RUN: SPAI001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SPAI005W.rwl.conv LOG FILE PROCESSED: SPAI005W.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: 495 1 Alcala de Selva WIDTH_RING PIMU - 495 2 Spain krummholz pine 1960 4023-40 1820 1977 - 495 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 15 495101 MISSING VALUES FOUND: 3 IN 1 GAPS / 1939 1941 / -------------------------------------------------------------------- 16 495102 MISSING VALUES FOUND: 3 IN 1 GAPS / 1939 1941 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 2.206 0.776 0.105 1.834 0.190 0.769 2 495012 1914 1977 64 2.308 0.591 0.172 3.151 0.164 0.632 3 495021 1882 1977 96 2.051 1.295 1.433 4.059 0.204 0.909 4 495022 1886 1977 92 2.088 1.234 1.683 4.684 0.186 0.897 5 495031 1917 1977 61 3.062 0.919 0.328 3.430 0.159 0.760 6 495032 1922 1977 56 3.540 1.172 0.936 2.927 0.152 0.832 7 495041 1889 1977 89 2.045 0.791 0.411 2.478 0.191 0.825 8 495042 1885 1977 93 2.048 0.889 1.083 4.017 0.205 0.779 9 495051 1868 1977 110 2.219 1.593 1.613 5.589 0.180 0.890 10 495052 1864 1977 114 1.641 1.174 1.763 5.822 0.185 0.886 11 495081 1884 1977 94 1.934 0.723 1.159 3.920 0.194 0.756 12 495082 1868 1977 110 2.280 0.979 0.954 2.898 0.199 0.862 13 495091 1836 1977 142 1.515 0.620 0.486 2.893 0.192 0.818 14 495092 1854 1977 124 1.497 0.595 0.817 2.962 0.195 0.805 15 495101 1918 1977 60 3.425 1.528 0.399 2.372 0.193 0.850 16 495102 1917 1977 61 2.993 1.242 0.035 2.229 0.237 0.777 17 495111 1881 1977 97 2.193 1.009 0.165 2.087 0.158 0.907 18 495112 1893 1977 85 2.244 0.986 1.438 6.682 0.139 0.812 19 495141 1831 1977 147 1.769 0.637 0.448 2.844 0.243 0.640 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 1.550 0.488 0.391 2.985 0.223 0.588 21 495151 1900 1977 78 3.132 1.501 1.582 4.758 0.150 0.899 22 495152 1897 1977 81 2.713 1.253 0.684 3.150 0.154 0.899 NUMBER OF SERIES READ IN: 22 FROM 1820 TO 1977 158 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 2.293 1.000 0.822 3.535 0.186 0.809 STANDARD DEVIATION 29 0.604 0.328 0.570 1.283 0.028 0.092 MEDIAN (50TH QUANTILE) 92 2.200 0.982 0.751 3.067 0.190 0.821 INTERQUARTILE RANGE 45 0.779 0.520 1.043 1.215 0.041 0.121 MINIMUM VALUE 56 1.497 0.488 0.035 1.834 0.139 0.588 LOWER HINGE (25TH QUANTILE) 65 1.934 0.723 0.391 2.844 0.159 0.769 UPPER HINGE (75TH QUANTILE) 110 2.713 1.242 1.433 4.059 0.199 0.890 MAXIMUM VALUE 158 3.540 1.593 1.763 6.682 0.243 0.909 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.585 0.218 0.014 -1.285 5.557 -0.352 0.951 MINIMUM CORRELATION: -0.352 SERIES 495012 AND 495081 64 YEARS MAXIMUM CORRELATION: 0.951 SERIES 495021 AND 495022 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.421 0.479 0.509 SDEV 0.245 0.204 0.217 SERR 0.100 0.044 0.020 EPS 0.871 0.936 0.955 NSS 9.3 16.0 20.6 |======================== 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 1820 1977 158 1.969 0.595 0.536 2.828 0.153 0.808 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.669 0.434 -0.161 55 103 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.40 0.95 1.01 1.14 2.09 134.79 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.15 0.00 0.85 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 92. 45. 56. 65. 110. 158. |----------- 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 0.802 0.734 0.711 0.689 0.650 0.626 0.589 0.568 0.543 0.520 PACF 0.802 0.254 0.203 0.124 0.029 0.048 -0.016 0.026 0.006 0.007 95% C.L. 0.159 0.241 0.292 0.333 0.367 0.395 0.420 0.440 0.458 0.474 |------------------ 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 0.699 0.513 0.104 0.144 0.145 |================== 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 495011 3 0.00000000 0.00000000 -0.03127054 3.23838949 2 495012 3 0.00000000 0.00000000 -0.02010348 2.96180058 3 495021 1 4.36302567 0.03514021 0.00000000 0.82418686 4 495022 1 4.76699352 0.06205561 0.00000000 1.28085673 5 495031 3 0.00000000 0.00000000 -0.04064040 4.32165575 6 495032 1 4.19536400 0.04257025 0.00000000 1.97653568 7 495041 3 0.00000000 0.00000000 -0.02184985 3.02796221 8 495042 1 3.03876328 0.04031532 0.00000000 1.27294862 9 495051 1 6.04705429 0.03859234 0.00000000 0.84163702 10 495052 1 4.62661123 0.04299221 0.00000000 0.72392416 11 495081 1 2.17904067 0.06211286 0.00000000 1.57357311 12 495082 3 0.00000000 0.00000000 -0.01599031 3.16737127 13 495091 3 0.00000000 0.00000000 -0.00906430 2.16302657 14 495092 3 0.00000000 0.00000000 -0.01278546 2.29634929 15 495101 1 4.85906696 0.05237627 0.00000000 1.93164027 16 495102 1 2.45671511 0.03509762 0.00000000 1.94272339 17 495111 3 0.00000000 0.00000000 -0.03291316 3.80552840 18 495112 1 3.37094855 0.02603588 0.00000000 0.90523112 19 495141 3 0.00000000 0.00000000 -0.00650443 2.25051165 SERIES IDENT OPTION A B C D 20 495142 3 0.00000000 0.00000000 -0.00297817 1.78632188 21 495151 1 6.06715536 0.08896250 0.00000000 2.29645538 22 495152 3 0.00000000 0.00000000 -0.04768677 4.66836739 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 0.995 0.220 0.403 3.289 0.185 0.473 2 495012 1914 1977 64 0.999 0.200 0.085 2.736 0.162 0.414 3 495021 1882 1977 96 1.003 0.320 1.178 4.441 0.202 0.660 4 495022 1886 1977 92 1.001 0.267 0.715 2.951 0.183 0.635 5 495031 1917 1977 61 0.999 0.188 0.474 3.366 0.154 0.477 6 495032 1922 1977 56 1.000 0.151 0.165 2.176 0.148 0.191 7 495041 1889 1977 89 1.007 0.308 0.874 4.155 0.188 0.632 8 495042 1885 1977 93 1.000 0.242 0.410 2.552 0.201 0.424 9 495051 1868 1977 110 0.997 0.252 0.417 2.902 0.179 0.594 10 495052 1864 1977 114 0.995 0.213 0.052 3.174 0.181 0.395 11 495081 1884 1977 94 1.000 0.276 1.059 3.853 0.191 0.573 12 495082 1868 1977 110 0.996 0.328 0.431 2.392 0.198 0.713 13 495091 1836 1977 142 0.991 0.301 0.218 2.732 0.191 0.689 14 495092 1854 1977 124 1.004 0.244 0.807 3.365 0.194 0.494 15 495101 1918 1977 60 1.000 0.294 -0.186 3.365 0.195 0.663 16 495102 1917 1977 61 1.000 0.376 -0.116 2.343 0.237 0.736 17 495111 1881 1977 97 1.002 0.206 0.494 3.591 0.155 0.456 18 495112 1893 1977 85 0.998 0.230 0.119 2.541 0.138 0.629 19 495141 1831 1977 147 0.997 0.324 0.656 3.273 0.241 0.557 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 0.999 0.306 0.608 3.460 0.222 0.545 21 495151 1900 1977 78 1.001 0.255 0.340 2.248 0.149 0.712 22 495152 1897 1977 81 1.019 0.282 2.822 13.761 0.153 0.590 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.263 0.547 3.576 0.184 0.557 STANDARD DEVIATION 29 0.005 0.055 0.619 2.354 0.028 0.132 MEDIAN (50TH QUANTILE) 92 1.000 0.261 0.424 3.224 0.187 0.581 INTERQUARTILE RANGE 45 0.005 0.086 0.550 0.908 0.042 0.187 MINIMUM VALUE 56 0.991 0.151 -0.186 2.176 0.138 0.191 LOWER HINGE (25TH QUANTILE) 65 0.997 0.220 0.165 2.552 0.155 0.473 UPPER HINGE (75TH QUANTILE) 110 1.001 0.306 0.715 3.460 0.198 0.660 MAXIMUM VALUE 158 1.019 0.376 2.822 13.761 0.241 0.736 |------------------------ 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 495011 -67 43 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 495012 -67 42 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 495021 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 495022 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 495031 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 495032 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 495041 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 495042 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 495051 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 495052 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 495081 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 495082 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 495091 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 495092 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 495101 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 495102 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 495111 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 495112 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 495141 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 495142 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 495151 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 495152 -67 54 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 495011 1913 1977 65 0.998 0.197 0.333 2.896 0.186 0.317 2 495012 1914 1977 64 0.999 0.187 0.287 2.790 0.160 0.341 3 495021 1882 1977 96 0.994 0.279 0.813 3.518 0.201 0.581 4 495022 1886 1977 92 0.997 0.238 0.590 2.768 0.183 0.543 5 495031 1917 1977 61 0.997 0.159 0.626 3.882 0.153 0.277 6 495032 1922 1977 56 0.999 0.145 0.111 2.183 0.148 0.130 7 495041 1889 1977 89 0.991 0.217 0.184 2.994 0.187 0.402 8 495042 1885 1977 93 0.999 0.229 0.421 2.848 0.201 0.344 9 495051 1868 1977 110 0.995 0.214 0.432 3.287 0.179 0.440 10 495052 1864 1977 114 0.999 0.192 0.221 3.605 0.181 0.241 11 495081 1884 1977 94 0.997 0.222 0.783 3.249 0.192 0.430 12 495082 1868 1977 110 0.988 0.240 0.377 2.685 0.198 0.455 13 495091 1836 1977 142 0.994 0.235 0.195 2.858 0.190 0.514 14 495092 1854 1977 124 0.998 0.218 0.740 3.605 0.193 0.378 15 495101 1918 1977 60 0.994 0.266 -0.363 3.136 0.193 0.613 16 495102 1917 1977 61 0.986 0.341 0.063 2.674 0.237 0.687 17 495111 1881 1977 97 0.999 0.192 0.371 3.799 0.155 0.394 18 495112 1893 1977 85 0.995 0.174 0.309 2.653 0.137 0.402 19 495141 1831 1977 147 0.998 0.279 0.714 3.621 0.241 0.396 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 0.998 0.250 1.041 6.310 0.222 0.290 21 495151 1900 1977 78 0.994 0.210 0.486 3.120 0.148 0.561 22 495152 1897 1977 81 0.997 0.207 0.619 4.442 0.152 0.493 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 0.996 0.222 0.425 3.315 0.184 0.419 STANDARD DEVIATION 29 0.004 0.044 0.309 0.845 0.028 0.132 MEDIAN (50TH QUANTILE) 92 0.997 0.217 0.399 3.128 0.187 0.402 INTERQUARTILE RANGE 45 0.004 0.047 0.405 0.815 0.042 0.173 MINIMUM VALUE 56 0.986 0.145 -0.363 2.183 0.137 0.130 LOWER HINGE (25TH QUANTILE) 65 0.994 0.192 0.221 2.790 0.155 0.341 UPPER HINGE (75TH QUANTILE) 110 0.998 0.240 0.626 3.605 0.198 0.514 MAXIMUM VALUE 158 0.999 0.341 1.041 6.310 0.241 0.687 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.291 0.200 0.013 -0.356 2.938 -0.294 0.761 MINIMUM CORRELATION: -0.294 SERIES 495012 AND 495032 56 YEARS MAXIMUM CORRELATION: 0.761 SERIES 495021 AND 495022 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.397 0.208 0.297 SDEV 0.253 0.258 0.218 SERR 0.103 0.056 0.020 EPS 0.859 0.808 0.897 NSS 9.3 16.0 20.6 |======================== 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 1820 1977 158 0.985 0.151 0.259 3.299 0.145 0.257 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.183 0.099 0.068 28 130 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.60 1.00 1.06 1.66 7.98 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 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 0.255 0.112 0.148 0.062 0.027 -0.031 -0.030 -0.101 -0.106 -0.164 PACF 0.255 0.050 0.115 -0.006 -0.003 -0.059 -0.019 -0.095 -0.052 -0.122 95% C.L. 0.159 0.169 0.171 0.174 0.175 0.175 0.175 0.175 0.177 0.178 |------------------ 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 0.256 |======================= 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 0.345 0.139 0.203 0.018 -0.058 -0.046 -0.114 -0.151 -0.163 -0.202 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 0.345 2 0.338 0.023 3 0.334 -0.034 0.169 4 0.354 -0.039 0.209 -0.121 5 0.348 -0.028 0.207 -0.103 -0.051 6 0.346 -0.032 0.216 -0.104 -0.037 -0.042 7 0.343 -0.035 0.208 -0.088 -0.039 -0.016 -0.075 8 0.337 -0.036 0.205 -0.095 -0.023 -0.018 -0.049 -0.077 9 0.330 -0.041 0.203 -0.097 -0.032 0.000 -0.052 -0.047 -0.090 10 0.320 -0.046 0.198 -0.097 -0.035 -0.010 -0.030 -0.051 -0.054 -0.109 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) 1026.63 1008.55 1010.47 1007.91 1007.56 1009.14 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1010.87 1011.97 1013.03 1013.75 1013.88 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 0.345 R-SQUARED DUE TO POOLED AUTOREGRESSION: 11.93 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 113.55 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.345 0.119 0.041 0.014 0.005 0.002 0.001 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 495011 1 0.122 0.323 2 495012 1 0.168 0.362 3 495021 1 0.342 0.582 4 495022 1 0.301 0.548 5 495031 1 0.077 0.277 6 495032 1 0.048 0.131 7 495041 1 0.184 0.405 8 495042 1 0.123 0.351 9 495051 1 0.199 0.444 10 495052 1 0.061 0.244 11 495081 1 0.193 0.431 12 495082 1 0.213 0.455 13 495091 1 0.281 0.519 14 495092 1 0.190 0.379 15 495101 1 0.388 0.616 16 495102 1 0.488 0.688 17 495111 1 0.166 0.406 18 495112 1 0.191 0.431 19 495141 1 0.159 0.396 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 495142 1 0.088 0.294 21 495151 1 0.346 0.581 22 495152 1 0.264 0.513 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.209 0.426 STANDARD DEVIATION 0 0.112 0.133 MEDIAN 1 0.190 0.418 INTERQUARTILE RANGE 0 0.158 0.169 MINIMUM VALUE 1 0.048 0.131 LOWER HINGE 1 0.123 0.351 UPPER HINGE 1 0.281 0.519 MAXIMUM VALUE 1 0.488 0.688 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 1.000 0.186 0.411 2.955 0.209 0.042 2 495012 1914 1977 64 1.000 0.174 0.241 2.797 0.179 0.088 3 495021 1882 1977 96 1.000 0.227 0.492 3.493 0.246 0.044 4 495022 1886 1977 92 1.000 0.199 0.557 2.891 0.223 0.008 5 495031 1917 1977 61 1.000 0.153 0.617 3.887 0.172 0.002 6 495032 1922 1977 56 1.000 0.144 0.033 2.319 0.157 0.020 7 495041 1889 1977 89 1.000 0.198 0.620 3.519 0.221 -0.059 8 495042 1885 1977 93 1.000 0.214 0.546 3.815 0.244 0.002 9 495051 1868 1977 110 1.000 0.192 0.539 3.162 0.211 -0.027 10 495052 1864 1977 114 1.000 0.186 0.253 3.886 0.201 -0.011 11 495081 1884 1977 94 1.000 0.200 0.743 3.115 0.216 0.039 12 495082 1868 1977 110 1.000 0.213 0.393 2.783 0.236 -0.040 13 495091 1836 1977 142 1.000 0.200 0.246 3.090 0.234 -0.070 14 495092 1854 1977 124 1.000 0.202 0.581 3.707 0.243 -0.087 15 495101 1918 1977 60 1.000 0.210 0.012 3.156 0.249 -0.075 16 495102 1917 1977 61 1.000 0.248 0.383 3.322 0.297 -0.111 17 495111 1881 1977 97 1.000 0.176 0.091 4.179 0.182 0.026 18 495112 1893 1977 85 1.000 0.156 -0.153 3.425 0.168 -0.037 19 495141 1831 1977 147 1.000 0.256 0.604 3.894 0.290 -0.020 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 1.000 0.239 1.060 6.577 0.251 -0.007 21 495151 1900 1977 78 1.000 0.170 0.501 4.242 0.188 0.077 22 495152 1897 1977 81 1.000 0.177 0.816 5.734 0.185 0.008 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.196 0.436 3.634 0.218 -0.009 STANDARD DEVIATION 29 0.000 0.030 0.285 0.959 0.038 0.052 MEDIAN (50TH QUANTILE) 92 1.000 0.198 0.497 3.459 0.219 -0.003 INTERQUARTILE RANGE 45 0.000 0.038 0.359 0.796 0.058 0.066 MINIMUM VALUE 56 1.000 0.144 -0.153 2.319 0.157 -0.111 LOWER HINGE (25TH QUANTILE) 65 1.000 0.176 0.246 3.090 0.185 -0.040 UPPER HINGE (75TH QUANTILE) 110 1.000 0.213 0.604 3.887 0.244 0.026 MAXIMUM VALUE 158 1.000 0.256 1.060 6.577 0.297 0.088 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.332 0.192 0.013 -0.721 3.487 -0.326 0.748 MINIMUM CORRELATION: -0.326 SERIES 495012 AND 495032 56 YEARS MAXIMUM CORRELATION: 0.748 SERIES 495021 AND 495022 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.456 0.250 0.354 SDEV 0.174 0.218 0.176 SERR 0.071 0.048 0.016 EPS 0.886 0.842 0.918 NSS 9.3 16.0 20.6 |======================== 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 1820 1977 158 0.994 0.142 0.294 3.953 0.167 -0.127 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.262 0.133 0.003 30 128 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.70 1.00 1.06 1.77 18.69 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 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 -0.126 -0.045 0.091 0.023 0.009 -0.029 -0.010 -0.061 0.028 -0.108 PACF -0.126 -0.062 0.078 0.044 0.027 -0.029 -0.022 -0.075 0.014 -0.107 95% C.L. 0.159 0.162 0.162 0.163 0.163 0.163 0.163 0.163 0.164 0.164 |------------------ 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 0.020 -0.127 |---------- 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 -0.008 -0.049 0.091 0.037 0.010 -0.030 -0.022 -0.061 0.008 -0.113 PACF -0.008 -0.049 0.090 0.036 0.019 -0.035 -0.028 -0.069 0.009 -0.115 95% C.L. 0.159 0.159 0.160 0.161 0.161 0.161 0.161 0.161 0.162 0.162 |----------------- 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 0.003 -0.008 |========================= 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 1820 1977 158 0.993 0.150 0.234 3.131 0.136 0.336 |------------ 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 0.334 0.100 0.126 0.074 0.018 -0.034 -0.054 -0.086 -0.066 -0.148 PACF 0.334 -0.013 0.108 0.000 -0.013 -0.053 -0.037 -0.064 -0.010 -0.126 95% C.L. 0.159 0.176 0.177 0.180 0.180 0.180 0.181 0.181 0.182 0.183 |------------------- 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 0.112 0.334 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.23 MINUTES