RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit020l.rwl LOG FILE PROCESSED: brit020l.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: 569 1 Glen Derry WIDTH_LATE PISY - 569 2 Great Britain Scots pine, Scotch pine 457 5701-334 1773 1978 - 569 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 569012 MISSING VALUES FOUND: 1 IN 1 GAPS / 1970 1970 / -------------------------------------------------------------------- 3 569021 MISSING VALUES FOUND: 1 IN 1 GAPS / 1821 1821 / -------------------------------------------------------------------- 7 569041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1879 1879 / -------------------------------------------------------------------- 20 568102 MISSING VALUES FOUND: 1 IN 1 GAPS / 1953 1953 / -------------------------------------------------------------------- 21 568111 MISSING VALUES FOUND: 1 IN 1 GAPS / 1928 1928 / -------------------------------------------------------------------- 22 568112 MISSING VALUES FOUND: 15 IN 2 GAPS / 1907 1920 / 1940 1940 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 569011 1814 1978 165 0.358 0.241 1.603 8.175 0.466 0.636 2 569012 1773 1978 206 0.159 0.097 1.414 6.071 0.400 0.686 3 569021 1779 1978 200 0.317 0.208 1.273 4.099 0.396 0.708 4 569022 1809 1978 170 0.305 0.168 1.870 10.747 0.373 0.538 5 569031 1779 1978 200 0.269 0.167 0.817 2.892 0.359 0.742 6 569032 1806 1978 173 0.254 0.188 1.241 4.109 0.333 0.824 7 569041 1823 1978 156 0.325 0.215 1.431 5.558 0.413 0.660 8 569042 1820 1978 159 0.230 0.146 1.137 3.587 0.390 0.751 9 569051 1811 1978 168 0.321 0.314 1.811 5.621 0.477 0.805 10 569052 1784 1978 195 0.226 0.110 0.615 3.272 0.403 0.516 11 569061 1838 1978 141 0.449 0.233 0.796 3.794 0.404 0.528 12 569062 1796 1978 183 0.289 0.131 1.079 4.379 0.356 0.438 13 569071 1817 1978 162 0.436 0.272 1.966 7.616 0.369 0.629 14 569072 1790 1978 189 0.285 0.148 1.100 4.690 0.407 0.476 15 569081 1864 1978 115 0.276 0.145 1.087 4.311 0.421 0.505 16 569082 1810 1978 169 0.295 0.149 0.719 3.503 0.414 0.592 17 569091 1833 1978 146 0.287 0.166 1.141 6.122 0.505 0.394 18 569092 1833 1978 146 0.272 0.136 0.480 2.597 0.441 0.442 19 568101 1846 1978 133 0.415 0.193 1.574 8.397 0.336 0.546 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 0.287 0.181 1.206 4.409 0.303 0.772 21 568111 1786 1978 193 0.383 0.272 1.448 5.202 0.406 0.673 22 568112 1773 1978 206 0.299 0.136 1.013 4.107 0.343 0.483 23 568121 1810 1978 169 0.483 0.283 0.585 2.918 0.389 0.623 24 568122 1801 1978 178 0.289 0.161 0.866 3.649 0.431 0.553 25 572131 1878 1978 101 0.181 0.103 1.612 6.867 0.472 0.359 26 572132 1856 1978 123 0.581 0.264 0.941 3.659 0.382 0.466 NUMBER OF SERIES READ IN: 26 FROM 1773 TO 1978 206 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 165 0.318 0.186 1.186 5.013 0.400 0.590 STANDARD DEVIATION 27 0.094 0.060 0.404 1.987 0.048 0.130 MEDIAN (50TH QUANTILE) 169 0.292 0.167 1.139 4.345 0.401 0.573 INTERQUARTILE RANGE 43 0.086 0.088 0.582 2.422 0.052 0.204 MINIMUM VALUE 101 0.159 0.097 0.480 2.597 0.303 0.359 LOWER HINGE (25TH QUANTILE) 146 0.272 0.145 0.866 3.649 0.369 0.483 UPPER HINGE (75TH QUANTILE) 189 0.358 0.233 1.448 6.071 0.421 0.686 MAXIMUM VALUE 205 0.581 0.314 1.966 10.747 0.505 0.824 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.442 0.157 0.009 -0.581 3.618 -0.197 0.782 MINIMUM CORRELATION: -0.197 SERIES 569012 AND 568101 133 YEARS MAXIMUM CORRELATION: 0.782 SERIES 569021 AND 569022 170 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.86 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1798. 1830. 1855. 1880. 1905. 1930. CORR 1. 36. 171. 253. 325. 325. RBAR 0.271 0.355 0.448 0.350 0.338 0.258 SDEV 0.000 0.224 0.148 0.182 0.190 0.197 SERR 0.000 0.037 0.011 0.011 0.011 0.011 EPS 0.769 0.912 0.950 0.932 0.930 0.900 NSS 9.0 18.8 23.2 25.3 26.0 26.0 |======================== 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 1773 1978 206 0.319 0.134 0.709 3.099 0.297 0.596 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.774 0.395 0.028 119 87 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.76 1.00 1.08 1.84 6.80 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.09 0.62 0.88 0.97 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 169. 43. 101. 146. 189. 206. |----------- 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 0.593 0.579 0.482 0.546 0.491 0.539 0.490 0.514 0.437 0.458 PACF 0.593 0.350 0.091 0.246 0.089 0.167 0.068 0.093 -0.031 0.034 95% C.L. 0.139 0.182 0.215 0.235 0.258 0.276 0.295 0.311 0.327 0.338 |------------------ 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 2 0.441 0.384 0.356 |================== 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 569011 1 0.48302397 0.00880924 0.00000000 0.10486344 2 569012 1 0.24945582 0.03060909 0.00000000 0.11945824 3 569021 1 0.64363766 0.01393588 0.00000000 0.10251639 4 569022 1 0.46042964 0.01282072 0.00000000 0.11908323 5 569031 1 0.44716701 0.01069289 0.00000000 0.08604921 6 569032 3 0.00000000 0.00000000 -0.00245382 0.46747077 7 569041 1 0.56058544 0.01389120 0.00000000 0.09780087 8 569042 1 0.43248409 0.02721428 0.00000000 0.13252208 9 569051 1 1.15696144 0.03645338 0.00000000 0.13640428 10 569052 1 0.20538457 0.00718555 0.00000000 0.11619303 11 569061 3 0.00000000 0.00000000 -0.00366767 0.70919859 12 569062 1 0.26702425 0.03133864 0.00000000 0.24360420 13 569071 1 0.77694476 0.03042550 0.00000000 0.28168672 14 569072 1 0.26709148 0.01747563 0.00000000 0.20776406 15 569081 1 0.36486199 0.00944445 0.00000000 0.05433823 16 569082 1 0.35658124 0.02913638 0.00000000 0.22382927 17 569091 3 0.00000000 0.00000000 -0.00158767 0.40347472 18 569092 1 0.29700631 0.01090518 0.00000000 0.12462153 19 568101 3 0.00000000 0.00000000 -0.00105472 0.48547846 SERIES IDENT OPTION A B C D 20 568102 1 0.50494832 0.02822745 0.00000000 0.18361798 21 568111 1 0.78104788 0.02314318 0.00000000 0.21067621 22 568112 1 0.31033057 0.02804170 0.00000000 0.23539038 23 568121 3 0.00000000 0.00000000 -0.00385871 0.81059384 24 568122 3 0.00000000 0.00000000 -0.00164108 0.43620262 25 572131 1 0.29327282 0.10279247 0.00000000 0.15397179 26 572132 1 0.63131827 0.03027984 0.00000000 0.41797283 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 569011 1814 1978 165 1.000 0.656 2.100 11.196 0.463 0.568 2 569012 1773 1978 206 0.999 0.574 2.827 18.852 0.401 0.534 3 569021 1779 1978 200 1.002 0.402 0.600 3.255 0.391 0.325 4 569022 1809 1978 170 0.999 0.392 0.847 4.126 0.371 0.251 5 569031 1779 1978 200 1.001 0.516 1.497 7.270 0.358 0.575 6 569032 1806 1978 173 1.052 0.660 1.991 9.031 0.332 0.682 7 569041 1823 1978 156 0.999 0.522 1.199 4.780 0.414 0.486 8 569042 1820 1978 159 1.000 0.441 0.642 3.630 0.387 0.420 9 569051 1811 1978 168 1.000 0.640 2.053 9.148 0.474 0.534 10 569052 1784 1978 195 1.000 0.465 0.775 3.758 0.401 0.431 11 569061 1838 1978 141 0.993 0.403 0.957 4.982 0.401 0.255 12 569062 1796 1978 183 1.000 0.405 1.008 4.094 0.355 0.348 13 569071 1817 1978 162 0.999 0.414 0.649 3.067 0.366 0.321 14 569072 1790 1978 189 1.000 0.464 0.755 3.311 0.405 0.392 15 569081 1864 1978 115 1.000 0.459 1.003 4.507 0.416 0.356 16 569082 1810 1978 169 1.000 0.440 0.609 4.164 0.412 0.404 17 569091 1833 1978 146 0.997 0.518 1.081 6.604 0.502 0.287 18 569092 1833 1978 146 1.000 0.439 0.214 2.571 0.438 0.294 19 568101 1846 1978 133 0.999 0.459 1.485 7.373 0.333 0.530 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 1.000 0.488 0.679 2.980 0.304 0.673 21 568111 1786 1978 193 0.999 0.550 1.615 6.882 0.406 0.490 22 568112 1773 1978 206 0.999 0.396 0.437 2.799 0.339 0.446 23 568121 1810 1978 169 0.984 0.489 1.432 5.892 0.387 0.500 24 568122 1801 1978 178 0.994 0.480 0.945 4.083 0.429 0.348 25 572131 1878 1978 101 1.000 0.513 1.781 7.810 0.466 0.133 26 572132 1856 1978 123 1.000 0.360 0.447 3.024 0.378 0.203 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 166 1.001 0.483 1.140 5.738 0.397 0.415 STANDARD DEVIATION 27 0.011 0.081 0.629 3.523 0.047 0.139 MEDIAN (50TH QUANTILE) 169 1.000 0.464 0.980 4.336 0.401 0.412 INTERQUARTILE RANGE 43 0.001 0.105 0.849 3.958 0.050 0.209 MINIMUM VALUE 101 0.984 0.360 0.214 2.571 0.304 0.133 LOWER HINGE (25TH QUANTILE) 146 0.999 0.414 0.649 3.311 0.366 0.321 UPPER HINGE (75TH QUANTILE) 189 1.000 0.518 1.497 7.270 0.416 0.530 MAXIMUM VALUE 206 1.052 0.660 2.827 18.852 0.502 0.682 |------------------------ 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 569011 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 569012 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 569021 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 569022 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 569031 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 569032 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 569041 -67 104 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 569042 -67 106 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 569051 -67 112 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 569052 -67 130 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 569061 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 569062 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 569071 -67 108 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 569072 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 569081 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 569082 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 569091 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 569092 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 568101 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 568102 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 568111 -67 129 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 568112 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 568121 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 568122 -67 119 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 572131 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 572132 -67 82 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 569011 1814 1978 165 0.990 0.631 2.164 12.386 0.463 0.542 2 569012 1773 1978 206 0.994 0.534 2.314 13.885 0.401 0.495 3 569021 1779 1978 200 0.998 0.394 0.563 3.082 0.391 0.302 4 569022 1809 1978 170 0.996 0.380 0.900 4.425 0.371 0.195 5 569031 1779 1978 200 0.997 0.507 1.398 6.361 0.358 0.570 6 569032 1806 1978 173 0.972 0.469 1.036 3.898 0.332 0.612 7 569041 1823 1978 156 0.998 0.523 1.350 5.596 0.413 0.486 8 569042 1820 1978 159 0.994 0.420 0.564 3.551 0.386 0.363 9 569051 1811 1978 168 0.995 0.545 1.409 6.587 0.474 0.442 10 569052 1784 1978 195 0.993 0.443 0.680 3.697 0.401 0.377 11 569061 1838 1978 141 0.999 0.403 1.045 5.157 0.401 0.235 12 569062 1796 1978 183 0.998 0.395 1.004 4.149 0.355 0.310 13 569071 1817 1978 162 0.997 0.401 0.568 2.848 0.366 0.299 14 569072 1790 1978 189 0.998 0.450 0.668 3.137 0.405 0.362 15 569081 1864 1978 115 0.995 0.440 0.889 4.302 0.417 0.327 16 569082 1810 1978 169 0.997 0.415 0.462 4.009 0.412 0.339 17 569091 1833 1978 146 0.995 0.492 0.751 4.688 0.502 0.257 18 569092 1833 1978 146 0.996 0.434 0.321 2.826 0.438 0.259 19 568101 1846 1978 133 0.997 0.436 1.287 6.164 0.334 0.503 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 0.998 0.479 0.718 3.194 0.303 0.665 21 568111 1786 1978 193 0.998 0.550 1.685 7.268 0.406 0.488 22 568112 1773 1978 206 0.997 0.378 0.490 3.114 0.339 0.391 23 568121 1810 1978 169 0.988 0.433 1.236 5.138 0.387 0.383 24 568122 1801 1978 178 0.999 0.470 0.890 4.156 0.429 0.307 25 572131 1878 1978 101 0.996 0.461 1.355 5.770 0.465 0.030 26 572132 1856 1978 123 0.999 0.353 0.389 2.955 0.378 0.180 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 166 0.995 0.455 1.005 5.090 0.397 0.374 STANDARD DEVIATION 27 0.005 0.064 0.514 2.691 0.047 0.145 MEDIAN (50TH QUANTILE) 169 0.997 0.442 0.895 4.229 0.401 0.363 INTERQUARTILE RANGE 43 0.003 0.089 0.782 2.576 0.051 0.190 MINIMUM VALUE 101 0.972 0.353 0.321 2.826 0.303 0.030 LOWER HINGE (25TH QUANTILE) 146 0.995 0.403 0.568 3.194 0.366 0.299 UPPER HINGE (75TH QUANTILE) 189 0.998 0.492 1.350 5.770 0.417 0.488 MAXIMUM VALUE 206 0.999 0.631 2.314 13.885 0.502 0.665 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.292 0.124 0.007 -0.180 3.404 -0.133 0.662 MINIMUM CORRELATION: -0.133 SERIES 569012 AND 568101 133 YEARS MAXIMUM CORRELATION: 0.662 SERIES 569052 AND 569081 115 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.86 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1798. 1830. 1855. 1880. 1905. 1930. CORR 1. 36. 171. 253. 325. 325. RBAR 0.036 0.320 0.406 0.346 0.331 0.290 SDEV 0.000 0.194 0.142 0.171 0.182 0.180 SERR 0.000 0.032 0.011 0.011 0.010 0.010 EPS 0.249 0.898 0.941 0.931 0.928 0.914 NSS 9.0 18.8 23.2 25.3 26.0 26.0 |======================== 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 1773 1978 206 0.969 0.252 0.388 2.913 0.283 0.143 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.501 0.226 0.112 84 122 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.52 1.00 1.08 1.60 36.83 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.66 0.88 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 0.142 0.054 -0.064 -0.031 -0.017 0.006 0.016 -0.081 -0.144 -0.045 PACF 0.142 0.034 -0.078 -0.014 -0.004 0.007 0.013 -0.090 -0.126 0.002 95% C.L. 0.139 0.142 0.143 0.143 0.143 0.143 0.143 0.143 0.144 0.147 |------------------ 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 0.021 0.142 |======================= 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 0.158 0.016 -0.067 -0.040 0.007 0.006 0.051 -0.119 -0.187 -0.035 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 0.158 2 0.159 -0.009 3 0.159 0.002 -0.070 4 0.157 0.002 -0.067 -0.019 5 0.158 0.003 -0.067 -0.022 0.018 6 0.158 0.003 -0.067 -0.022 0.018 -0.002 7 0.158 0.002 -0.066 -0.018 0.018 -0.009 0.047 8 0.164 0.001 -0.064 -0.021 0.009 -0.009 0.069 -0.138 9 0.143 0.011 -0.065 -0.020 0.005 -0.019 0.069 -0.113 -0.155 10 0.147 0.015 -0.067 -0.019 0.005 -0.018 0.071 -0.113 -0.159 0.028 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) 1821.42 1818.23 1820.22 1821.20 1823.13 1825.07 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1827.07 1828.61 1826.64 1823.64 1825.47 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 0.158 R-SQUARED DUE TO POOLED AUTOREGRESSION: 2.49 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 102.55 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.158 0.025 0.004 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 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 569011 1 0.295 0.543 2 569012 1 0.259 0.496 3 569021 1 0.099 0.303 4 569022 1 0.041 0.197 5 569031 1 0.329 0.572 6 569032 1 0.420 0.626 7 569041 1 0.237 0.487 8 569042 1 0.133 0.364 9 569051 1 0.203 0.445 10 569052 1 0.154 0.377 11 569061 1 0.096 0.236 12 569062 1 0.111 0.311 13 569071 1 0.092 0.302 14 569072 1 0.133 0.363 15 569081 1 0.110 0.328 16 569082 1 0.123 0.341 17 569091 1 0.068 0.259 18 569092 1 0.068 0.259 19 568101 1 0.256 0.504 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 568102 1 0.448 0.665 21 568111 1 0.243 0.489 22 568112 1 0.191 0.391 23 568121 1 0.168 0.383 24 568122 1 0.095 0.308 25 572131 1 0.048 0.030 26 572132 1 0.033 0.180 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.171 0.375 STANDARD DEVIATION 0 0.112 0.146 MEDIAN 1 0.133 0.363 INTERQUARTILE RANGE 0 0.148 0.188 MINIMUM VALUE 1 0.033 0.030 LOWER HINGE 1 0.095 0.302 UPPER HINGE 1 0.243 0.489 MAXIMUM VALUE 1 0.448 0.665 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 569011 1814 1978 165 1.001 0.527 2.120 12.184 0.517 0.022 2 569012 1773 1978 206 1.002 0.460 2.085 14.271 0.461 -0.048 3 569021 1779 1978 200 1.000 0.376 0.683 3.287 0.433 -0.027 4 569022 1809 1978 170 1.000 0.372 0.968 4.626 0.403 -0.007 5 569031 1779 1978 200 1.000 0.415 1.459 8.841 0.435 0.029 6 569032 1806 1978 173 1.000 0.366 0.718 3.861 0.425 -0.120 7 569041 1823 1978 156 1.000 0.457 1.366 6.382 0.499 -0.004 8 569042 1820 1978 159 1.000 0.391 0.494 3.890 0.443 0.012 9 569051 1811 1978 168 1.000 0.488 1.096 5.798 0.542 -0.030 10 569052 1784 1978 195 1.000 0.410 0.719 3.932 0.459 -0.044 11 569061 1838 1978 141 1.000 0.391 1.086 5.440 0.437 -0.048 12 569062 1796 1978 183 1.000 0.375 1.110 4.592 0.404 -0.040 13 569071 1817 1978 162 1.000 0.382 0.713 3.402 0.411 -0.007 14 569072 1790 1978 189 1.000 0.419 0.611 2.881 0.463 0.013 15 569081 1864 1978 115 1.000 0.416 0.769 3.909 0.469 0.017 16 569082 1810 1978 169 1.000 0.390 0.493 3.699 0.452 -0.028 17 569091 1833 1978 146 1.000 0.475 0.711 4.947 0.554 -0.007 18 569092 1833 1978 146 1.000 0.419 0.534 3.214 0.459 -0.009 19 568101 1846 1978 133 1.000 0.376 0.999 5.652 0.426 -0.025 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568102 1808 1978 171 1.000 0.357 0.617 3.497 0.390 -0.062 21 568111 1786 1978 193 1.000 0.479 1.150 5.293 0.493 -0.032 22 568112 1773 1978 206 1.000 0.347 0.410 2.896 0.405 -0.082 23 568121 1810 1978 169 1.000 0.400 1.071 4.857 0.460 -0.059 24 568122 1801 1978 178 1.001 0.445 1.006 4.678 0.460 0.009 25 572131 1878 1978 101 1.000 0.461 1.345 5.740 0.470 -0.006 26 572132 1856 1978 123 1.000 0.347 0.534 2.884 0.396 0.005 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 166 1.000 0.413 0.956 5.179 0.452 -0.022 STANDARD DEVIATION 27 0.000 0.048 0.446 2.732 0.043 0.035 MEDIAN (50TH QUANTILE) 169 1.000 0.405 0.868 4.609 0.455 -0.017 INTERQUARTILE RANGE 43 0.000 0.081 0.494 2.155 0.044 0.048 MINIMUM VALUE 101 1.000 0.347 0.410 2.881 0.390 -0.120 LOWER HINGE (25TH QUANTILE) 146 1.000 0.376 0.617 3.497 0.425 -0.044 UPPER HINGE (75TH QUANTILE) 189 1.000 0.457 1.110 5.652 0.469 0.005 MAXIMUM VALUE 206 1.002 0.527 2.120 14.271 0.554 0.029 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.370 0.103 0.006 -0.085 3.111 0.035 0.682 MINIMUM CORRELATION: 0.035 SERIES 569012 AND 572131 101 YEARS MAXIMUM CORRELATION: 0.682 SERIES 569052 AND 569081 115 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.86 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1798. 1830. 1855. 1880. 1905. 1930. CORR 1. 36. 171. 253. 325. 325. RBAR 0.311 0.380 0.482 0.455 0.399 0.344 SDEV 0.000 0.145 0.103 0.118 0.146 0.157 SERR 0.000 0.024 0.008 0.007 0.008 0.009 EPS 0.802 0.920 0.956 0.955 0.945 0.932 NSS 9.0 18.8 23.2 25.3 26.0 26.0 |======================== 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 1773 1978 206 0.982 0.251 0.328 2.661 0.331 -0.227 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.483 0.181 0.109 81 125 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.53 1.00 1.12 1.65 21.17 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.61 0.87 0.96 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 -0.226 0.024 -0.095 -0.001 -0.008 0.028 0.037 -0.046 -0.120 0.011 PACF -0.226 -0.029 -0.101 -0.048 -0.023 0.013 0.044 -0.031 -0.142 -0.048 95% C.L. 0.139 0.146 0.146 0.148 0.148 0.148 0.148 0.148 0.148 0.150 |------------------ 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 0.052 -0.227 |---------- 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 -0.007 -0.049 -0.101 -0.027 -0.002 0.039 0.037 -0.072 -0.140 -0.028 PACF -0.007 -0.049 -0.102 -0.032 -0.013 0.025 0.032 -0.071 -0.135 -0.033 95% C.L. 0.139 0.139 0.140 0.141 0.141 0.141 0.141 0.142 0.142 0.145 |----------------- 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 -0.007 |========================= 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 1773 1978 206 0.981 0.247 0.273 2.825 0.276 0.141 |------------ 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 0.141 -0.042 -0.111 -0.044 -0.002 0.041 0.028 -0.089 -0.155 -0.054 PACF 0.141 -0.063 -0.098 -0.016 -0.003 0.029 0.013 -0.096 -0.127 -0.018 95% C.L. 0.139 0.142 0.142 0.144 0.144 0.144 0.144 0.145 0.146 0.149 |------------------- 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 0.024 0.141 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.31 MINUTES