RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN022W.rwl.conv LOG FILE PROCESSED: FRAN022W.rwl.conv_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: 481 1 Llipodre WIDTH_RING PIMU - 481 2 France krummholz pine 1950 4227-223 1839 1977 - 481 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 481011 1848 1977 130 2.012 0.999 0.870 2.675 0.164 0.917 2 481012 1848 1977 130 1.831 0.797 0.531 2.294 0.175 0.843 3 481021 1870 1977 108 1.998 0.695 0.478 2.772 0.164 0.806 4 481022 1862 1977 116 1.916 0.779 0.411 2.715 0.178 0.832 5 481031 1850 1977 128 1.521 0.742 0.832 3.310 0.170 0.854 6 481032 1853 1977 125 1.501 0.711 1.406 4.625 0.177 0.861 7 481051 1861 1977 117 1.525 0.460 0.503 3.171 0.200 0.634 8 481052 1858 1977 120 1.646 0.468 0.255 2.818 0.161 0.762 9 481061 1886 1977 92 1.303 0.465 1.407 5.183 0.141 0.814 10 481062 1868 1977 110 1.271 0.401 0.683 3.204 0.161 0.809 11 481081 1844 1977 134 1.486 0.702 0.736 3.111 0.142 0.886 12 481082 1839 1977 139 1.439 0.568 0.257 2.552 0.160 0.856 13 481091 1860 1977 118 1.953 1.040 0.486 2.041 0.168 0.914 14 481092 1855 1977 123 2.109 0.777 0.819 3.440 0.144 0.886 15 481101 1842 1977 136 1.117 0.526 1.459 4.912 0.197 0.877 16 481102 1853 1977 125 1.345 0.690 1.156 3.346 0.192 0.880 17 481111 1862 1977 116 2.001 0.882 0.575 2.312 0.156 0.909 18 481112 1877 1977 101 1.892 0.910 1.644 5.937 0.192 0.799 19 481131 1853 1977 125 2.442 0.782 0.306 2.358 0.151 0.817 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 2.179 0.833 0.563 2.650 0.167 0.861 NUMBER OF SERIES READ IN: 20 FROM 1839 TO 1977 139 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.724 0.711 0.769 3.271 0.168 0.841 STANDARD DEVIATION 11 0.356 0.182 0.427 1.066 0.018 0.064 MEDIAN (50TH QUANTILE) 121 1.738 0.727 0.629 2.965 0.166 0.855 INTERQUARTILE RANGE 15 0.537 0.268 0.531 0.792 0.020 0.071 MINIMUM VALUE 92 1.117 0.401 0.255 2.041 0.141 0.634 LOWER HINGE (25TH QUANTILE) 114 1.463 0.547 0.482 2.601 0.158 0.811 UPPER HINGE (75TH QUANTILE) 129 1.999 0.815 1.013 3.393 0.177 0.883 MAXIMUM VALUE 139 2.442 1.040 1.644 5.937 0.200 0.917 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.550 0.229 0.017 -0.862 3.008 -0.123 0.879 MINIMUM CORRELATION: -0.123 SERIES 481051 AND 481132 112 YEARS MAXIMUM CORRELATION: 0.879 SERIES 481101 AND 481102 125 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 81.64 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 105. 190. 190. RBAR 0.330 0.361 0.381 SDEV 0.315 0.310 0.221 SERR 0.031 0.022 0.016 EPS 0.904 0.919 0.925 NSS 19.2 20.0 20.0 |======================== 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 1839 1977 139 1.778 0.595 0.361 2.234 0.116 0.902 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.716 0.291 0.063 38 101 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.09 0.20 1.00 1.03 1.23 2.06 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.07 0.00 0.86 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 122. 15. 92. 114. 129. 139. |----------- 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 0.896 0.872 0.859 0.800 0.786 0.742 0.717 0.704 0.684 0.651 PACF 0.896 0.350 0.218 -0.144 0.078 -0.098 0.068 0.056 0.092 -0.115 95% C.L. 0.170 0.274 0.344 0.401 0.445 0.483 0.515 0.543 0.569 0.592 |------------------ 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 0.855 0.507 0.255 0.325 -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 481011 1 3.23897934 0.01686312 0.00000000 0.71027738 2 481012 3 0.00000000 0.00000000 -0.01612612 2.88687658 3 481021 3 0.00000000 0.00000000 -0.01387479 2.75386119 4 481022 3 0.00000000 0.00000000 -0.01719536 2.92239428 5 481031 1 2.78936982 0.01434446 0.00000000 0.25292608 6 481032 1 2.50558424 0.03604043 0.00000000 0.96088165 7 481051 3 0.00000000 0.00000000 -0.00365276 1.74081194 8 481052 3 0.00000000 0.00000000 -0.00129780 1.72435009 9 481061 1 1.50893402 0.03913235 0.00000000 0.90318173 10 481062 3 0.00000000 0.00000000 -0.00767870 1.69698584 11 481081 3 0.00000000 0.00000000 -0.01625205 2.58305812 12 481082 3 0.00000000 0.00000000 -0.01157040 2.24935246 13 481091 3 0.00000000 0.00000000 -0.02615027 3.50865269 14 481092 3 0.00000000 0.00000000 -0.01535786 3.06088638 15 481101 1 1.79088485 0.02667921 0.00000000 0.64254546 16 481102 1 2.48904252 0.03864959 0.00000000 0.84377337 17 481111 3 0.00000000 0.00000000 -0.02235528 3.30881858 18 481112 1 3.16564417 0.04110016 0.00000000 1.15652573 19 481131 3 0.00000000 0.00000000 -0.01604098 3.45218182 SERIES IDENT OPTION A B C D 20 481132 1 2.18598127 0.05803670 0.00000000 1.85270131 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 481011 1848 1977 130 1.002 0.300 0.607 2.670 0.163 0.752 2 481012 1848 1977 130 0.999 0.260 0.427 2.981 0.173 0.610 3 481021 1870 1977 108 1.000 0.272 0.416 2.863 0.163 0.655 4 481022 1862 1977 116 0.995 0.277 0.816 2.887 0.176 0.633 5 481031 1850 1977 128 1.000 0.244 0.827 3.643 0.169 0.594 6 481032 1853 1977 125 1.000 0.237 0.425 3.332 0.176 0.553 7 481051 1861 1977 117 1.000 0.288 0.384 3.005 0.199 0.617 8 481052 1858 1977 120 1.000 0.281 0.176 2.708 0.160 0.752 9 481061 1886 1977 92 1.000 0.197 0.836 3.277 0.140 0.536 10 481062 1868 1977 110 0.999 0.240 0.474 3.148 0.160 0.647 11 481081 1844 1977 134 1.013 0.197 0.429 3.012 0.141 0.560 12 481082 1839 1977 139 0.993 0.221 0.418 2.707 0.159 0.539 13 481091 1860 1977 118 1.043 0.363 0.531 3.193 0.167 0.782 14 481092 1855 1977 123 0.996 0.230 0.498 3.685 0.143 0.695 15 481101 1842 1977 136 1.001 0.226 0.653 3.711 0.196 0.411 16 481102 1853 1977 125 1.001 0.278 0.728 3.601 0.191 0.595 17 481111 1862 1977 116 1.010 0.247 0.668 3.206 0.155 0.653 18 481112 1877 1977 101 0.999 0.227 0.375 2.877 0.189 0.478 19 481131 1853 1977 125 1.001 0.227 0.626 3.319 0.150 0.602 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 0.999 0.318 0.320 2.719 0.166 0.796 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.002 0.257 0.532 3.127 0.167 0.623 STANDARD DEVIATION 11 0.011 0.041 0.182 0.342 0.017 0.100 MEDIAN (50TH QUANTILE) 121 1.000 0.246 0.486 3.080 0.164 0.614 INTERQUARTILE RANGE 15 0.002 0.053 0.243 0.456 0.019 0.118 MINIMUM VALUE 92 0.993 0.197 0.176 2.670 0.140 0.411 LOWER HINGE (25TH QUANTILE) 114 0.999 0.227 0.417 2.870 0.157 0.556 UPPER HINGE (75TH QUANTILE) 129 1.001 0.280 0.660 3.325 0.176 0.675 MAXIMUM VALUE 139 1.043 0.363 0.836 3.711 0.199 0.796 |------------------------ 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 481011 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 481012 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 481021 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 481022 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 481031 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 481032 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 481051 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 481052 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 481061 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 481062 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 481081 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 481082 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 481091 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 481092 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 481101 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 481102 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 481111 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 481112 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 481131 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 481132 -67 75 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 481011 1848 1977 130 0.996 0.283 0.779 2.958 0.163 0.726 2 481012 1848 1977 130 0.997 0.236 0.247 2.839 0.174 0.525 3 481021 1870 1977 108 0.992 0.212 0.537 3.149 0.162 0.465 4 481022 1862 1977 116 0.998 0.261 0.742 2.848 0.176 0.573 5 481031 1850 1977 128 0.997 0.222 0.591 3.366 0.169 0.524 6 481032 1853 1977 125 0.998 0.219 0.330 3.291 0.176 0.488 7 481051 1861 1977 117 0.996 0.268 0.324 2.893 0.198 0.552 8 481052 1858 1977 120 0.997 0.246 0.380 3.370 0.160 0.677 9 481061 1886 1977 92 0.999 0.192 0.919 3.587 0.140 0.509 10 481062 1868 1977 110 0.996 0.203 0.240 2.924 0.159 0.510 11 481081 1844 1977 134 0.999 0.175 0.224 2.596 0.141 0.473 12 481082 1839 1977 139 0.998 0.204 0.649 3.107 0.158 0.465 13 481091 1860 1977 118 0.992 0.244 -0.125 2.798 0.166 0.639 14 481092 1855 1977 123 0.995 0.189 0.354 3.046 0.142 0.564 15 481101 1842 1977 136 0.999 0.201 0.387 3.420 0.196 0.280 16 481102 1853 1977 125 0.999 0.266 0.732 3.475 0.191 0.574 17 481111 1862 1977 116 0.997 0.213 0.709 4.325 0.155 0.579 18 481112 1877 1977 101 0.999 0.211 0.212 2.672 0.188 0.396 19 481131 1853 1977 125 0.999 0.219 0.669 3.166 0.150 0.583 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 0.993 0.283 0.315 2.711 0.165 0.754 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 0.997 0.227 0.461 3.127 0.166 0.543 STANDARD DEVIATION 11 0.002 0.032 0.258 0.401 0.017 0.109 MEDIAN (50TH QUANTILE) 121 0.997 0.219 0.383 3.076 0.164 0.539 INTERQUARTILE RANGE 15 0.003 0.050 0.408 0.525 0.019 0.101 MINIMUM VALUE 92 0.992 0.175 -0.125 2.596 0.140 0.280 LOWER HINGE (25TH QUANTILE) 114 0.996 0.203 0.281 2.843 0.156 0.480 UPPER HINGE (75TH QUANTILE) 129 0.999 0.254 0.689 3.368 0.176 0.581 MAXIMUM VALUE 139 0.999 0.283 0.919 4.325 0.198 0.754 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.267 0.146 0.011 -0.419 3.535 -0.160 0.698 MINIMUM CORRELATION: -0.160 SERIES 481011 AND 481051 117 YEARS MAXIMUM CORRELATION: 0.698 SERIES 481011 AND 481132 112 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 81.64 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 105. 190. 190. RBAR 0.240 0.242 0.322 SDEV 0.200 0.216 0.200 SERR 0.020 0.016 0.015 EPS 0.858 0.865 0.905 NSS 19.2 20.0 20.0 |======================== 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 1839 1977 139 0.985 0.129 0.171 2.852 0.119 0.362 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.504 0.235 -0.050 44 95 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.41 1.00 1.11 1.52 4.27 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.87 0.92 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 0.360 0.191 0.222 0.053 -0.043 -0.191 -0.242 -0.186 -0.172 -0.288 PACF 0.360 0.070 0.153 -0.091 -0.080 -0.214 -0.128 -0.027 -0.006 -0.188 95% C.L. 0.170 0.190 0.196 0.203 0.203 0.204 0.209 0.217 0.221 0.225 |------------------ 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 0.134 0.360 |======================= 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 0.412 0.201 0.225 0.085 -0.039 -0.215 -0.235 -0.222 -0.189 -0.313 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 0.412 2 0.396 0.038 3 0.390 -0.023 0.156 4 0.402 -0.025 0.186 -0.077 5 0.395 -0.008 0.184 -0.041 -0.090 6 0.373 -0.018 0.229 -0.043 0.006 -0.244 7 0.351 -0.018 0.225 -0.023 0.004 -0.211 -0.088 8 0.345 -0.033 0.225 -0.024 0.021 -0.213 -0.062 -0.074 9 0.347 -0.032 0.230 -0.025 0.021 -0.218 -0.061 -0.081 0.022 10 0.351 -0.050 0.216 -0.074 0.026 -0.223 -0.010 -0.088 0.099 -0.224 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) 914.05 890.25 892.05 890.62 891.79 892.65 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 886.12 887.04 888.29 890.22 885.09 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 0.412 R-SQUARED DUE TO POOLED AUTOREGRESSION: 16.94 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 120.39 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.412 0.169 0.070 0.029 0.012 0.005 0.002 0.001 0.000 0.0001 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 481011 1 0.535 0.731 2 481012 1 0.276 0.525 3 481021 1 0.221 0.467 4 481022 1 0.338 0.576 5 481031 1 0.279 0.525 6 481032 1 0.249 0.496 7 481051 1 0.311 0.557 8 481052 1 0.462 0.678 9 481061 1 0.261 0.511 10 481062 1 0.262 0.512 11 481081 1 0.228 0.477 12 481082 1 0.220 0.469 13 481091 1 0.417 0.641 14 481092 1 0.330 0.574 15 481101 1 0.110 0.284 16 481102 1 0.337 0.575 17 481111 1 0.350 0.590 18 481112 1 0.169 0.399 19 481131 1 0.343 0.586 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 481132 1 0.574 0.757 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.314 0.547 STANDARD DEVIATION 0 0.115 0.109 MEDIAN 1 0.295 0.541 INTERQUARTILE RANGE 0 0.109 0.102 MINIMUM VALUE 1 0.110 0.284 LOWER HINGE 1 0.238 0.486 UPPER HINGE 1 0.347 0.588 MAXIMUM VALUE 1 0.574 0.757 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 481011 1848 1977 130 1.000 0.192 0.112 3.277 0.214 -0.038 2 481012 1848 1977 130 1.000 0.201 0.397 3.198 0.214 -0.005 3 481021 1870 1977 108 1.000 0.187 0.423 3.103 0.200 0.030 4 481022 1862 1977 116 1.000 0.214 0.507 3.600 0.226 0.057 5 481031 1850 1977 128 1.000 0.189 0.440 3.248 0.210 -0.035 6 481032 1853 1977 125 1.000 0.190 0.180 3.099 0.210 0.025 7 481051 1861 1977 117 1.000 0.222 -0.228 4.215 0.247 0.016 8 481052 1858 1977 120 1.000 0.181 0.757 4.597 0.198 0.050 9 481061 1886 1977 92 1.000 0.165 0.526 3.055 0.182 0.015 10 481062 1868 1977 110 1.000 0.174 -0.160 3.587 0.188 -0.002 11 481081 1844 1977 134 1.000 0.154 0.380 3.095 0.172 -0.009 12 481082 1839 1977 139 1.000 0.180 0.357 2.809 0.197 0.004 13 481091 1860 1977 118 1.000 0.187 -0.082 3.112 0.227 -0.070 14 481092 1855 1977 123 1.000 0.154 0.106 2.415 0.174 -0.002 15 481101 1842 1977 136 1.000 0.192 0.367 3.421 0.225 -0.054 16 481102 1853 1977 125 1.000 0.217 0.593 3.380 0.240 -0.054 17 481111 1862 1977 116 1.000 0.171 0.301 3.740 0.190 -0.033 18 481112 1877 1977 101 1.000 0.193 0.193 2.577 0.226 -0.046 19 481131 1853 1977 125 1.000 0.178 0.230 3.128 0.199 -0.006 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 1.000 0.184 -0.084 3.180 0.216 -0.034 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.186 0.266 3.292 0.208 -0.010 STANDARD DEVIATION 11 0.000 0.018 0.263 0.499 0.021 0.036 MEDIAN (50TH QUANTILE) 121 1.000 0.187 0.329 3.189 0.210 -0.006 INTERQUARTILE RANGE 15 0.000 0.017 0.323 0.407 0.032 0.052 MINIMUM VALUE 92 1.000 0.154 -0.228 2.415 0.172 -0.070 LOWER HINGE (25TH QUANTILE) 114 1.000 0.176 0.109 3.097 0.193 -0.036 UPPER HINGE (75TH QUANTILE) 129 1.000 0.193 0.432 3.504 0.225 0.016 MAXIMUM VALUE 139 1.000 0.222 0.757 4.597 0.247 0.057 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.343 0.096 0.007 0.398 4.077 0.100 0.737 MINIMUM CORRELATION: 0.100 SERIES 481021 AND 481102 108 YEARS MAXIMUM CORRELATION: 0.737 SERIES 481111 AND 481112 101 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 81.64 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 105. 190. 190. RBAR 0.303 0.334 0.396 SDEV 0.129 0.141 0.138 SERR 0.013 0.010 0.010 EPS 0.893 0.909 0.929 NSS 19.2 20.0 20.0 |======================== 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 1839 1977 139 0.994 0.120 -0.013 2.711 0.149 -0.187 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.402 0.147 -0.002 36 103 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.51 1.01 1.09 1.59 5.41 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.07 0.00 0.86 0.93 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 -0.186 -0.116 0.224 -0.072 0.026 -0.097 -0.135 -0.022 0.050 -0.175 PACF -0.186 -0.156 0.181 -0.011 0.064 -0.145 -0.171 -0.139 0.050 -0.134 95% C.L. 0.170 0.175 0.178 0.186 0.186 0.186 0.188 0.191 0.191 0.191 |------------------ 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 3 0.089 -0.187 -0.116 0.182 |---------- 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 -0.029 -0.116 0.204 -0.028 -0.004 -0.126 -0.167 -0.039 0.016 -0.212 PACF -0.029 -0.117 0.200 -0.036 0.044 -0.185 -0.162 -0.100 0.045 -0.185 95% C.L. 0.170 0.170 0.172 0.179 0.179 0.179 0.182 0.186 0.186 0.186 |----------------- 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 0.015 -0.029 |========================= 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 1839 1977 139 0.993 0.127 0.028 2.878 0.117 0.374 |------------ 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 0.372 0.117 0.202 0.027 -0.065 -0.206 -0.258 -0.173 -0.154 -0.297 PACF 0.372 -0.025 0.194 -0.134 -0.040 -0.242 -0.106 -0.037 -0.011 -0.237 95% C.L. 0.170 0.192 0.194 0.200 0.200 0.200 0.206 0.215 0.219 0.222 |------------------- 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 0.139 0.372 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES