RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit018l.rwl LOG FILE PROCESSED: brit018l.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_LATE 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 0.452 0.340 1.350 4.215 0.362 0.762 2 572012 1808 1978 171 0.521 0.292 1.506 5.230 0.421 0.479 3 572021 1885 1978 94 0.494 0.134 0.883 4.762 0.246 0.273 4 572022 1906 1978 73 0.592 0.186 0.724 4.702 0.296 0.206 5 572031 1871 1978 108 0.465 0.240 1.349 6.486 0.402 0.481 6 572032 1845 1978 134 0.563 0.282 0.621 2.796 0.319 0.602 7 572041 1834 1978 145 0.616 0.254 0.594 3.186 0.278 0.608 8 572042 1855 1978 124 0.508 0.196 0.278 2.837 0.337 0.480 9 572051 1812 1978 167 0.532 0.268 0.627 3.229 0.300 0.755 10 572052 1853 1978 126 0.362 0.270 2.028 7.308 0.373 0.794 11 572061 1765 1978 214 0.379 0.330 1.905 7.278 0.424 0.706 12 572062 1795 1978 184 0.332 0.270 1.534 5.558 0.367 0.747 13 572071 1877 1978 102 0.449 0.200 1.268 5.863 0.375 0.379 14 572072 1822 1958 137 0.328 0.264 1.521 4.934 0.410 0.685 15 572091 1846 1978 133 0.243 0.202 1.603 5.016 0.389 0.810 16 572092 1756 1978 223 0.451 0.290 1.343 4.624 0.375 0.764 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 0.456 0.251 1.196 4.876 0.355 0.596 STANDARD DEVIATION 43 0.104 0.055 0.512 1.425 0.053 0.192 MEDIAN (50TH QUANTILE) 133 0.459 0.266 1.346 4.848 0.370 0.647 INTERQUARTILE RANGE 59 0.156 0.085 0.852 1.989 0.085 0.279 MINIMUM VALUE 73 0.243 0.134 0.278 2.796 0.246 0.206 LOWER HINGE (25TH QUANTILE) 116 0.371 0.201 0.675 3.722 0.310 0.480 UPPER HINGE (75TH QUANTILE) 175 0.527 0.286 1.527 5.710 0.395 0.759 MAXIMUM VALUE 218 0.616 0.340 2.028 7.308 0.424 0.810 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.441 0.206 0.019 -0.758 3.557 -0.194 0.822 MINIMUM CORRELATION: -0.194 SERIES 572021 AND 572061 94 YEARS MAXIMUM CORRELATION: 0.822 SERIES 572062 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 0.073 0.361 0.320 0.527 0.501 0.387 SDEV 0.376 0.172 0.227 0.174 0.185 0.197 SERR 0.217 0.054 0.043 0.021 0.018 0.019 EPS 0.286 0.820 0.841 0.940 0.940 0.910 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 0.502 0.223 1.148 4.625 0.294 0.601 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.494 0.293 0.085 35 188 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.59 1.01 1.10 1.69 6.25 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 0.598 0.502 0.437 0.487 0.401 0.398 0.407 0.443 0.453 0.379 PACF 0.598 0.224 0.115 0.234 -0.005 0.084 0.112 0.118 0.127 -0.051 95% C.L. 0.134 0.175 0.200 0.216 0.235 0.247 0.258 0.269 0.282 0.295 |------------------ 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 0.433 0.411 0.132 0.012 0.236 |================== 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 1.11974108 0.01493213 0.00000000 0.11006319 2 572012 1 0.64286041 0.03733194 0.00000000 0.39175236 3 572021 3 0.00000000 0.00000000 0.00190462 0.40280655 4 572022 1 0.34876415 0.08776915 0.00000000 0.53978759 5 572031 1 0.56857407 0.03514358 0.00000000 0.32158914 6 572032 3 0.00000000 0.00000000 -0.00440385 0.86039388 7 572041 1 0.27481782 0.01658843 0.00000000 0.51149279 8 572042 1 0.24873404 0.04054323 0.00000000 0.45966169 9 572051 3 0.00000000 0.00000000 -0.00169035 0.67384607 10 572052 1 1.16098356 0.07281175 0.00000000 0.24000371 11 572061 1 0.96742207 0.01303557 0.00000000 0.05607035 12 572062 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 572071 1 0.26674074 0.07919984 0.00000000 0.41730148 14 572072 1 0.86555564 0.02180540 0.00000000 0.05618821 15 572091 1 0.72789103 0.03539899 0.00000000 0.09181044 16 572092 3 0.00000000 0.00000000 -0.00178196 0.65548098 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.003 0.429 1.025 4.016 0.360 0.450 2 572012 1808 1978 171 1.000 0.432 0.675 3.155 0.414 0.241 3 572021 1885 1978 94 1.000 0.256 1.152 5.093 0.242 0.184 4 572022 1906 1978 73 1.000 0.291 0.559 3.577 0.291 0.090 5 572031 1871 1978 108 1.000 0.417 0.778 4.437 0.397 0.304 6 572032 1845 1978 134 1.004 0.451 1.601 7.625 0.317 0.417 7 572041 1834 1978 145 1.000 0.411 0.960 4.510 0.281 0.595 8 572042 1855 1978 124 1.000 0.376 0.334 2.961 0.334 0.443 9 572051 1812 1978 167 0.998 0.478 0.464 2.779 0.298 0.731 10 572052 1853 1978 126 0.999 0.446 0.925 4.102 0.370 0.526 11 572061 1765 1978 214 0.987 0.535 1.659 7.731 0.422 0.422 12 572062 1795 1978 184 1.001 0.399 0.539 2.728 0.364 0.339 13 572071 1877 1978 102 1.000 0.433 1.374 6.999 0.371 0.339 14 572072 1822 1958 137 1.002 0.521 3.366 22.079 0.404 0.219 15 572091 1846 1978 133 1.006 0.430 0.741 4.288 0.384 0.407 16 572092 1756 1978 223 0.992 0.560 1.043 3.766 0.372 0.683 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.429 1.075 5.615 0.351 0.399 STANDARD DEVIATION 44 0.005 0.079 0.723 4.676 0.052 0.176 MEDIAN (50TH QUANTILE) 135 1.000 0.431 0.943 4.195 0.367 0.412 INTERQUARTILE RANGE 61 0.002 0.059 0.646 2.680 0.083 0.216 MINIMUM VALUE 73 0.987 0.256 0.334 2.728 0.242 0.090 LOWER HINGE (25TH QUANTILE) 116 0.999 0.405 0.617 3.366 0.307 0.272 UPPER HINGE (75TH QUANTILE) 177 1.002 0.464 1.263 6.046 0.391 0.488 MAXIMUM VALUE 223 1.006 0.560 3.366 22.079 0.422 0.731 |------------------------ 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 0.999 0.417 0.939 3.763 0.360 0.427 2 572012 1808 1978 171 1.000 0.431 0.703 3.284 0.414 0.227 3 572021 1885 1978 94 0.998 0.239 0.914 4.625 0.242 0.095 4 572022 1906 1978 73 0.999 0.285 0.512 3.640 0.291 0.067 5 572031 1871 1978 108 0.997 0.393 0.601 3.586 0.397 0.182 6 572032 1845 1978 134 0.994 0.419 1.491 7.693 0.316 0.367 7 572041 1834 1978 145 0.992 0.372 0.776 4.404 0.280 0.532 8 572042 1855 1978 124 0.992 0.337 0.446 3.356 0.334 0.307 9 572051 1812 1978 167 0.970 0.353 0.231 2.669 0.297 0.545 10 572052 1853 1978 126 0.993 0.320 0.240 3.922 0.370 0.029 11 572061 1765 1978 214 0.997 0.515 1.384 5.981 0.422 0.393 12 572062 1795 1978 184 0.995 0.380 0.527 2.735 0.364 0.278 13 572071 1877 1978 102 0.998 0.415 1.103 5.621 0.371 0.304 14 572072 1822 1958 137 0.997 0.491 2.897 18.009 0.405 0.195 15 572091 1846 1978 133 0.991 0.378 0.579 3.790 0.385 0.261 16 572092 1756 1978 223 0.988 0.491 0.742 3.360 0.372 0.575 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 0.994 0.390 0.880 5.027 0.351 0.299 STANDARD DEVIATION 44 0.007 0.075 0.646 3.699 0.052 0.167 MEDIAN (50TH QUANTILE) 135 0.996 0.387 0.722 3.776 0.367 0.291 INTERQUARTILE RANGE 61 0.006 0.080 0.502 1.765 0.084 0.221 MINIMUM VALUE 73 0.970 0.239 0.231 2.669 0.242 0.029 LOWER HINGE (25TH QUANTILE) 116 0.992 0.345 0.520 3.358 0.307 0.188 UPPER HINGE (75TH QUANTILE) 177 0.998 0.425 1.021 5.123 0.391 0.410 MAXIMUM VALUE 223 1.000 0.515 2.897 18.009 0.422 0.575 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.364 0.132 0.012 -0.358 2.987 -0.024 0.659 MINIMUM CORRELATION: -0.024 SERIES 572021 AND 572041 94 YEARS MAXIMUM CORRELATION: 0.659 SERIES 572012 AND 572031 108 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 0.275 0.368 0.388 0.452 0.413 0.399 SDEV 0.169 0.179 0.162 0.132 0.151 0.169 SERR 0.098 0.057 0.031 0.016 0.015 0.017 EPS 0.658 0.824 0.877 0.920 0.916 0.914 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 0.982 0.277 0.432 2.948 0.282 0.258 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.420 0.243 0.044 49 174 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.66 1.00 1.13 1.79 5.07 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 0.257 0.109 -0.076 0.002 -0.087 -0.032 -0.054 -0.045 -0.063 -0.162 PACF 0.257 0.046 -0.123 0.049 -0.087 -0.005 -0.026 -0.044 -0.036 -0.159 95% C.L. 0.134 0.142 0.144 0.145 0.145 0.146 0.146 0.146 0.146 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 0.068 0.257 |======================= 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 0.248 0.213 -0.047 0.017 -0.030 0.019 0.002 -0.010 -0.100 -0.130 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 0.248 2 0.208 0.161 3 0.232 0.191 -0.144 4 0.235 0.186 -0.149 0.025 5 0.235 0.187 -0.149 0.025 0.001 6 0.235 0.186 -0.148 0.023 -0.002 0.012 7 0.235 0.186 -0.148 0.023 -0.003 0.011 0.004 8 0.235 0.187 -0.148 0.024 -0.006 0.015 0.010 -0.024 9 0.233 0.188 -0.146 0.023 -0.004 0.001 0.029 -0.001 -0.101 10 0.224 0.187 -0.144 0.023 -0.004 0.003 0.016 0.016 -0.080 -0.089 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) 1713.72 1701.51 1697.63 1694.99 1696.85 1698.85 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1700.82 1702.81 1704.68 1704.41 1704.65 SELECTED AUTOREGRESSION ORDER: 3 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 0.232 0.191 -0.144 R-SQUARED DUE TO POOLED AUTOREGRESSION: 10.50 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 111.73 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.232 0.245 -0.043 0.004 -0.042 -0.003 -0.009 0.003 -0.001 0.0018 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 572011 3 0.202 0.441 0.005 -0.091 2 572012 3 0.089 0.212 0.162 -0.114 3 572021 3 0.069 0.097 0.154 -0.106 4 572022 3 0.045 0.066 0.003 -0.149 5 572031 3 0.176 0.187 0.080 -0.356 6 572032 3 0.153 0.319 0.137 0.000 7 572041 3 0.344 0.432 0.307 -0.135 8 572042 3 0.120 0.291 0.138 -0.131 9 572051 3 0.323 0.481 0.175 -0.080 10 572052 3 0.040 0.034 0.189 -0.056 11 572061 3 0.168 0.349 0.061 0.086 12 572062 3 0.110 0.228 0.127 0.073 13 572071 3 0.133 0.308 0.031 -0.170 14 572072 3 0.039 0.191 0.029 -0.022 15 572091 3 0.146 0.231 0.178 -0.072 16 572092 3 0.356 0.478 0.148 0.029 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.157 0.272 0.120 -0.081 STANDARD DEVIATION 0 0.104 0.142 0.081 0.107 MEDIAN 3 0.140 0.261 0.138 -0.085 INTERQUARTILE RANGE 0 0.110 0.202 0.123 0.122 MINIMUM VALUE 3 0.039 0.034 0.003 -0.356 LOWER HINGE 3 0.079 0.189 0.046 -0.133 UPPER HINGE 3 0.189 0.391 0.169 -0.011 MAXIMUM VALUE 3 0.356 0.481 0.307 0.086 |------------------- 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 0.375 0.702 3.557 0.421 0.009 2 572012 1808 1978 171 1.000 0.413 0.685 3.499 0.447 -0.008 3 572021 1885 1978 94 1.000 0.234 0.862 4.368 0.251 -0.017 4 572022 1906 1978 73 1.000 0.281 0.563 3.776 0.303 -0.021 5 572031 1871 1978 108 1.000 0.361 0.390 3.313 0.419 -0.044 6 572032 1845 1978 134 1.000 0.385 1.787 10.575 0.371 -0.001 7 572041 1834 1978 145 1.000 0.301 0.761 4.031 0.316 -0.009 8 572042 1855 1978 124 1.000 0.316 0.356 3.265 0.363 0.002 9 572051 1812 1978 167 1.000 0.293 0.342 3.203 0.333 0.009 10 572052 1853 1978 126 1.000 0.313 0.390 3.922 0.366 0.001 11 572061 1765 1978 214 1.000 0.469 1.297 5.760 0.491 -0.001 12 572062 1795 1978 184 1.000 0.360 0.472 2.855 0.404 -0.007 13 572071 1877 1978 102 1.000 0.389 1.146 5.295 0.411 0.019 14 572072 1822 1958 137 1.000 0.482 3.203 19.899 0.413 -0.001 15 572091 1846 1978 133 1.000 0.359 0.746 4.149 0.397 0.017 16 572092 1756 1978 223 1.000 0.396 0.599 3.649 0.438 -0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.358 0.894 5.320 0.384 -0.003 STANDARD DEVIATION 44 0.000 0.067 0.728 4.295 0.061 0.015 MEDIAN (50TH QUANTILE) 135 1.000 0.361 0.694 3.849 0.401 -0.001 INTERQUARTILE RANGE 61 0.000 0.085 0.573 1.425 0.072 0.013 MINIMUM VALUE 73 1.000 0.234 0.342 2.855 0.251 -0.044 LOWER HINGE (25TH QUANTILE) 116 1.000 0.307 0.431 3.406 0.348 -0.008 UPPER HINGE (75TH QUANTILE) 177 1.000 0.392 1.004 4.831 0.420 0.005 MAXIMUM VALUE 223 1.000 0.482 3.203 19.899 0.491 0.019 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.398 0.120 0.011 -0.492 3.004 0.073 0.648 MINIMUM CORRELATION: 0.073 SERIES 572022 AND 572072 53 YEARS MAXIMUM CORRELATION: 0.648 SERIES 572011 AND 572012 171 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 0.428 0.469 0.500 0.529 0.443 0.397 SDEV 0.048 0.130 0.113 0.110 0.137 0.145 SERR 0.028 0.041 0.021 0.013 0.013 0.014 EPS 0.792 0.877 0.918 0.940 0.925 0.913 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 0.987 0.267 0.476 3.552 0.319 -0.046 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.464 0.236 0.005 52 171 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 1.02 1.01 1.09 2.11 9.11 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 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 -0.045 -0.090 -0.102 0.033 -0.078 0.005 -0.033 0.002 -0.002 -0.166 PACF -0.045 -0.092 -0.112 0.013 -0.098 -0.013 -0.047 -0.024 -0.009 -0.192 95% C.L. 0.134 0.134 0.135 0.137 0.137 0.138 0.138 0.138 0.138 0.138 |------------------ 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 0.002 -0.010 -0.010 0.002 -0.103 -0.012 -0.058 -0.037 -0.013 -0.160 PACF 0.002 -0.010 -0.010 0.002 -0.104 -0.012 -0.061 -0.040 -0.015 -0.176 95% C.L. 0.134 0.134 0.134 0.134 0.134 0.135 0.135 0.136 0.136 0.136 |----------------- 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 3 0.000 0.001 -0.010 -0.010 |========================= 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 0.988 0.280 0.365 3.044 0.284 0.247 |------------ 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 0.246 0.208 -0.075 -0.030 -0.152 -0.058 -0.098 -0.082 -0.097 -0.168 PACF 0.246 0.158 -0.171 -0.012 -0.104 -0.007 -0.043 -0.078 -0.053 -0.158 95% C.L. 0.134 0.142 0.147 0.148 0.148 0.151 0.151 0.152 0.153 0.154 |------------------- 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 3 0.111 0.234 0.194 -0.173 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 76.51 MINUTES