . | . | . | . | 5 0.008 0.006 3.4246 0.489 . |** | . |*. | 6 0.204 0.175 6.1405 0.293 . | . | .*| . | 7-0.033-0.106 6.2138 0.400 .*| . | .*| . | 8-0.163-0.135 8.0067 0.332 .*| . | . | . | 9-0.078-0.010 8.4242 0.393 . |*. | . |*. | 10 0.153 0.181 10.069 0.345 .*| . | **| . | 11-0.090-0.201 10.653 0.385 . | . | .*| . | 12-0.036-0.076 10.748 0.465 ============================================================== ============================================================ White Heteroskedasticity Test: ============================================================ F-statistic 5.583933 Probability 0.002135 Obs*R-squared 13.64474 Probability 0.003431 ============================================================ Test Equation: LS // Dependent Variable is RESID^2 Date: 12/05/97 Time: 21:51 Sample: 1883 1938 Included observations: 56 ============================================================ Variable CoefficienStd. Errort-Statistic Prob. ============================================================ C 0.005192 0.002600 1.996797 0.0511 YR 0.000422 0.000112 3.773545 0.0004 YR^2 3.11E-05 1.66E-05 1.877062 0.0661 YR2^2 -5.00E-08 1.94E-08 -2.578029 0.0128 ============================================================ R-squared 0.243656 Mean dependent var 0.008117 Adjusted R-squared 0.200021 S.D. dependent var 0.012268 S.E. of regression 0.010973 Akaike info criter-8.955934 Sum squared resid 0.006261 Schwarz criterion -8.811266 Log likelihood 175.3056 F-statistic 5.583933 Durbin-Watson stat 2.055698 Prob(F-statistic) 0.002135 ============================================================ percentage change in real price of cotton Correlogram of PCTCOTTON ============================================================== Date: 12/05/97 Time: 21:52 Sample: 1882 1938 Included observations: 56 ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1 0.008 0.008 0.0034 0.953 .*| . | .*| . | 2-0.168-0.168 1.7006 0.427 .*| . | .*| . | 3-0.143-0.145 2.9624 0.397 .*| . | **| . | 4-0.164-0.203 4.6470 0.325 . | . | .*| . | 5 0.001-0.064 4.6470 0.460 . |** | . |*. | 6 0.218 0.139 7.7201 0.259 . | . | . | . | 7-0.003-0.057 7.7205 0.358 .*| . | .*| . | 8-0.135-0.126 8.9599 0.346 .*| . | .*| . | 9-0.094-0.085 9.5752 0.386 . |*. | . |*. | 10 0.151 0.176 11.175 0.344 . | . | . | . | 11-0.001-0.054 11.175 0.429 . | . | .*| . | 12-0.028-0.094 11.232 0.509 ============================================================== Correlogram of PRPCGNP ============================================================== Date: 12/05/97 Time: 21:52 Sample: 1882 1938 Included observations: 56 ============================================================== Autocorrelation Partial Correlation AC PAC Q-Stat Prob ============================================================== . | . | . | . | 1 0.020 0.020 0.0248 0.875 .*| . | .*| . | 2-0.087-0.087 0.4787 0.787 .*| . | .*| . | 3-0.147-0.145 1.8062 0.614 .*| . | .*| . | 4-0.108-0.115 2.5387 0.638 .*| . | **| . | 5-0.173-0.207 4.4533 0.486 . |*. | . | . | 6 0.076 0.030 4.8298 0.566 . | . | .*| . | 7 0.016-0.060 4.8461 0.679 .*| . | **| . | 8-0.131-0.208 6.0145 0.646 . | . | .*| . | 9-0.017-0.065 6.0335 0.737 . | . | .*| . | 10-0.035-0.128 6.1213 0.805 . |*. | . |*. | 11 0.139 0.090 7.5245 0.755 . |*. | . | . | 12 0.095 0.022 8.1870 0.770 ============================================================== west1=hepworth and west's prewhitened lynching series west4=hepworth and west's prewhitened ayres index Cross Correlogram of WEST4 and WEST1 ============================================================= Date: 12/05/97 Time: 21:57 Sample: 1882 1938 Included observations: 49 Correlations are asymptotically consistent approximations ============================================================= WEST4,WEST1(-i) WEST4,WEST1(+i) i lag lead ============================================================= ****| . | ****| . | 0-0.4168-0.4168 . *| . | . | . | 1-0.0413 0.0200 . | . | . |*** | 2-0.0063 0.2972 .**| . | . |*** | 3-0.1559 0.3008 . *| . | . | . | 4-0.0688-0.0088 . *| . | . |**. | 5-0.1020 0.1563 . | . | . *| . | 6 0.0245-0.0558 . | . | . | . | 7 0.0268-0.0278 . | . | . | . | 8 0.0293 0.0231 . | . | . | . | 9-0.0194-0.0394 . |* . | . | . | 10 0.0626 0.0115 .**| . | . *| . | 11-0.1985-0.0903 . | . | . *| . | 12-0.0097-0.1050 ============================================================= west6=hepworth and west's prewhitened log-cotton prices Cross Correlogram of WEST6 and WEST1 ============================================================= Date: 12/05/97 Time: 21:58 Sample: 1882 1938 Included observations: 49 Correlations are asymptotically consistent approximations ============================================================= WEST6,WEST1(-i) WEST6,WEST1(+i) i lag lead ============================================================= .**| . | .**| . | 0-0.2012-0.2012 . | . | . | . | 1 0.0396 0.0027 . | . | . |* . | 2-0.0395 0.1544 . | . | . |**** | 3 0.0060 0.3712 . | . | . *| . | 4-0.0379-0.0786 . *| . | .**| . | 5-0.0790-0.1956 . |* . | .**| . | 6 0.0661-0.1845 . | . | .**| . | 7 0.0200-0.1781 . |* . | . | . | 8 0.1265-0.0290 . |* . | . | . | 9 0.1459-0.0310 . |* . | .**| . | 10 0.0857-0.2369 . |* . | . |* . | 11 0.0668 0.1152 . *| . | . *| . | 12-0.0993-0.0457 =============================================================