RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN025P.rwl.conv LOG FILE PROCESSED: FRAN025P.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: 482 1 Miraules Refuge LATEWOOD_PERCENT ABAL - 482 2 France silver fir, European fir 1720 4228-224 1831 1977 - 482 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 482011 1838 1977 140 2.114 0.790 3.413 22.481 0.218 0.477 2 482012 1846 1977 132 1.851 0.454 0.813 4.515 0.249 0.172 3 482021 1891 1977 87 2.155 0.474 -0.110 3.080 0.215 0.275 4 482022 1889 1977 89 2.382 0.529 0.211 3.232 0.214 0.226 5 482031 1849 1977 129 2.186 1.129 2.540 9.913 0.254 0.783 6 482032 1863 1977 115 1.903 0.482 0.112 2.194 0.271 0.196 7 482041 1831 1977 147 1.715 0.528 1.593 6.734 0.240 0.523 8 482042 1855 1977 123 1.890 0.462 0.914 5.367 0.237 0.307 9 482051 1883 1977 95 1.773 0.437 0.859 4.793 0.227 0.272 10 482052 1888 1977 90 2.075 0.597 0.618 3.066 0.254 0.334 11 482061 1836 1977 142 1.494 0.455 0.670 3.804 0.267 0.444 12 482062 1842 1977 136 1.515 0.365 0.749 4.087 0.239 0.239 13 482071 1879 1977 99 2.468 0.637 1.369 6.921 0.218 0.308 14 482072 1875 1977 103 2.670 0.628 0.478 3.123 0.245 0.157 15 482081 1853 1977 125 1.706 0.533 1.162 4.861 0.220 0.573 16 482082 1849 1977 129 1.837 0.476 0.379 3.116 0.230 0.439 17 482091 1846 1977 132 2.261 0.722 0.813 3.427 0.226 0.636 18 482092 1852 1977 126 2.051 0.499 0.558 3.413 0.199 0.496 19 482101 1838 1977 140 2.230 0.585 1.177 4.765 0.214 0.483 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 2.437 0.638 0.435 2.939 0.210 0.523 21 482111 1896 1977 82 2.454 0.592 0.410 2.569 0.213 0.357 22 482112 1889 1977 89 2.491 0.664 -0.268 2.387 0.202 0.569 23 482121 1861 1977 117 1.767 0.613 0.494 2.720 0.264 0.612 24 482122 1842 1977 136 1.783 0.621 -0.063 4.853 0.355 0.201 NUMBER OF SERIES READ IN: 24 FROM 1831 TO 1977 147 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 2.050 0.580 0.805 4.932 0.237 0.400 STANDARD DEVIATION 20 0.328 0.154 0.818 4.127 0.033 0.170 MEDIAN (50TH QUANTILE) 125 2.063 0.559 0.644 3.615 0.228 0.398 INTERQUARTILE RANGE 39 0.543 0.157 0.643 1.784 0.037 0.267 MINIMUM VALUE 82 1.494 0.365 -0.268 2.194 0.199 0.157 LOWER HINGE (25TH QUANTILE) 97 1.778 0.475 0.395 3.073 0.215 0.256 UPPER HINGE (75TH QUANTILE) 136 2.321 0.632 1.038 4.857 0.251 0.523 MAXIMUM VALUE 147 2.670 1.129 3.413 22.481 0.355 0.783 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.340 0.169 0.010 0.046 2.553 -0.108 0.752 MINIMUM CORRELATION: -0.108 SERIES 482112 AND 482121 89 YEARS MAXIMUM CORRELATION: 0.752 SERIES 482061 AND 482062 136 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.456 0.412 0.433 SDEV 0.164 0.179 0.145 SERR 0.015 0.012 0.009 EPS 0.945 0.943 0.948 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 2.091 0.474 1.683 7.561 0.182 0.476 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.219 0.089 0.364 48 99 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 1.01 1.00 1.07 2.08 13.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.00 0.85 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 126. 39. 82. 97. 136. 147. |----------- 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 0.473 0.364 0.440 0.334 0.382 0.406 0.377 0.315 0.319 0.223 PACF 0.473 0.181 0.284 0.038 0.183 0.128 0.109 -0.019 0.045 -0.117 95% C.L. 0.165 0.198 0.216 0.239 0.251 0.267 0.283 0.296 0.305 0.314 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.319 0.327 0.085 0.287 |================== 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 482011 1 5.50714159 0.22106314 0.00000000 1.95471597 2 482012 3 0.00000000 0.00000000 -0.00112865 1.92626762 3 482021 3 0.00000000 0.00000000 -0.00467340 2.36057210 4 482022 1 1.57626390 0.00450807 0.00000000 1.08624518 5 482031 1 2.51286697 0.02571639 0.00000000 1.46513867 6 482032 1 0.70407104 0.02002174 0.00000000 1.63024724 7 482041 1 2.01393795 0.08531027 0.00000000 1.56146801 8 482042 1 0.72759145 0.05614857 0.00000000 1.78751957 9 482051 3 0.00000000 0.00000000 -0.00580193 2.05144000 10 482052 3 0.00000000 0.00000000 -0.00950158 2.50698876 11 482061 1 1.02653599 0.06045816 0.00000000 1.37811387 12 482062 3 0.00000000 0.00000000 0.00029784 1.49489212 13 482071 3 0.00000000 0.00000000 -0.00555745 2.74595332 14 482072 1 2.13603163 0.59263378 0.00000000 2.64445472 15 482081 1 2.08599901 0.09386872 0.00000000 1.53675652 16 482082 3 0.00000000 0.00000000 0.00357553 1.60487771 17 482091 1 2.00198460 0.04427078 0.00000000 1.92690456 18 482092 1 1.20148551 0.02932983 0.00000000 1.73846698 19 482101 1 1.54647875 0.04553919 0.00000000 1.99368083 SERIES IDENT OPTION A B C D 20 482102 1 1.35688913 0.03950676 0.00000000 2.19386554 21 482111 3 0.00000000 0.00000000 0.01129461 1.98541999 22 482112 3 0.00000000 0.00000000 0.01488168 1.82111084 23 482121 1 1.85723245 0.02570408 0.00000000 1.18707395 24 482122 1 1.07002175 0.02100920 0.00000000 1.43394268 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.000 0.233 0.250 2.776 0.218 0.297 2 482012 1846 1977 132 1.000 0.243 0.750 4.438 0.247 0.164 3 482021 1891 1977 87 1.000 0.216 0.007 2.864 0.213 0.253 4 482022 1889 1977 89 1.000 0.215 0.346 3.673 0.212 0.148 5 482031 1849 1977 129 1.000 0.349 1.219 5.288 0.252 0.577 6 482032 1863 1977 115 1.000 0.238 0.150 2.581 0.268 0.064 7 482041 1831 1977 147 1.000 0.226 0.619 3.706 0.238 0.121 8 482042 1855 1977 123 1.000 0.224 0.297 2.879 0.235 0.167 9 482051 1883 1977 95 1.000 0.229 0.757 4.108 0.225 0.175 10 482052 1888 1977 90 0.999 0.255 0.514 3.154 0.252 0.218 11 482061 1836 1977 142 1.000 0.283 1.229 6.660 0.265 0.327 12 482062 1842 1977 136 1.000 0.241 0.748 4.084 0.237 0.237 13 482071 1879 1977 99 1.000 0.248 1.282 6.015 0.216 0.274 14 482072 1875 1977 103 1.000 0.231 0.496 3.261 0.241 0.134 15 482081 1853 1977 125 1.000 0.230 0.490 4.484 0.218 0.291 16 482082 1849 1977 129 1.000 0.249 0.259 2.909 0.228 0.393 17 482091 1846 1977 132 1.000 0.255 1.065 5.847 0.224 0.445 18 482092 1852 1977 126 1.000 0.196 0.247 2.961 0.198 0.199 19 482101 1838 1977 140 1.000 0.207 0.783 4.195 0.212 0.238 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.232 0.494 3.598 0.208 0.406 21 482111 1896 1977 82 0.999 0.214 0.756 4.512 0.210 0.172 22 482112 1889 1977 89 0.998 0.222 0.052 2.547 0.199 0.362 23 482121 1861 1977 117 1.000 0.241 0.263 3.589 0.260 0.083 24 482122 1842 1977 136 1.000 0.337 0.340 7.454 0.352 0.018 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.242 0.559 4.066 0.235 0.240 STANDARD DEVIATION 20 0.001 0.036 0.370 1.335 0.032 0.131 MEDIAN (50TH QUANTILE) 125 1.000 0.232 0.495 3.690 0.226 0.228 INTERQUARTILE RANGE 39 0.000 0.026 0.495 1.563 0.037 0.156 MINIMUM VALUE 82 0.998 0.196 0.007 2.547 0.198 0.018 LOWER HINGE (25TH QUANTILE) 97 1.000 0.223 0.261 2.935 0.212 0.156 UPPER HINGE (75TH QUANTILE) 136 1.000 0.249 0.756 4.498 0.249 0.312 MAXIMUM VALUE 147 1.000 0.349 1.282 7.454 0.352 0.577 |------------------------ 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 482011 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 482012 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 482021 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 482022 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 482031 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 482032 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 482041 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 482042 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 482051 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 482052 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 482061 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 482062 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 482071 -67 66 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 482072 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 482081 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 482082 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 482091 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 482092 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 482101 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 482102 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 482111 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 482112 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 482121 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 482122 -67 91 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 482011 1838 1977 140 0.999 0.225 0.289 2.956 0.218 0.234 2 482012 1846 1977 132 0.999 0.232 0.584 4.051 0.247 0.093 3 482021 1891 1977 87 0.999 0.208 -0.005 2.899 0.213 0.206 4 482022 1889 1977 89 0.999 0.210 0.261 3.580 0.212 0.112 5 482031 1849 1977 129 0.994 0.293 1.111 5.228 0.252 0.394 6 482032 1863 1977 115 0.999 0.235 0.185 2.571 0.268 0.037 7 482041 1831 1977 147 1.000 0.218 0.549 3.300 0.238 0.062 8 482042 1855 1977 123 1.000 0.223 0.292 2.860 0.235 0.159 9 482051 1883 1977 95 0.999 0.224 0.858 4.473 0.225 0.140 10 482052 1888 1977 90 0.999 0.226 0.218 3.191 0.252 0.031 11 482061 1836 1977 142 0.998 0.246 0.361 3.404 0.266 0.136 12 482062 1842 1977 136 0.998 0.215 0.472 3.173 0.237 0.092 13 482071 1879 1977 99 0.997 0.227 1.235 6.235 0.215 0.173 14 482072 1875 1977 103 0.999 0.222 0.360 3.054 0.241 0.071 15 482081 1853 1977 125 0.999 0.208 0.106 3.468 0.219 0.164 16 482082 1849 1977 129 0.997 0.214 0.195 3.205 0.228 0.172 17 482091 1846 1977 132 0.998 0.213 0.240 3.310 0.224 0.223 18 482092 1852 1977 126 0.999 0.183 0.157 3.095 0.197 0.092 19 482101 1838 1977 140 0.999 0.191 0.737 4.267 0.212 0.120 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.998 0.197 0.052 2.661 0.208 0.197 21 482111 1896 1977 82 0.999 0.199 1.159 7.023 0.210 0.052 22 482112 1889 1977 89 0.998 0.194 0.329 2.820 0.198 0.173 23 482121 1861 1977 117 1.000 0.237 0.215 3.662 0.260 0.070 24 482122 1842 1977 136 0.999 0.341 0.789 9.893 0.352 -0.032 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.999 0.224 0.448 3.932 0.234 0.132 STANDARD DEVIATION 20 0.001 0.033 0.356 1.681 0.032 0.087 MEDIAN (50TH QUANTILE) 125 0.999 0.220 0.311 3.305 0.226 0.128 INTERQUARTILE RANGE 39 0.001 0.022 0.456 1.155 0.037 0.103 MINIMUM VALUE 82 0.994 0.183 -0.005 2.571 0.197 -0.032 LOWER HINGE (25TH QUANTILE) 97 0.998 0.208 0.205 3.005 0.212 0.071 UPPER HINGE (75TH QUANTILE) 136 0.999 0.230 0.660 4.159 0.250 0.173 MAXIMUM VALUE 147 1.000 0.341 1.235 9.893 0.352 0.394 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.395 0.110 0.007 0.172 3.674 0.082 0.752 MINIMUM CORRELATION: 0.082 SERIES 482022 AND 482052 89 YEARS MAXIMUM CORRELATION: 0.752 SERIES 482081 AND 482082 125 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.453 0.458 0.459 SDEV 0.138 0.140 0.126 SERR 0.013 0.009 0.008 EPS 0.945 0.953 0.953 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.990 0.147 -0.157 2.788 0.182 -0.048 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.299 0.105 0.057 52 95 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.81 1.01 1.08 1.89 16.80 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.87 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 -0.047 -0.069 -0.077 -0.149 0.052 -0.083 0.053 -0.030 0.116 0.048 PACF -0.047 -0.071 -0.084 -0.164 0.022 -0.115 0.022 -0.065 0.119 0.029 95% C.L. 0.165 0.165 0.166 0.167 0.171 0.171 0.172 0.173 0.173 0.175 |------------------ 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 0 0.000 |======================= 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 -0.026 -0.017 -0.076 -0.165 0.063 -0.158 0.060 0.027 0.140 0.049 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 -0.026 2 -0.027 -0.018 3 -0.028 -0.020 -0.077 4 -0.041 -0.023 -0.082 -0.171 5 -0.032 -0.019 -0.080 -0.168 0.051 6 -0.024 -0.048 -0.094 -0.172 0.045 -0.173 7 -0.019 -0.050 -0.089 -0.169 0.046 -0.173 0.029 8 -0.019 -0.050 -0.089 -0.169 0.046 -0.173 0.029 -0.001 9 -0.019 -0.054 -0.064 -0.176 0.071 -0.160 0.036 0.002 0.145 10 -0.019 -0.054 -0.065 -0.175 0.071 -0.159 0.036 0.002 0.145 0.005 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) 1060.26 1062.16 1064.11 1065.24 1062.90 1064.52 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1062.03 1063.91 1065.91 1064.79 1066.79 SELECTED AUTOREGRESSION ORDER: 0 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 482011 0 0.056 2 482012 0 0.009 3 482021 0 0.044 4 482022 0 0.013 5 482031 0 0.159 6 482032 0 0.001 7 482041 0 0.004 8 482042 0 0.026 9 482051 0 0.020 10 482052 0 0.001 11 482061 0 0.018 12 482062 0 0.008 13 482071 0 0.031 14 482072 0 0.005 15 482081 0 0.027 16 482082 0 0.031 17 482091 0 0.050 18 482092 0 0.009 19 482101 0 0.014 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 482102 0 0.040 21 482111 0 0.003 22 482112 0 0.032 23 482121 0 0.005 24 482122 0 0.001 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.025 STANDARD DEVIATION 0 0.033 MEDIAN 0 0.016 INTERQUARTILE RANGE 0 0.026 MINIMUM VALUE 0 0.001 LOWER HINGE 0 0.005 UPPER HINGE 0 0.031 MAXIMUM VALUE 0 0.159 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.000 0.225 0.289 2.956 0.217 0.234 2 482012 1846 1977 132 1.000 0.232 0.584 4.051 0.247 0.093 3 482021 1891 1977 87 1.000 0.208 -0.005 2.899 0.212 0.206 4 482022 1889 1977 89 1.000 0.210 0.261 3.580 0.212 0.112 5 482031 1849 1977 129 1.000 0.293 1.111 5.228 0.251 0.394 6 482032 1863 1977 115 1.000 0.235 0.185 2.571 0.268 0.037 7 482041 1831 1977 147 1.000 0.218 0.549 3.300 0.238 0.062 8 482042 1855 1977 123 1.000 0.223 0.292 2.860 0.234 0.159 9 482051 1883 1977 95 1.000 0.224 0.858 4.473 0.225 0.140 10 482052 1888 1977 90 1.000 0.226 0.218 3.191 0.252 0.031 11 482061 1836 1977 142 1.000 0.246 0.361 3.404 0.265 0.136 12 482062 1842 1977 136 1.000 0.215 0.472 3.173 0.236 0.092 13 482071 1879 1977 99 1.000 0.227 1.235 6.235 0.215 0.173 14 482072 1875 1977 103 1.000 0.222 0.360 3.054 0.241 0.071 15 482081 1853 1977 125 1.000 0.208 0.106 3.468 0.218 0.164 16 482082 1849 1977 129 1.000 0.214 0.195 3.205 0.227 0.172 17 482091 1846 1977 132 1.000 0.213 0.240 3.310 0.223 0.223 18 482092 1852 1977 126 1.000 0.183 0.157 3.095 0.197 0.092 19 482101 1838 1977 140 1.000 0.191 0.737 4.267 0.212 0.120 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.197 0.052 2.661 0.208 0.197 21 482111 1896 1977 82 1.000 0.199 1.159 7.023 0.210 0.052 22 482112 1889 1977 89 1.000 0.194 0.329 2.820 0.198 0.173 23 482121 1861 1977 117 1.000 0.237 0.215 3.662 0.260 0.070 24 482122 1842 1977 136 1.000 0.341 0.789 9.893 0.352 -0.032 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.224 0.448 3.932 0.234 0.132 STANDARD DEVIATION 20 0.000 0.033 0.356 1.681 0.032 0.087 MEDIAN (50TH QUANTILE) 125 1.000 0.220 0.311 3.305 0.226 0.128 INTERQUARTILE RANGE 39 0.000 0.022 0.456 1.155 0.037 0.103 MINIMUM VALUE 82 1.000 0.183 -0.005 2.571 0.197 -0.032 LOWER HINGE (25TH QUANTILE) 97 1.000 0.208 0.205 3.005 0.212 0.071 UPPER HINGE (75TH QUANTILE) 136 1.000 0.230 0.660 4.159 0.249 0.173 MAXIMUM VALUE 147 1.000 0.341 1.235 9.893 0.352 0.394 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.395 0.110 0.007 0.172 3.674 0.082 0.752 MINIMUM CORRELATION: 0.082 SERIES 482022 AND 482052 89 YEARS MAXIMUM CORRELATION: 0.752 SERIES 482081 AND 482082 125 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.453 0.458 0.459 SDEV 0.138 0.140 0.126 SERR 0.013 0.009 0.008 EPS 0.945 0.953 0.953 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.992 0.147 -0.158 2.792 0.182 -0.048 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.303 0.106 0.055 52 95 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.79 1.00 1.08 1.87 16.73 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.87 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 -0.047 -0.069 -0.077 -0.149 0.053 -0.084 0.053 -0.030 0.116 0.049 PACF -0.047 -0.071 -0.084 -0.165 0.022 -0.115 0.022 -0.065 0.119 0.029 95% C.L. 0.165 0.165 0.166 0.167 0.171 0.171 0.172 0.173 0.173 0.175 |------------------ 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 |========================= 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 1831 1977 147 0.992 0.147 -0.158 2.792 0.182 -0.048 |------------ 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 -0.047 -0.069 -0.077 -0.149 0.053 -0.084 0.053 -0.030 0.116 0.049 PACF -0.047 -0.071 -0.084 -0.165 0.022 -0.115 0.022 -0.065 0.119 0.029 95% C.L. 0.165 0.165 0.166 0.167 0.171 0.171 0.172 0.173 0.173 0.175 |------------------- 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 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES