RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit017l.rwl LOG FILE PROCESSED: brit017l.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: 568 1 Ballochbuite WIDTH_LATE PISY - 568 2 Great Britain Scots pine, Scotch pine 381 5657-319 1712 1978 - 568 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 9 568052 MISSING VALUES FOUND: 2 IN 2 GAPS / 1921 1921 / 1956 1956 / -------------------------------------------------------------------- 18 568101 MISSING VALUES FOUND: 1 IN 1 GAPS / 1756 1756 / -------------------------------------------------------------------- 19 568102 MISSING VALUES FOUND: 1 IN 1 GAPS / 1953 1953 / -------------------------------------------------------------------- 20 568111 MISSING VALUES FOUND: 1 IN 1 GAPS / 1928 1928 / -------------------------------------------------------------------- 21 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 568012 1747 1862 116 0.425 0.203 0.552 3.989 0.485 0.334 2 568021 1712 1978 267 0.385 0.234 0.681 3.134 0.394 0.687 3 568022 1737 1978 242 0.386 0.166 0.554 3.395 0.320 0.557 4 568031 1782 1978 197 0.418 0.242 0.932 3.799 0.490 0.441 5 568032 1740 1978 239 0.233 0.140 1.765 7.959 0.439 0.537 6 568041 1728 1978 251 0.471 0.251 1.358 5.711 0.331 0.605 7 568042 1729 1978 250 0.300 0.142 1.026 4.541 0.382 0.378 8 568051 1770 1978 209 0.466 0.314 1.344 4.938 0.405 0.635 9 568052 1798 1978 181 0.418 0.267 1.401 4.829 0.408 0.640 10 568061 1762 1978 217 0.272 0.195 1.818 7.823 0.564 0.353 11 568062 1724 1978 255 0.221 0.136 1.199 5.033 0.512 0.513 12 568071 1729 1978 250 0.403 0.206 1.108 4.887 0.378 0.543 13 568072 1740 1978 239 0.300 0.164 0.987 4.018 0.335 0.687 14 568081 1855 1978 124 0.218 0.148 1.134 4.055 0.464 0.628 15 568082 1720 1978 259 0.210 0.126 1.069 4.414 0.502 0.433 16 568091 1780 1948 169 0.308 0.216 0.975 3.269 0.400 0.720 17 568092 1761 1978 218 0.288 0.167 1.002 4.478 0.313 0.686 18 568101 1732 1978 247 0.427 0.209 1.683 8.367 0.335 0.546 19 568102 1780 1978 199 0.311 0.188 0.989 3.774 0.293 0.784 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568111 1769 1978 210 0.400 0.276 1.306 4.697 0.412 0.631 21 568112 1762 1978 217 0.309 0.142 0.947 3.781 0.340 0.522 NUMBER OF SERIES READ IN: 21 FROM 1712 TO 1978 267 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 216 0.341 0.197 1.135 4.804 0.405 0.565 STANDARD DEVIATION 41 0.084 0.052 0.348 1.502 0.075 0.124 MEDIAN (50TH QUANTILE) 218 0.311 0.195 1.069 4.478 0.400 0.557 INTERQUARTILE RANGE 52 0.130 0.086 0.369 1.139 0.128 0.128 MINIMUM VALUE 116 0.210 0.126 0.552 3.134 0.293 0.334 LOWER HINGE (25TH QUANTILE) 198 0.288 0.148 0.975 3.799 0.335 0.513 UPPER HINGE (75TH QUANTILE) 250 0.418 0.234 1.344 4.938 0.464 0.640 MAXIMUM VALUE 267 0.471 0.314 1.818 8.367 0.564 0.784 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 209 0.340 0.192 0.013 -0.552 3.119 -0.239 0.767 MINIMUM CORRELATION: -0.239 SERIES 568062 AND 568102 199 YEARS MAXIMUM CORRELATION: 0.767 SERIES 568021 AND 568051 209 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 99.52 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 71.99 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 45. 120. 171. 171. 171. 190. 190. 171. RBAR 0.358 0.375 0.257 0.375 0.332 0.273 0.301 0.394 SDEV 0.164 0.193 0.221 0.220 0.226 0.221 0.252 0.231 SERR 0.024 0.018 0.017 0.017 0.017 0.016 0.018 0.018 EPS 0.892 0.919 0.873 0.924 0.909 0.882 0.896 0.927 NSS 14.8 18.8 19.9 20.2 20.2 20.0 20.0 19.6 |======================== 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 1712 1978 267 0.331 0.132 0.690 4.172 0.303 0.535 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.719 0.410 0.025 111 156 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.38 0.71 1.00 1.13 1.85 5.22 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.86 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 218. 51. 116. 199. 250. 267. |----------- 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 0.533 0.515 0.416 0.468 0.370 0.444 0.363 0.376 0.324 0.334 PACF 0.533 0.322 0.091 0.208 0.010 0.169 0.015 0.037 0.015 0.012 95% C.L. 0.122 0.153 0.177 0.191 0.208 0.217 0.231 0.239 0.248 0.254 |------------------ 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 4 0.406 0.307 0.224 0.024 0.230 |================== 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 568012 1 0.25597233 0.00932685 0.00000000 0.26890442 2 568021 3 0.00000000 0.00000000 -0.00163563 0.60449213 3 568022 3 0.00000000 0.00000000 -0.00118412 0.52969652 4 568031 3 0.00000000 0.00000000 0.00018774 0.39923081 5 568032 1 0.39496469 0.04290363 0.00000000 0.19548427 6 568041 1 0.24576920 0.01949318 0.00000000 0.42134970 7 568042 1 0.19689447 0.04008008 0.00000000 0.28110239 8 568051 1 0.80913281 0.00891283 0.00000000 0.10058656 9 568052 1 0.79422045 0.02528014 0.00000000 0.24511868 10 568061 1 0.31917897 0.00837267 0.00000000 0.12553173 11 568062 3 0.00000000 0.00000000 0.00043189 0.16550224 12 568071 1 0.37311116 0.04014454 0.00000000 0.36628696 13 568072 1 0.40170944 0.00993747 0.00000000 0.14743905 14 568081 3 0.00000000 0.00000000 -0.00271871 0.38790321 15 568082 3 0.00000000 0.00000000 -0.00088862 0.32532728 16 568091 1 0.51136845 0.01213644 0.00000000 0.09223648 17 568092 3 0.00000000 0.00000000 -0.00142201 0.44332474 18 568101 3 0.00000000 0.00000000 -0.00037984 0.47359401 19 568102 3 0.00000000 0.00000000 -0.00192326 0.50279957 SERIES IDENT OPTION A B C D 20 568111 1 0.76897895 0.00831307 0.00000000 0.03657484 21 568112 1 0.33236796 0.02199423 0.00000000 0.22851333 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 568012 1747 1862 116 1.000 0.471 0.434 3.247 0.481 0.330 2 568021 1712 1978 267 1.005 0.530 0.719 3.683 0.393 0.552 3 568022 1737 1978 242 1.001 0.398 0.870 4.172 0.319 0.441 4 568031 1782 1978 197 1.000 0.578 0.934 3.818 0.488 0.436 5 568032 1740 1978 239 1.001 0.492 0.750 3.095 0.438 0.439 6 568041 1728 1978 251 1.000 0.538 1.685 7.000 0.330 0.604 7 568042 1729 1978 250 1.000 0.465 1.088 4.759 0.381 0.344 8 568051 1770 1978 209 1.002 0.519 1.152 4.371 0.403 0.441 9 568052 1798 1978 181 0.999 0.449 1.039 4.533 0.407 0.283 10 568061 1762 1978 217 1.000 0.602 1.034 4.657 0.562 0.196 11 568062 1724 1978 255 1.003 0.621 1.372 5.776 0.510 0.472 12 568071 1729 1978 250 1.000 0.491 1.130 4.753 0.377 0.491 13 568072 1740 1978 239 1.000 0.458 1.351 7.184 0.333 0.543 14 568081 1855 1978 124 1.011 0.485 0.628 3.275 0.461 0.343 15 568082 1720 1978 259 1.005 0.518 1.026 4.978 0.500 0.282 16 568091 1780 1948 169 1.002 0.652 1.822 8.353 0.398 0.606 17 568092 1761 1978 218 1.003 0.548 1.855 8.479 0.312 0.637 18 568101 1732 1978 247 1.000 0.484 1.627 8.052 0.334 0.538 19 568102 1780 1978 199 1.024 0.571 1.298 5.132 0.295 0.734 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568111 1769 1978 210 1.004 0.567 1.634 6.560 0.412 0.508 21 568112 1762 1978 217 1.000 0.402 0.477 2.766 0.336 0.457 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 217 1.003 0.516 1.139 5.174 0.403 0.461 STANDARD DEVIATION 41 0.006 0.067 0.422 1.777 0.075 0.133 MEDIAN (50TH QUANTILE) 218 1.001 0.518 1.088 4.753 0.398 0.457 INTERQUARTILE RANGE 51 0.003 0.096 0.503 2.742 0.127 0.198 MINIMUM VALUE 116 0.999 0.398 0.434 2.766 0.295 0.196 LOWER HINGE (25TH QUANTILE) 199 1.000 0.471 0.870 3.818 0.334 0.344 UPPER HINGE (75TH QUANTILE) 250 1.003 0.567 1.372 6.560 0.461 0.543 MAXIMUM VALUE 267 1.024 0.652 1.855 8.479 0.562 0.734 |------------------------ 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 568012 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 568021 -67 178 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 568022 -67 162 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 568031 -67 131 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 568032 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 568041 -67 168 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 568042 -67 167 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 568051 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 568052 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 568061 -67 145 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 568062 -67 170 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 568071 -67 167 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 568072 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 568081 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 568082 -67 173 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 568091 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 568092 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 568101 -67 165 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 568102 -67 133 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 568111 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 568112 -67 145 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 568012 1747 1862 116 0.994 0.449 0.402 3.531 0.481 0.241 2 568021 1712 1978 267 0.969 0.429 0.709 3.881 0.393 0.373 3 568022 1737 1978 242 0.995 0.383 0.882 4.100 0.319 0.400 4 568031 1782 1978 197 0.982 0.488 0.621 3.302 0.487 0.266 5 568032 1740 1978 239 0.997 0.460 0.708 3.089 0.438 0.356 6 568041 1728 1978 251 0.992 0.500 1.521 6.359 0.330 0.577 7 568042 1729 1978 250 0.998 0.446 1.184 5.546 0.381 0.318 8 568051 1770 1978 209 0.994 0.497 1.065 4.115 0.403 0.406 9 568052 1798 1978 181 0.999 0.445 1.005 4.424 0.407 0.273 10 568061 1762 1978 217 0.996 0.595 1.070 4.910 0.562 0.186 11 568062 1724 1978 255 0.992 0.567 1.139 4.648 0.510 0.398 12 568071 1729 1978 250 0.998 0.481 1.088 4.689 0.377 0.479 13 568072 1740 1978 239 0.997 0.447 1.245 6.574 0.333 0.525 14 568081 1855 1978 124 0.995 0.467 0.709 3.692 0.461 0.311 15 568082 1720 1978 259 0.995 0.504 1.240 6.294 0.500 0.241 16 568091 1780 1948 169 0.995 0.653 2.135 10.124 0.398 0.610 17 568092 1761 1978 218 0.997 0.537 1.888 8.601 0.312 0.630 18 568101 1732 1978 247 0.997 0.474 1.632 8.018 0.334 0.525 19 568102 1780 1978 199 0.992 0.462 0.665 3.002 0.294 0.659 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568111 1769 1978 210 0.998 0.549 1.598 6.816 0.411 0.480 21 568112 1762 1978 217 0.997 0.381 0.534 3.078 0.336 0.395 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 217 0.994 0.486 1.097 5.181 0.403 0.412 STANDARD DEVIATION 41 0.007 0.066 0.458 1.984 0.075 0.139 MEDIAN (50TH QUANTILE) 218 0.995 0.474 1.070 4.648 0.398 0.398 INTERQUARTILE RANGE 51 0.003 0.056 0.536 2.667 0.127 0.214 MINIMUM VALUE 116 0.969 0.381 0.402 3.002 0.294 0.186 LOWER HINGE (25TH QUANTILE) 199 0.994 0.447 0.709 3.692 0.334 0.311 UPPER HINGE (75TH QUANTILE) 250 0.997 0.504 1.245 6.359 0.461 0.525 MAXIMUM VALUE 267 0.999 0.653 2.135 10.124 0.562 0.659 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 209 0.307 0.141 0.010 0.028 2.630 -0.020 0.693 MINIMUM CORRELATION: -0.020 SERIES 568072 AND 568111 210 YEARS MAXIMUM CORRELATION: 0.693 SERIES 568021 AND 568022 242 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 99.52 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 71.99 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 45. 120. 171. 171. 171. 190. 190. 171. RBAR 0.371 0.353 0.271 0.315 0.312 0.261 0.323 0.398 SDEV 0.170 0.187 0.201 0.217 0.206 0.210 0.232 0.224 SERR 0.025 0.017 0.015 0.017 0.016 0.015 0.017 0.017 EPS 0.897 0.911 0.881 0.903 0.902 0.876 0.905 0.928 NSS 14.8 18.8 19.9 20.2 20.2 20.0 20.0 19.6 |======================== 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 1712 1978 267 0.953 0.293 0.887 4.572 0.292 0.218 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.579 0.299 0.071 93 174 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.88 1.00 1.08 1.97 8.14 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.86 0.93 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 0.217 0.144 0.025 0.106 0.000 0.061 0.017 -0.016 -0.088 -0.043 PACF 0.217 0.102 -0.027 0.098 -0.041 0.048 0.003 -0.045 -0.078 -0.014 95% C.L. 0.122 0.128 0.130 0.130 0.132 0.132 0.132 0.132 0.132 0.133 |------------------ 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 2 0.058 0.196 0.102 |======================= 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 0.194 0.102 -0.021 0.073 -0.038 0.050 -0.015 -0.052 -0.113 -0.061 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 0.194 2 0.181 0.067 3 0.184 0.077 -0.055 4 0.189 0.070 -0.070 0.083 5 0.194 0.066 -0.066 0.095 -0.063 6 0.198 0.060 -0.062 0.092 -0.074 0.057 7 0.199 0.059 -0.060 0.090 -0.072 0.061 -0.021 8 0.198 0.063 -0.065 0.096 -0.076 0.065 -0.007 -0.069 9 0.192 0.063 -0.060 0.090 -0.069 0.060 -0.002 -0.053 -0.079 10 0.190 0.061 -0.060 0.092 -0.071 0.063 -0.004 -0.051 -0.074 -0.029 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) 2358.63 2350.41 2351.22 2352.42 2352.55 2353.51 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2354.64 2356.52 2357.25 2357.57 2359.34 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 0.194 R-SQUARED DUE TO POOLED AUTOREGRESSION: 3.75 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 103.90 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.194 0.038 0.007 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 568012 1 0.074 0.244 2 568021 1 0.169 0.379 3 568022 1 0.165 0.401 4 568031 1 0.117 0.268 5 568032 1 0.144 0.356 6 568041 1 0.369 0.577 7 568042 1 0.174 0.320 8 568051 1 0.165 0.406 9 568052 1 0.075 0.274 10 568061 1 0.077 0.186 11 568062 1 0.174 0.399 12 568071 1 0.248 0.480 13 568072 1 0.302 0.526 14 568081 1 0.098 0.312 15 568082 1 0.070 0.242 16 568091 1 0.383 0.610 17 568092 1 0.419 0.632 18 568101 1 0.279 0.525 19 568102 1 0.441 0.659 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 568111 1 0.239 0.481 21 568112 1 0.203 0.396 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.209 0.413 STANDARD DEVIATION 0 0.117 0.138 MEDIAN 1 0.174 0.399 INTERQUARTILE RANGE 0 0.162 0.213 MINIMUM VALUE 1 0.070 0.186 LOWER HINGE 1 0.117 0.312 UPPER HINGE 1 0.279 0.525 MAXIMUM VALUE 1 0.441 0.659 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 568012 1747 1862 116 1.000 0.435 0.483 3.578 0.511 -0.029 2 568021 1712 1978 267 1.000 0.397 0.813 4.167 0.422 -0.065 3 568022 1737 1978 242 1.000 0.350 0.859 3.820 0.383 -0.027 4 568031 1782 1978 197 1.000 0.470 0.726 3.533 0.535 -0.058 5 568032 1740 1978 239 1.000 0.430 0.730 3.168 0.503 -0.049 6 568041 1728 1978 251 1.000 0.408 1.423 6.706 0.439 -0.133 7 568042 1729 1978 250 1.000 0.422 1.078 5.603 0.446 -0.088 8 568051 1770 1978 209 1.000 0.454 1.067 4.151 0.471 -0.001 9 568052 1798 1978 181 1.000 0.428 1.038 4.578 0.442 -0.001 10 568061 1762 1978 217 1.001 0.583 1.137 5.157 0.596 -0.031 11 568062 1724 1978 255 1.001 0.519 1.042 4.558 0.595 -0.051 12 568071 1729 1978 250 1.000 0.422 1.172 5.237 0.451 -0.074 13 568072 1740 1978 239 1.001 0.379 1.123 6.750 0.410 -0.096 14 568081 1855 1978 124 1.000 0.443 0.883 4.240 0.505 -0.009 15 568082 1720 1978 259 1.000 0.489 1.265 6.074 0.522 0.027 16 568091 1780 1948 169 1.000 0.517 1.991 9.641 0.472 0.080 17 568092 1761 1978 218 1.000 0.416 2.187 11.828 0.385 -0.111 18 568101 1732 1978 247 1.000 0.404 1.423 7.480 0.439 -0.037 19 568102 1780 1978 199 1.000 0.347 0.589 3.460 0.377 -0.070 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 568111 1769 1978 210 1.000 0.481 1.104 5.071 0.504 -0.047 21 568112 1762 1978 217 1.000 0.349 0.465 2.949 0.404 -0.092 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 217 1.000 0.435 1.076 5.321 0.467 -0.046 STANDARD DEVIATION 41 0.000 0.060 0.431 2.209 0.064 0.049 MEDIAN (50TH QUANTILE) 218 1.000 0.428 1.067 4.578 0.451 -0.049 INTERQUARTILE RANGE 51 0.000 0.066 0.359 2.255 0.083 0.046 MINIMUM VALUE 116 1.000 0.347 0.465 2.949 0.377 -0.133 LOWER HINGE (25TH QUANTILE) 199 1.000 0.404 0.813 3.820 0.422 -0.074 UPPER HINGE (75TH QUANTILE) 250 1.000 0.470 1.172 6.074 0.505 -0.027 MAXIMUM VALUE 267 1.001 0.583 2.187 11.828 0.596 0.080 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 209 0.389 0.115 0.008 0.213 2.591 0.154 0.685 MINIMUM CORRELATION: 0.154 SERIES 568032 AND 568111 210 YEARS MAXIMUM CORRELATION: 0.685 SERIES 568021 AND 568022 242 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 99.52 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 71.99 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 45. 120. 171. 171. 171. 190. 190. 171. RBAR 0.455 0.449 0.328 0.355 0.403 0.358 0.395 0.465 SDEV 0.158 0.156 0.160 0.166 0.144 0.157 0.186 0.173 SERR 0.023 0.014 0.012 0.013 0.011 0.011 0.014 0.013 EPS 0.925 0.939 0.907 0.917 0.932 0.918 0.929 0.945 NSS 14.8 18.8 19.9 20.2 20.2 20.0 20.0 19.6 |======================== 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 1712 1978 267 0.971 0.281 0.774 4.220 0.338 -0.208 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.523 0.272 0.037 97 170 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.78 1.00 1.12 1.90 8.81 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.09 0.00 0.85 0.95 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 -0.207 0.054 -0.069 0.113 -0.071 0.080 0.002 0.013 -0.073 -0.013 PACF -0.207 0.011 -0.058 0.091 -0.030 0.056 0.042 0.006 -0.059 -0.055 95% C.L. 0.122 0.128 0.128 0.128 0.130 0.130 0.131 0.131 0.131 0.132 |------------------ 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 0.044 -0.209 |---------- 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 0.003 -0.001 -0.040 0.092 -0.036 0.072 0.022 -0.002 -0.079 -0.026 PACF 0.003 -0.001 -0.040 0.092 -0.037 0.072 0.028 -0.013 -0.068 -0.038 95% C.L. 0.122 0.122 0.122 0.123 0.124 0.124 0.124 0.124 0.124 0.125 |----------------- 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 0.003 |========================= 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 1712 1978 267 0.971 0.280 0.829 4.408 0.281 0.196 |------------ 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 0.196 0.034 -0.015 0.082 -0.004 0.072 0.032 -0.011 -0.081 -0.032 PACF 0.196 -0.005 -0.021 0.092 -0.039 0.081 0.008 -0.032 -0.068 -0.015 95% C.L. 0.122 0.127 0.127 0.127 0.128 0.128 0.129 0.129 0.129 0.129 |------------------- 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 0.039 0.197 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.23 MINUTES