RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit026w.rwl LOG FILE PROCESSED: brit026w.rwl_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 50 25 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 570 1 Coulin WIDTH_RING PISY - 570 2 Great Britain Scots pine, Scotch pine 250 5732-521 1671 1978 - 570 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 8 570042 MISSING VALUES FOUND: 1 IN 1 GAPS / 1844 1844 / -------------------------------------------------------------------- 12 570062 MISSING VALUES FOUND: 1 IN 1 GAPS / 1826 1826 / -------------------------------------------------------------------- 13 570071 MISSING VALUES FOUND: 5 IN 1 GAPS / 1899 1903 / -------------------------------------------------------------------- 14 570072 MISSING VALUES FOUND: 1 IN 1 GAPS / 1861 1861 / -------------------------------------------------------------------- 15 570081 MISSING VALUES FOUND: 35 IN 1 GAPS / 1876 1910 / -------------------------------------------------------------------- 16 570082 MISSING VALUES FOUND: 8 IN 2 GAPS / 1734 1734 / 1793 1799 / -------------------------------------------------------------------- 18 570092 MISSING VALUES FOUND: 5 IN 1 GAPS / 1928 1932 / -------------------------------------------------------------------- 19 570101 MISSING VALUES FOUND: 4 IN 1 GAPS / 1837 1840 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 570011 1825 1978 154 1.353 0.623 0.736 2.883 0.213 0.792 2 570012 1840 1978 139 1.272 0.852 0.508 2.637 0.205 0.867 3 570021 1794 1978 185 0.935 0.560 0.939 3.437 0.233 0.870 4 570022 1687 1978 292 0.689 0.366 1.413 5.994 0.233 0.794 5 570031 1702 1978 277 0.991 0.567 1.001 3.335 0.208 0.877 6 570032 1830 1978 149 0.882 0.536 1.141 3.803 0.211 0.893 7 570041 1851 1978 128 1.213 0.429 0.402 2.214 0.158 0.811 8 570042 1807 1978 172 1.543 0.622 0.773 3.241 0.161 0.842 9 570051 1823 1912 90 1.442 0.801 0.708 2.779 0.203 0.877 10 570052 1793 1978 186 0.963 0.393 0.997 3.653 0.195 0.792 11 570061 1742 1978 237 0.738 0.484 1.798 6.946 0.238 0.870 12 570062 1722 1943 222 1.009 0.436 1.395 5.018 0.178 0.867 13 570071 1690 1960 271 0.708 0.582 2.126 9.487 0.237 0.833 14 570072 1806 1920 115 0.448 0.183 0.594 2.471 0.221 0.751 15 570081 1739 1966 228 0.715 0.510 1.547 4.789 0.226 0.902 16 570082 1705 1978 274 0.774 0.384 2.753 12.435 0.184 0.821 17 570091 1851 1940 90 1.183 0.924 1.578 4.961 0.282 0.862 18 570092 1809 1978 170 0.859 0.372 1.360 4.378 0.194 0.792 19 570101 1734 1976 243 1.014 0.500 1.524 7.278 0.228 0.786 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 570102 1671 1978 308 0.995 1.038 2.001 6.438 0.216 0.932 21 570111 1833 1978 146 1.456 0.864 3.126 15.659 0.217 0.753 NUMBER OF SERIES READ IN: 21 FROM 1671 TO 1978 308 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 191 1.009 0.573 1.353 5.421 0.211 0.837 STANDARD DEVIATION 66 0.292 0.215 0.715 3.453 0.028 0.050 MEDIAN (50TH QUANTILE) 185 0.991 0.536 1.360 4.378 0.213 0.842 INTERQUARTILE RANGE 93 0.439 0.194 0.806 3.197 0.033 0.078 MINIMUM VALUE 90 0.448 0.183 0.402 2.214 0.158 0.751 LOWER HINGE (25TH QUANTILE) 146 0.774 0.429 0.773 3.241 0.195 0.792 UPPER HINGE (75TH QUANTILE) 239 1.213 0.623 1.578 6.438 0.228 0.870 MAXIMUM VALUE 308 1.543 1.038 3.126 15.659 0.282 0.932 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.376 0.293 0.020 -0.891 3.416 -0.527 0.868 MINIMUM CORRELATION: -0.527 SERIES 570012 AND 570081 127 YEARS MAXIMUM CORRELATION: 0.868 SERIES 570041 AND 570051 62 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 48.68 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1730. 1755. 1780. 1805. 1830. 1855. 1880. 1905. 1930. CORR 10. 15. 36. 36. 55. 136. 210. 171. 136. RBAR 0.227 0.315 0.329 0.282 0.121 0.308 0.262 0.216 0.265 SDEV 0.261 0.343 0.228 0.295 0.251 0.223 0.241 0.262 0.271 SERR 0.082 0.089 0.038 0.049 0.034 0.019 0.017 0.020 0.023 EPS 0.662 0.796 0.823 0.826 0.694 0.898 0.882 0.850 0.872 NSS 6.7 8.5 9.5 12.1 16.5 19.9 21.0 20.5 19.0 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1671 1978 308 1.128 0.734 3.035 14.542 0.144 0.889 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.066 0.027 0.475 84 224 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.54 1.01 1.09 1.63 5.34 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.12 0.00 0.84 0.96 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 185. 97. 90. 146. 243. 308. |----------- RAW DATA CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.886 0.774 0.700 0.654 0.657 0.670 0.666 0.620 0.543 0.505 PACF 0.886 -0.051 0.115 0.088 0.230 0.106 0.033 -0.120 -0.127 0.110 95% C.L. 0.114 0.183 0.221 0.248 0.270 0.290 0.309 0.327 0.342 0.353 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.823 0.907 |================== DETRENDED DATA CURVE FITS AND STATISTICS ==================| |------------------------ RESULTS OF FIRST DETRENDING -------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 570011 3 0.00000000 0.00000000 -0.00923570 2.06829906 2 570012 3 0.00000000 0.00000000 -0.01744064 2.49329066 3 570021 3 0.00000000 0.00000000 -0.00555790 1.45169568 4 570022 1 1.86898768 0.14998059 0.00000000 0.64972472 5 570031 3 0.00000000 0.00000000 -0.00506745 1.69542301 6 570032 1 1.79363716 0.01892684 0.00000000 0.28977013 7 570041 1 0.97572488 0.04930628 0.00000000 1.06242371 8 570042 1 2.63362432 0.00686068 0.00000000 0.00322693 9 570051 3 0.00000000 0.00000000 -0.02736684 2.68719101 10 570052 3 0.00000000 0.00000000 -0.00434226 1.36863530 11 570061 1 1.40124547 0.01135174 0.00000000 0.25510180 12 570062 1 1.23537707 0.00472566 0.00000000 0.24745473 13 570071 -67 181 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 570072 1 0.60030770 0.01458724 0.00000000 0.15953732 15 570081 1 1.84307253 0.03218872 0.00000000 0.41769141 16 570082 1 1.70441103 0.04182235 0.00000000 0.62492037 17 570091 1 2.81365919 0.02348014 0.00000000 0.02635617 18 570092 1 1.16079044 0.03007899 0.00000000 0.61978853 19 570101 3 0.00000000 0.00000000 -0.00136431 1.18930936 SERIES IDENT OPTION A B C D 20 570102 1 3.91508150 0.01833376 0.00000000 0.31099212 21 570111 3 0.00000000 0.00000000 -0.00989627 2.18347192 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 570011 1825 1978 154 0.998 0.320 0.347 2.592 0.211 0.665 2 570012 1840 1978 139 1.103 0.822 3.989 20.622 0.203 0.788 3 570021 1794 1978 185 0.981 0.442 0.617 3.130 0.232 0.792 4 570022 1687 1978 292 1.000 0.477 1.041 4.432 0.232 0.801 5 570031 1702 1978 277 1.014 0.374 0.469 2.914 0.207 0.733 6 570032 1830 1978 149 1.000 0.354 1.253 5.128 0.208 0.705 7 570041 1851 1978 128 1.000 0.323 0.799 3.321 0.157 0.769 8 570042 1807 1978 172 1.001 0.220 0.496 2.972 0.160 0.584 9 570051 1823 1912 90 1.045 0.352 2.684 12.901 0.201 0.665 10 570052 1793 1978 186 1.000 0.294 0.270 3.177 0.194 0.655 11 570061 1742 1978 237 0.997 0.405 1.053 4.080 0.237 0.746 12 570062 1722 1943 222 1.000 0.326 0.554 3.190 0.177 0.793 13 570071 1690 1960 271 1.002 0.435 0.776 3.457 0.237 0.713 14 570072 1806 1920 115 1.000 0.262 0.138 3.543 0.220 0.422 15 570081 1739 1966 228 1.001 0.423 0.886 3.509 0.224 0.761 16 570082 1705 1978 274 1.000 0.258 0.613 3.561 0.184 0.575 17 570091 1851 1940 90 1.015 0.510 1.010 3.438 0.280 0.698 18 570092 1809 1978 170 1.000 0.292 0.073 2.762 0.192 0.628 19 570101 1734 1976 243 0.999 0.454 1.006 5.014 0.226 0.767 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 570102 1671 1978 308 1.022 0.371 1.292 7.778 0.215 0.699 21 570111 1833 1978 146 1.003 0.453 2.824 14.878 0.215 0.669 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 194 1.009 0.389 1.057 5.543 0.210 0.697 STANDARD DEVIATION 67 0.025 0.127 0.972 4.744 0.028 0.092 MEDIAN (50TH QUANTILE) 185 1.000 0.371 0.799 3.509 0.211 0.705 INTERQUARTILE RANGE 97 0.003 0.122 0.557 1.837 0.032 0.103 MINIMUM VALUE 90 0.981 0.220 0.073 2.592 0.157 0.422 LOWER HINGE (25TH QUANTILE) 146 1.000 0.320 0.496 3.177 0.194 0.665 UPPER HINGE (75TH QUANTILE) 243 1.003 0.442 1.053 5.014 0.226 0.767 MAXIMUM VALUE 308 1.103 0.822 3.989 20.622 0.280 0.801 |------------------------ RESULTS OF SECOND DETRENDING ------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 570011 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 570012 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 570021 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 570022 -67 195 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 570031 -67 185 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 570032 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 570041 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 570042 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 570051 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 570052 -67 124 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 570061 -67 158 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 570062 -67 148 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 570071 -67 181 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 570072 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 570081 -67 152 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 570082 -67 183 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 570091 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 570092 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 570101 -67 162 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 570102 -67 206 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 570111 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 570011 1825 1978 154 0.995 0.293 0.232 2.547 0.211 0.609 2 570012 1840 1978 139 0.975 0.392 1.048 3.685 0.202 0.747 3 570021 1794 1978 185 0.981 0.361 0.843 3.792 0.232 0.689 4 570022 1687 1978 292 0.989 0.432 0.869 3.796 0.232 0.761 5 570031 1702 1978 277 0.996 0.342 0.307 2.444 0.207 0.706 6 570032 1830 1978 149 0.994 0.319 0.962 4.307 0.208 0.661 7 570041 1851 1978 128 0.989 0.229 0.444 2.752 0.157 0.587 8 570042 1807 1978 172 0.999 0.215 0.411 2.846 0.160 0.564 9 570051 1823 1912 90 0.996 0.239 0.940 4.135 0.200 0.485 10 570052 1793 1978 186 0.993 0.254 0.310 3.281 0.194 0.551 11 570061 1742 1978 237 0.994 0.360 0.892 3.635 0.237 0.671 12 570062 1722 1943 222 0.997 0.316 0.496 3.134 0.177 0.781 13 570071 1690 1960 271 0.996 0.422 0.796 3.589 0.237 0.708 14 570072 1806 1920 115 0.998 0.250 0.036 3.699 0.219 0.379 15 570081 1739 1966 228 0.992 0.293 0.729 4.378 0.224 0.478 16 570082 1705 1978 274 0.998 0.243 0.501 3.601 0.184 0.529 17 570091 1851 1940 90 0.994 0.463 0.807 2.882 0.278 0.687 18 570092 1809 1978 170 0.998 0.287 0.159 2.876 0.192 0.616 19 570101 1734 1976 243 0.990 0.411 1.645 9.709 0.226 0.712 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 570102 1671 1978 308 0.996 0.336 2.051 13.264 0.215 0.636 21 570111 1833 1978 146 0.989 0.373 2.496 12.786 0.215 0.595 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 194 0.993 0.325 0.808 4.626 0.210 0.626 STANDARD DEVIATION 67 0.006 0.073 0.614 3.159 0.028 0.103 MEDIAN (50TH QUANTILE) 185 0.994 0.319 0.796 3.635 0.211 0.636 INTERQUARTILE RANGE 97 0.006 0.119 0.528 1.253 0.032 0.141 MINIMUM VALUE 90 0.975 0.215 0.036 2.444 0.157 0.379 LOWER HINGE (25TH QUANTILE) 146 0.990 0.254 0.411 2.882 0.194 0.564 UPPER HINGE (75TH QUANTILE) 243 0.996 0.373 0.940 4.135 0.226 0.706 MAXIMUM VALUE 308 0.999 0.463 2.496 13.264 0.278 0.781 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.219 0.154 0.011 0.021 2.707 -0.162 0.650 MINIMUM CORRELATION: -0.162 SERIES 570071 AND 570091 90 YEARS MAXIMUM CORRELATION: 0.650 SERIES 570101 AND 570102 243 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 48.68 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1730. 1755. 1780. 1805. 1830. 1855. 1880. 1905. 1930. CORR 10. 15. 36. 36. 55. 136. 210. 171. 136. RBAR 0.253 0.251 0.391 0.297 0.141 0.234 0.248 0.230 0.265 SDEV 0.259 0.304 0.182 0.236 0.232 0.187 0.193 0.232 0.226 SERR 0.082 0.078 0.030 0.039 0.031 0.016 0.013 0.018 0.019 EPS 0.693 0.740 0.859 0.836 0.731 0.859 0.874 0.859 0.873 NSS 6.7 8.5 9.5 12.1 16.5 19.9 21.0 20.5 19.0 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1671 1978 308 0.975 0.205 0.735 5.422 0.137 0.664 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.442 0.316 -0.034 84 224 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.95 1.00 1.08 2.03 18.42 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.11 0.00 0.84 0.96 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.662 0.424 0.229 0.110 0.010 -0.012 -0.061 -0.056 -0.091 -0.073 PACF 0.662 -0.025 -0.076 -0.010 -0.062 0.039 -0.073 0.025 -0.075 0.030 95% C.L. 0.114 0.156 0.170 0.174 0.175 0.175 0.175 0.176 0.176 0.176 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.439 0.663 |======================= POOLED AUTOREGRESSION ANALYSIS =======================| POOLED AUTOCORRELATIONS: LAG T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.587 0.365 0.147 0.054 -0.013 -0.048 -0.117 -0.103 -0.104 -0.090 YULE-WALKER ESTIMATES OF AUTOREGRESSION: ORDER T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 1 0.587 2 0.570 0.030 3 0.573 0.099 -0.121 4 0.574 0.099 -0.125 0.007 5 0.574 0.095 -0.122 0.023 -0.027 6 0.573 0.096 -0.126 0.026 -0.009 -0.031 7 0.570 0.095 -0.124 0.013 0.001 0.026 -0.099 8 0.573 0.094 -0.124 0.013 0.003 0.024 -0.112 0.023 9 0.573 0.092 -0.123 0.013 0.004 0.021 -0.110 0.037 -0.024 10 0.572 0.093 -0.126 0.013 0.004 0.021 -0.114 0.039 -0.007 -0.030 LAST TERM IN EACH ROW ABOVE EQUALS THE PARTIAL AUTOCORRELATION COEFFICIENT AKAIKE INFORMATION CRITERION: AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) 2319.09 2190.74 2192.45 2189.92 2191.90 2193.68 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2195.39 2194.34 2196.18 2198.00 2199.73 SELECTED AUTOREGRESSION ORDER: 1 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.587 R-SQUARED DUE TO POOLED AUTOREGRESSION: 34.51 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 152.69 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.587 0.345 0.203 0.119 0.070 0.041 0.024 0.014 0.008 0.0049 0.003 0.002 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 570011 1 0.389 0.610 2 570012 1 0.645 0.770 3 570021 1 0.482 0.694 4 570022 1 0.584 0.763 5 570031 1 0.506 0.710 6 570032 1 0.449 0.662 7 570041 1 0.402 0.589 8 570042 1 0.324 0.565 9 570051 1 0.245 0.488 10 570052 1 0.309 0.556 11 570061 1 0.464 0.679 12 570062 1 0.613 0.782 13 570071 1 0.524 0.724 14 570072 1 0.155 0.381 15 570081 1 0.229 0.479 16 570082 1 0.282 0.530 17 570091 1 0.487 0.689 18 570092 1 0.386 0.618 19 570101 1 0.543 0.736 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 570102 1 0.406 0.637 21 570111 1 0.373 0.595 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.419 0.631 STANDARD DEVIATION 0 0.131 0.106 MEDIAN 1 0.406 0.637 INTERQUARTILE RANGE 0 0.182 0.146 MINIMUM VALUE 1 0.155 0.381 LOWER HINGE 1 0.324 0.565 UPPER HINGE 1 0.506 0.710 MAXIMUM VALUE 1 0.645 0.782 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 570011 1825 1978 154 1.000 0.232 0.450 3.113 0.278 -0.100 2 570012 1840 1978 139 1.000 0.250 0.766 4.314 0.286 -0.242 3 570021 1794 1978 185 1.000 0.259 0.547 3.128 0.288 0.022 4 570022 1687 1978 292 1.000 0.279 0.552 5.346 0.308 -0.058 5 570031 1702 1978 277 1.000 0.241 0.368 3.280 0.276 -0.043 6 570032 1830 1978 149 1.000 0.239 0.952 4.749 0.263 -0.088 7 570041 1851 1978 128 1.000 0.185 0.449 3.184 0.206 -0.173 8 570042 1807 1978 172 1.000 0.177 0.380 3.585 0.202 -0.049 9 570051 1823 1912 90 1.000 0.209 0.746 3.638 0.230 0.047 10 570052 1793 1978 186 1.000 0.211 0.589 3.610 0.228 0.007 11 570061 1742 1978 237 1.000 0.264 0.365 3.570 0.298 -0.047 12 570062 1722 1943 222 1.000 0.197 0.178 3.558 0.229 -0.054 13 570071 1690 1960 271 1.000 0.288 0.961 4.778 0.299 -0.031 14 570072 1806 1920 115 1.000 0.231 0.174 4.130 0.255 -0.041 15 570081 1739 1966 228 1.000 0.257 1.007 8.237 0.268 -0.002 16 570082 1705 1978 274 1.000 0.206 0.539 3.695 0.227 -0.019 17 570091 1851 1940 90 1.000 0.335 0.251 3.520 0.357 0.107 18 570092 1809 1978 170 1.000 0.225 0.235 3.385 0.249 0.048 19 570101 1734 1976 243 1.000 0.273 1.434 9.171 0.276 0.007 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 570102 1671 1978 308 1.000 0.259 1.154 7.636 0.288 -0.004 21 570111 1833 1978 146 1.000 0.300 2.462 12.792 0.264 0.102 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 194 1.000 0.244 0.693 4.877 0.266 -0.029 STANDARD DEVIATION 67 0.000 0.039 0.528 2.514 0.037 0.081 MEDIAN (50TH QUANTILE) 185 1.000 0.241 0.547 3.638 0.268 -0.031 INTERQUARTILE RANGE 97 0.000 0.053 0.583 1.258 0.058 0.062 MINIMUM VALUE 90 1.000 0.177 0.174 3.113 0.202 -0.242 LOWER HINGE (25TH QUANTILE) 146 1.000 0.211 0.368 3.520 0.230 -0.054 UPPER HINGE (75TH QUANTILE) 243 1.000 0.264 0.952 4.778 0.288 0.007 MAXIMUM VALUE 308 1.000 0.335 2.462 12.792 0.357 0.107 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.263 0.121 0.008 0.400 2.822 0.008 0.589 MINIMUM CORRELATION: 0.008 SERIES 570082 AND 570091 90 YEARS MAXIMUM CORRELATION: 0.589 SERIES 570051 AND 570052 90 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 48.68 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1730. 1755. 1780. 1805. 1830. 1855. 1880. 1905. 1930. CORR 10. 15. 36. 36. 55. 136. 210. 171. 136. RBAR 0.228 0.328 0.299 0.221 0.170 0.217 0.318 0.304 0.282 SDEV 0.189 0.152 0.137 0.146 0.142 0.171 0.152 0.136 0.136 SERR 0.060 0.039 0.023 0.024 0.019 0.015 0.010 0.010 0.012 EPS 0.663 0.806 0.801 0.774 0.772 0.847 0.907 0.899 0.882 NSS 6.7 8.5 9.5 12.1 16.5 19.9 21.0 20.5 19.0 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1671 1978 308 0.989 0.141 0.556 4.801 0.152 0.106 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.361 0.221 -0.033 102 206 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 0.86 1.00 1.10 1.96 9.50 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.11 0.00 0.86 0.97 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.106 0.053 -0.030 0.011 -0.072 -0.015 -0.087 -0.021 -0.088 -0.010 PACF 0.106 0.042 -0.040 0.017 -0.072 -0.003 -0.078 -0.008 -0.078 -0.002 95% C.L. 0.114 0.115 0.116 0.116 0.116 0.116 0.116 0.117 0.117 0.118 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.013 0.106 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.004 0.046 -0.037 0.023 -0.073 0.002 -0.085 -0.002 -0.086 0.004 PACF -0.004 0.046 -0.037 0.021 -0.070 -0.002 -0.078 -0.008 -0.078 -0.006 95% C.L. 0.114 0.114 0.114 0.114 0.114 0.115 0.115 0.116 0.116 0.117 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.002 -0.004 |========================= ARSTAN CHRONOLOGY STATISTICS =======================| |----------------- ROBUST MEAN ARSTAN CHRONOLOGY STATISTICS -------------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1671 1978 308 0.989 0.173 0.694 5.663 0.127 0.589 |------------ ARSTAN CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.587 0.350 0.163 0.066 -0.034 -0.066 -0.120 -0.113 -0.135 -0.099 PACF 0.587 0.009 -0.070 -0.007 -0.081 -0.009 -0.078 -0.001 -0.064 0.017 95% C.L. 0.114 0.148 0.158 0.161 0.161 0.161 0.161 0.163 0.164 0.165 |------------------- ARSTAN CHRONOLOGY AUTOREGRESSIVE MODEL -------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.345 0.587 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 2.50 MINUTES