RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit018w.rwl LOG FILE PROCESSED: brit018w.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: 572 1 Loch Maree WIDTH_RING PISY - 572 2 Great Britain Scots pine, Scotch pine 100 5731-520 1756 1978 - 572 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 572012 MISSING VALUES FOUND: 43 IN 1 GAPS / 1902 1944 / -------------------------------------------------------------------- 3 572021 MISSING VALUES FOUND: 1 IN 1 GAPS / 1903 1903 / -------------------------------------------------------------------- 7 572041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1910 1910 / -------------------------------------------------------------------- 15 572091 MISSING VALUES FOUND: 1 IN 1 GAPS / 1934 1934 / -------------------------------------------------------------------- 16 572092 MISSING VALUES FOUND: 5 IN 2 GAPS / 1799 1801 / 1837 1838 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.267 0.769 1.357 4.054 0.186 0.919 2 572012 1808 1978 171 1.492 0.620 1.636 5.483 0.194 0.797 3 572021 1885 1978 94 1.775 0.372 0.209 2.792 0.137 0.659 4 572022 1906 1978 73 2.336 0.663 0.448 3.630 0.159 0.690 5 572031 1871 1978 108 1.483 0.564 1.053 4.291 0.182 0.790 6 572032 1845 1978 134 1.949 1.138 1.087 3.706 0.167 0.937 7 572041 1834 1978 145 1.829 0.709 0.464 2.510 0.180 0.833 8 572042 1855 1978 124 1.537 0.470 0.915 4.073 0.165 0.765 9 572051 1812 1978 167 1.413 0.674 0.436 2.814 0.186 0.886 10 572052 1853 1978 126 0.933 0.722 2.532 9.406 0.188 0.887 11 572061 1765 1978 214 1.307 0.987 1.524 4.955 0.222 0.872 12 572062 1795 1978 184 1.033 0.639 1.323 4.670 0.198 0.883 13 572071 1877 1978 102 1.177 0.514 1.079 4.151 0.279 0.635 14 572072 1822 1958 137 1.013 0.875 1.645 5.284 0.257 0.891 15 572091 1846 1978 133 0.681 0.498 1.268 3.727 0.201 0.915 16 572092 1756 1978 223 1.344 0.618 1.388 5.131 0.236 0.798 NUMBER OF SERIES READ IN: 16 FROM 1756 TO 1978 223 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 143 1.411 0.677 1.148 4.417 0.196 0.822 STANDARD DEVIATION 43 0.419 0.196 0.583 1.601 0.037 0.095 MEDIAN (50TH QUANTILE) 133 1.379 0.651 1.177 4.112 0.187 0.853 INTERQUARTILE RANGE 59 0.551 0.207 0.766 1.374 0.038 0.112 MINIMUM VALUE 73 0.681 0.372 0.209 2.510 0.137 0.635 LOWER HINGE (25TH QUANTILE) 116 1.105 0.539 0.690 3.668 0.174 0.777 UPPER HINGE (75TH QUANTILE) 175 1.656 0.746 1.456 5.043 0.212 0.889 MAXIMUM VALUE 218 2.336 1.138 2.532 9.406 0.279 0.937 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.415 0.284 0.026 -0.884 3.695 -0.451 0.848 MINIMUM CORRELATION: -0.451 SERIES 572021 AND 572062 94 YEARS MAXIMUM CORRELATION: 0.848 SERIES 572032 AND 572091 133 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.007 0.384 0.225 0.440 0.441 0.352 SDEV 0.468 0.156 0.251 0.283 0.262 0.248 SERR 0.270 0.049 0.047 0.035 0.026 0.024 EPS 0.036 0.834 0.765 0.917 0.925 0.897 NSS 5.1 8.1 11.3 14.0 15.6 16.0 |======================== 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 1756 1978 223 1.536 0.597 0.934 3.538 0.157 0.823 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.395 0.284 0.233 58 165 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.84 1.01 1.12 1.97 24.01 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.16 0.00 0.84 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 136. 62. 73. 116. 178. 223. |----------- 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 0.819 0.786 0.743 0.709 0.694 0.660 0.647 0.657 0.614 0.606 PACF 0.819 0.348 0.134 0.068 0.100 0.015 0.054 0.139 -0.059 0.020 95% C.L. 0.134 0.205 0.253 0.290 0.319 0.345 0.367 0.387 0.407 0.423 |------------------ 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 3 0.721 0.485 0.275 0.140 |================== 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 572011 1 2.75447917 0.01854623 0.00000000 0.57446104 2 572012 1 1.63518441 0.03715269 0.00000000 1.15892541 3 572021 3 0.00000000 0.00000000 0.00828721 1.37777710 4 572022 1 2.49698544 0.24770795 0.00000000 2.21447515 5 572031 1 1.70188177 0.03233027 0.00000000 1.01828110 6 572032 1 3.93629670 0.01832157 0.00000000 0.49664536 7 572041 1 1.35568130 0.01931594 0.00000000 1.37615728 8 572042 1 0.60632479 0.07807685 0.00000000 1.47632289 9 572051 3 0.00000000 0.00000000 -0.00619990 1.93420458 10 572052 1 3.68655276 0.09012467 0.00000000 0.62262714 11 572061 1 3.44583845 0.01889545 0.00000000 0.47794437 12 572062 1 2.20750928 0.01409449 0.00000000 0.25062338 13 572071 1 1.18681479 0.04951394 0.00000000 0.94950444 14 572072 1 3.32947993 0.03575042 0.00000000 0.34984469 15 572091 1 1.82287848 0.02895195 0.00000000 0.22155730 16 572092 3 0.00000000 0.00000000 -0.00339508 1.73350990 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.001 0.257 0.787 3.894 0.184 0.572 2 572012 1808 1978 171 1.000 0.265 0.458 3.337 0.187 0.596 3 572021 1885 1978 94 1.001 0.176 0.834 4.298 0.136 0.442 4 572022 1906 1978 73 1.000 0.251 0.072 2.538 0.155 0.709 5 572031 1871 1978 108 1.000 0.252 0.718 3.513 0.181 0.587 6 572032 1845 1978 134 1.005 0.324 1.372 7.211 0.166 0.745 7 572041 1834 1978 145 1.000 0.358 0.864 3.747 0.183 0.812 8 572042 1855 1978 124 1.000 0.304 1.289 5.292 0.164 0.757 9 572051 1812 1978 167 0.995 0.419 0.190 2.490 0.185 0.862 10 572052 1853 1978 126 0.999 0.357 1.059 4.594 0.184 0.800 11 572061 1765 1978 214 0.993 0.372 1.404 6.548 0.221 0.639 12 572062 1795 1978 184 0.994 0.262 0.231 2.548 0.197 0.551 13 572071 1877 1978 102 1.000 0.383 1.553 7.707 0.275 0.552 14 572072 1822 1958 137 0.991 0.442 1.323 6.517 0.253 0.696 15 572091 1846 1978 133 1.007 0.335 0.435 3.150 0.199 0.735 16 572092 1756 1978 223 0.998 0.404 1.088 4.318 0.234 0.751 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 0.999 0.322 0.855 4.481 0.194 0.675 STANDARD DEVIATION 44 0.004 0.074 0.473 1.701 0.036 0.116 MEDIAN (50TH QUANTILE) 135 1.000 0.330 0.849 4.096 0.185 0.703 INTERQUARTILE RANGE 61 0.004 0.118 0.859 2.661 0.036 0.175 MINIMUM VALUE 73 0.991 0.176 0.072 2.490 0.136 0.442 LOWER HINGE (25TH QUANTILE) 116 0.996 0.259 0.447 3.244 0.174 0.580 UPPER HINGE (75TH QUANTILE) 177 1.000 0.377 1.306 5.904 0.210 0.754 MAXIMUM VALUE 223 1.007 0.442 1.553 7.707 0.275 0.862 |------------------------ 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 572011 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 572012 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 572021 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 572022 -67 48 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 572031 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 572032 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 572041 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 572042 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 572051 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 572052 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 572061 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 572062 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 572071 -67 68 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 572072 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 572091 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 572092 -67 149 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 572011 1771 1978 208 1.000 0.255 0.767 3.778 0.184 0.565 2 572012 1808 1978 171 0.999 0.261 0.455 3.379 0.187 0.579 3 572021 1885 1978 94 0.999 0.151 0.263 3.695 0.136 0.324 4 572022 1906 1978 73 0.996 0.208 -0.229 2.556 0.153 0.586 5 572031 1871 1978 108 0.997 0.203 0.526 3.195 0.181 0.350 6 572032 1845 1978 134 0.996 0.292 1.267 7.123 0.166 0.699 7 572041 1834 1978 145 0.992 0.305 0.551 3.568 0.183 0.747 8 572042 1855 1978 124 0.995 0.255 0.793 4.350 0.163 0.667 9 572051 1812 1978 167 0.972 0.288 0.067 2.858 0.183 0.709 10 572052 1853 1978 126 0.992 0.218 0.024 3.596 0.184 0.440 11 572061 1765 1978 214 0.997 0.334 1.364 5.790 0.221 0.590 12 572062 1795 1978 184 0.996 0.233 0.176 2.697 0.198 0.435 13 572071 1877 1978 102 0.998 0.368 1.417 7.248 0.275 0.525 14 572072 1822 1958 137 0.994 0.464 3.035 17.034 0.253 0.690 15 572091 1846 1978 133 0.991 0.263 0.084 2.823 0.199 0.585 16 572092 1756 1978 223 0.996 0.361 0.649 3.181 0.234 0.687 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 0.994 0.279 0.701 4.804 0.194 0.574 STANDARD DEVIATION 44 0.006 0.076 0.793 3.576 0.036 0.129 MEDIAN (50TH QUANTILE) 135 0.996 0.262 0.539 3.582 0.184 0.586 INTERQUARTILE RANGE 61 0.004 0.094 0.900 2.050 0.037 0.206 MINIMUM VALUE 73 0.972 0.151 -0.229 2.556 0.136 0.324 LOWER HINGE (25TH QUANTILE) 116 0.993 0.226 0.130 3.020 0.173 0.482 UPPER HINGE (75TH QUANTILE) 177 0.997 0.320 1.030 5.070 0.210 0.688 MAXIMUM VALUE 223 1.000 0.464 3.035 17.034 0.275 0.747 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.287 0.170 0.016 0.088 2.490 -0.079 0.719 MINIMUM CORRELATION: -0.079 SERIES 572021 AND 572051 94 YEARS MAXIMUM CORRELATION: 0.719 SERIES 572041 AND 572042 124 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.218 0.305 0.275 0.323 0.286 0.352 SDEV 0.123 0.193 0.176 0.143 0.192 0.221 SERR 0.071 0.061 0.033 0.018 0.019 0.022 EPS 0.586 0.779 0.811 0.870 0.862 0.897 NSS 5.1 8.1 11.3 14.0 15.6 16.0 |======================== 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 1756 1978 223 0.990 0.181 0.364 3.161 0.151 0.479 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.270 0.171 0.037 52 171 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.40 0.95 1.00 1.08 2.03 118.92 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.16 0.00 0.84 1.00 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 0.477 0.259 0.104 0.076 -0.054 -0.103 -0.172 -0.137 -0.125 -0.146 PACF 0.477 0.041 -0.045 0.044 -0.129 -0.053 -0.100 -0.006 -0.024 -0.089 95% C.L. 0.134 0.162 0.169 0.170 0.171 0.171 0.172 0.175 0.177 0.179 |------------------ 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 0.229 0.477 |======================= 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 0.606 0.395 0.168 0.078 -0.026 -0.089 -0.156 -0.127 -0.116 -0.117 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 0.606 2 0.580 0.043 3 0.586 0.123 -0.138 4 0.589 0.120 -0.152 0.024 5 0.591 0.109 -0.143 0.068 -0.075 6 0.586 0.113 -0.152 0.075 -0.037 -0.065 7 0.581 0.110 -0.146 0.063 -0.028 -0.019 -0.077 8 0.584 0.111 -0.145 0.061 -0.022 -0.024 -0.100 0.039 9 0.585 0.109 -0.146 0.060 -0.021 -0.027 -0.097 0.052 -0.024 10 0.584 0.112 -0.152 0.059 -0.022 -0.023 -0.107 0.060 0.016 -0.068 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) 1520.73 1420.59 1422.18 1419.89 1421.77 1422.50 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1423.57 1424.23 1425.90 1427.77 1428.75 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 0.606 R-SQUARED DUE TO POOLED AUTOREGRESSION: 36.75 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 158.10 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.606 0.367 0.223 0.135 0.082 0.050 0.030 0.018 0.011 0.0067 0.004 0.002 0.001 0.001 0.001 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 572011 1 0.338 0.569 2 572012 1 0.340 0.581 3 572021 1 0.108 0.328 4 572022 1 0.352 0.589 5 572031 1 0.133 0.354 6 572032 1 0.500 0.707 7 572041 1 0.566 0.748 8 572042 1 0.452 0.670 9 572051 1 0.511 0.715 10 572052 1 0.196 0.440 11 572061 1 0.352 0.591 12 572062 1 0.211 0.436 13 572071 1 0.290 0.525 14 572072 1 0.511 0.692 15 572091 1 0.345 0.587 16 572092 1 0.479 0.687 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.355 0.576 STANDARD DEVIATION 0 0.141 0.130 MEDIAN 1 0.348 0.588 INTERQUARTILE RANGE 0 0.239 0.207 MINIMUM VALUE 1 0.108 0.328 LOWER HINGE 1 0.251 0.483 UPPER HINGE 1 0.490 0.690 MAXIMUM VALUE 1 0.566 0.748 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.000 0.209 0.711 3.939 0.218 0.080 2 572012 1808 1978 171 1.000 0.213 0.649 3.829 0.229 -0.029 3 572021 1885 1978 94 1.000 0.142 0.315 3.830 0.158 0.005 4 572022 1906 1978 73 1.000 0.168 0.099 2.773 0.199 -0.053 5 572031 1871 1978 108 1.000 0.189 0.516 3.548 0.209 -0.034 6 572032 1845 1978 134 1.000 0.205 1.130 6.364 0.217 -0.020 7 572041 1834 1978 145 1.000 0.203 0.353 2.928 0.242 -0.088 8 572042 1855 1978 124 1.000 0.189 0.367 3.923 0.208 0.055 9 572051 1812 1978 167 1.000 0.201 0.444 3.633 0.215 0.012 10 572052 1853 1978 126 1.000 0.196 0.367 3.992 0.219 -0.024 11 572061 1765 1978 214 1.000 0.269 1.198 5.618 0.283 -0.042 12 572062 1795 1978 184 1.000 0.210 0.156 2.904 0.246 -0.070 13 572071 1877 1978 102 1.000 0.313 1.504 7.604 0.319 0.073 14 572072 1822 1958 137 1.002 0.328 1.243 6.807 0.317 0.189 15 572091 1846 1978 133 1.000 0.213 0.308 3.437 0.242 0.005 16 572092 1756 1978 223 1.000 0.262 0.782 3.769 0.294 -0.077 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.219 0.634 4.306 0.238 -0.001 STANDARD DEVIATION 44 0.000 0.050 0.425 1.465 0.044 0.071 MEDIAN (50TH QUANTILE) 135 1.000 0.207 0.480 3.830 0.224 -0.022 INTERQUARTILE RANGE 61 0.000 0.045 0.621 1.313 0.052 0.081 MINIMUM VALUE 73 1.000 0.142 0.099 2.773 0.158 -0.088 LOWER HINGE (25TH QUANTILE) 116 1.000 0.192 0.334 3.492 0.212 -0.047 UPPER HINGE (75TH QUANTILE) 177 1.000 0.238 0.956 4.805 0.264 0.033 MAXIMUM VALUE 223 1.002 0.328 1.504 7.604 0.319 0.189 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.298 0.134 0.012 -0.244 2.632 -0.001 0.618 MINIMUM CORRELATION: -0.001 SERIES 572021 AND 572072 74 YEARS MAXIMUM CORRELATION: 0.618 SERIES 572041 AND 572042 124 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.361 0.341 0.402 0.440 0.332 0.283 SDEV 0.090 0.145 0.147 0.121 0.150 0.163 SERR 0.052 0.046 0.028 0.015 0.015 0.016 EPS 0.742 0.806 0.883 0.917 0.886 0.863 NSS 5.1 8.1 11.3 14.0 15.6 16.0 |======================== 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 1756 1978 223 0.996 0.160 0.698 3.488 0.181 -0.086 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.288 0.170 -0.001 57 166 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 1.04 1.00 1.05 2.09 340.40 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.15 0.00 0.85 1.00 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 -0.085 0.005 -0.090 0.080 -0.080 -0.014 -0.106 -0.028 -0.010 -0.133 PACF -0.085 -0.002 -0.090 0.066 -0.069 -0.034 -0.101 -0.064 -0.015 -0.163 95% C.L. 0.134 0.135 0.135 0.136 0.137 0.138 0.138 0.139 0.139 0.139 |------------------ 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 0 0.000 |---------- 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 0.000 -0.010 -0.084 0.067 -0.075 -0.030 -0.111 -0.038 -0.024 -0.140 PACF 0.000 -0.010 -0.084 0.067 -0.078 -0.036 -0.103 -0.057 -0.024 -0.167 95% C.L. 0.134 0.134 0.134 0.135 0.135 0.136 0.136 0.138 0.138 0.138 |----------------- 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 0.000 0.000 |========================= 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 1756 1978 223 0.996 0.196 0.393 3.361 0.144 0.579 |------------ 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 0.577 0.302 0.115 0.051 -0.075 -0.137 -0.201 -0.194 -0.194 -0.217 PACF 0.577 -0.046 -0.061 0.029 -0.148 -0.049 -0.101 -0.031 -0.061 -0.118 95% C.L. 0.134 0.173 0.182 0.183 0.184 0.184 0.186 0.190 0.193 0.197 |------------------- 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 0.334 0.577 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.24 MINUTES