RUN: AK001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: AK010N.rwl.conv LOG FILE PROCESSED: AK010N.rwl.conv_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -999 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: 737 1 Eureka Summit DENSITY_MINIMUM PCGL - 737 2 United States of America White Spruce 960 6150-14720 1654 1983 - 737 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 737011 MISSING VALUES FOUND: 5 IN 1 GAPS / 1745 1749 / -------------------------------------------------------------------- 3 737021 MISSING VALUES FOUND: 5 IN 1 GAPS / 1906 1910 / -------------------------------------------------------------------- 5 737030 MISSING VALUES FOUND: 5 IN 1 GAPS / 1898 1902 / -------------------------------------------------------------------- 6 737041 MISSING VALUES FOUND: 10 IN 2 GAPS / 1773 1777 / 1799 1803 / -------------------------------------------------------------------- 7 737042 MISSING VALUES FOUND: 4 IN 1 GAPS / 1699 1702 / -------------------------------------------------------------------- 8 737051 MISSING VALUES FOUND: 21 IN 3 GAPS / 1805 1814 / 1905 1909 / 1945 1950 / -------------------------------------------------------------------- 9 737052 MISSING VALUES FOUND: 5 IN 1 GAPS / 1920 1924 / -------------------------------------------------------------------- 11 737071 MISSING VALUES FOUND: 5 IN 1 GAPS / 1978 1982 / -------------------------------------------------------------------- 14 737082 MISSING VALUES FOUND: 5 IN 1 GAPS / 1755 1759 / -------------------------------------------------------------------- 15 737091 MISSING VALUES FOUND: 5 IN 1 GAPS / 1972 1976 / -------------------------------------------------------------------- 16 737092 MISSING VALUES FOUND: 5 IN 1 GAPS / 1765 1769 / -------------------------------------------------------------------- 17 737101 MISSING VALUES FOUND: 12 IN 2 GAPS / 1863 1867 / 1940 1946 / -------------------------------------------------------------------- 19 737111 MISSING VALUES FOUND: 18 IN 3 GAPS / 1834 1840 / 1872 1876 / 1898 1903 / -------------------------------------------------------------------- 22 737122 MISSING VALUES FOUND: 10 IN 2 GAPS / 1797 1801 / 1849 1853 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 737011 1654 1983 330 0.362 0.045 0.669 3.110 0.063 0.752 2 737012 1696 1961 266 0.352 0.058 0.930 3.743 0.081 0.784 3 737021 1745 1983 239 0.252 0.025 0.860 3.854 0.059 0.685 4 737022 1759 1983 225 0.287 0.035 1.292 5.744 0.057 0.796 5 737030 1863 1983 121 0.303 0.019 0.130 2.772 0.063 0.197 6 737041 1684 1983 300 0.271 0.024 1.066 6.526 0.047 0.741 7 737042 1654 1983 330 0.311 0.038 1.281 5.276 0.047 0.842 8 737051 1801 1983 183 0.300 0.021 0.539 2.969 0.048 0.561 9 737052 1801 1983 183 0.299 0.030 1.290 4.713 0.056 0.729 10 737060 1876 1983 108 0.261 0.026 0.652 3.483 0.059 0.667 11 737071 1859 1983 125 0.317 0.025 -0.163 2.650 0.056 0.588 12 737072 1835 1983 149 0.324 0.024 0.694 3.008 0.045 0.716 13 737081 1735 1983 249 0.319 0.047 2.294 11.166 0.050 0.877 14 737082 1725 1983 259 0.326 0.039 0.820 3.823 0.051 0.843 15 737091 1750 1983 234 0.287 0.027 0.403 2.888 0.055 0.727 16 737092 1762 1983 222 0.307 0.021 0.109 2.981 0.047 0.594 17 737101 1851 1983 133 0.319 0.028 1.297 6.207 0.064 0.481 18 737102 1788 1983 196 0.348 0.033 0.149 4.124 0.053 0.715 19 737111 1792 1983 192 0.271 0.025 0.006 4.519 0.057 0.635 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 737112 1775 1983 209 0.267 0.019 0.823 3.468 0.045 0.586 21 737121 1713 1983 271 0.330 0.027 -0.017 3.139 0.045 0.719 22 737122 1725 1983 259 0.355 0.030 0.556 3.311 0.050 0.680 NUMBER OF SERIES READ IN: 22 FROM 1654 TO 1983 330 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 212 0.308 0.030 0.713 4.249 0.055 0.678 STANDARD DEVIATION 65 0.032 0.010 0.579 1.915 0.009 0.146 MEDIAN (50TH QUANTILE) 221 0.309 0.027 0.682 3.613 0.054 0.716 INTERQUARTILE RANGE 92 0.039 0.011 0.917 1.704 0.011 0.157 MINIMUM VALUE 108 0.252 0.019 -0.163 2.650 0.045 0.197 LOWER HINGE (25TH QUANTILE) 162 0.287 0.024 0.149 3.008 0.047 0.594 UPPER HINGE (75TH QUANTILE) 254 0.326 0.035 1.066 4.713 0.059 0.752 MAXIMUM VALUE 326 0.362 0.058 2.294 11.166 0.081 0.877 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.228 0.276 0.018 -0.277 2.246 -0.496 0.753 MINIMUM CORRELATION: -0.496 SERIES 737082 AND 737091 234 YEARS MAXIMUM CORRELATION: 0.753 SERIES 737021 AND 737052 183 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.95 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1679. 1710. 1735. 1760. 1785. 1810. 1835. 1860. 1885. 1910. CORR 1. 3. 6. 28. 55. 78. 136. 153. 190. 231. RBAR -0.204 0.025 0.240 0.191 0.184 0.172 0.254 0.185 0.256 0.214 SDEV 0.000 0.234 0.292 0.209 0.229 0.203 0.218 0.270 0.187 0.250 SERR 0.000 0.135 0.119 0.040 0.031 0.023 0.019 0.022 0.014 0.016 EPS -0.768 0.106 0.699 0.716 0.757 0.771 0.858 0.818 0.882 0.857 NSS 2.6 4.6 7.4 10.7 13.8 16.2 17.7 19.8 21.6 22.0 YEAR 1935. CORR 231. RBAR 0.169 SDEV 0.273 SERR 0.018 EPS 0.818 NSS 22.0 |======================== 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 1654 1983 330 0.317 0.029 1.436 4.681 0.034 0.870 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.489 0.268 -0.040 48 282 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.44 1.00 1.06 1.50 4.44 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.13 0.55 0.87 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 224. 76. 108. 183. 259. 330. |----------- 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 0.867 0.835 0.820 0.806 0.778 0.748 0.746 0.718 0.688 0.663 PACF 0.867 0.334 0.217 0.139 0.022 -0.022 0.092 -0.029 -0.048 -0.030 95% C.L. 0.110 0.174 0.217 0.252 0.282 0.307 0.328 0.348 0.365 0.381 |------------------ 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 0.818 0.384 0.194 0.205 0.171 |================== 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 737011 1 0.10265546 0.02905305 0.00000000 0.35117099 2 737012 3 0.00000000 0.00000000 0.00011671 0.33611122 3 737021 1 0.04995326 0.03428907 0.00000000 0.24554349 4 737022 3 0.00000000 0.00000000 0.00029279 0.25429207 5 737030 3 0.00000000 0.00000000 0.00014814 0.29307312 6 737041 3 0.00000000 0.00000000 0.00006344 0.26202509 7 737042 1 0.08492519 0.02487498 0.00000000 0.30121395 8 737051 3 0.00000000 0.00000000 0.00004314 0.29789224 9 737052 3 0.00000000 0.00000000 0.00011992 0.28746945 10 737060 3 0.00000000 0.00000000 0.00016296 0.25232258 11 737071 3 0.00000000 0.00000000 -0.00025979 0.33227098 12 737072 3 0.00000000 0.00000000 -0.00010009 0.33193633 13 737081 3 0.00000000 0.00000000 0.00033107 0.27741158 14 737082 3 0.00000000 0.00000000 0.00025549 0.29278585 15 737091 3 0.00000000 0.00000000 -0.00011593 0.30033621 16 737092 3 0.00000000 0.00000000 -0.00004314 0.31165543 17 737101 3 0.00000000 0.00000000 0.00043710 0.28814903 18 737102 3 0.00000000 0.00000000 0.00030854 0.31756830 19 737111 3 0.00000000 0.00000000 0.00025068 0.24740790 SERIES IDENT OPTION A B C D 20 737112 3 0.00000000 0.00000000 0.00014710 0.25149199 21 737121 3 0.00000000 0.00000000 0.00019306 0.30359575 22 737122 3 0.00000000 0.00000000 0.00022425 0.32464507 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 737011 1654 1983 330 1.000 0.111 1.030 4.696 0.064 0.682 2 737012 1696 1961 266 1.000 0.162 0.733 3.477 0.081 0.776 3 737021 1745 1983 239 1.000 0.089 1.441 6.246 0.059 0.615 4 737022 1759 1983 225 1.000 0.102 0.612 4.395 0.057 0.711 5 737030 1863 1983 121 1.000 0.062 0.319 2.771 0.061 0.215 6 737041 1684 1983 300 1.000 0.082 0.510 5.287 0.047 0.718 7 737042 1654 1983 330 1.000 0.106 1.030 4.259 0.047 0.799 8 737051 1801 1983 183 1.000 0.072 0.514 2.876 0.046 0.628 9 737052 1801 1983 183 1.000 0.097 0.971 4.002 0.055 0.708 10 737060 1876 1983 108 1.000 0.096 0.658 3.616 0.058 0.647 11 737071 1859 1983 125 1.000 0.072 -0.437 3.274 0.055 0.515 12 737072 1835 1983 149 1.000 0.072 0.554 2.919 0.045 0.697 13 737081 1735 1983 249 1.000 0.121 1.421 8.615 0.050 0.824 14 737082 1725 1983 259 1.000 0.103 0.311 3.109 0.051 0.775 15 737091 1750 1983 234 1.000 0.088 0.413 3.075 0.055 0.681 16 737092 1762 1983 222 1.000 0.067 0.119 3.098 0.046 0.579 17 737101 1851 1983 133 1.000 0.068 1.070 5.619 0.061 0.246 18 737102 1788 1983 196 1.000 0.080 0.053 4.099 0.053 0.615 19 737111 1792 1983 192 1.000 0.075 -0.348 5.410 0.056 0.472 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 737112 1775 1983 209 1.000 0.061 0.297 3.167 0.045 0.473 21 737121 1713 1983 271 1.000 0.068 0.071 3.580 0.045 0.607 22 737122 1725 1983 259 1.000 0.073 0.206 2.865 0.050 0.585 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 217 1.000 0.088 0.525 4.112 0.054 0.617 STANDARD DEVIATION 64 0.000 0.024 0.500 1.424 0.008 0.158 MEDIAN (50TH QUANTILE) 223 1.000 0.081 0.512 3.598 0.054 0.638 INTERQUARTILE RANGE 76 0.000 0.030 0.765 1.597 0.011 0.133 MINIMUM VALUE 108 1.000 0.061 -0.437 2.771 0.045 0.215 LOWER HINGE (25TH QUANTILE) 183 1.000 0.072 0.206 3.098 0.047 0.579 UPPER HINGE (75TH QUANTILE) 259 1.000 0.102 0.971 4.696 0.058 0.711 MAXIMUM VALUE 330 1.000 0.162 1.441 8.615 0.081 0.824 |------------------------ 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 737011 -67 221 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 737012 -67 178 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 737021 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 737022 -67 150 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 737030 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 737041 -67 201 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 737042 -67 221 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 737051 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 737052 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 737060 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 737071 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 737072 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 737081 -67 166 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 737082 -67 173 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 737091 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 737092 -67 148 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 737101 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 737102 -67 131 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 737111 -67 128 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 737112 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 737121 -67 181 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 737122 -67 173 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 737011 1654 1983 330 1.000 0.095 0.938 4.183 0.064 0.579 2 737012 1696 1961 266 0.998 0.125 0.887 3.667 0.081 0.640 3 737021 1745 1983 239 0.999 0.063 0.165 3.234 0.059 0.275 4 737022 1759 1983 225 1.000 0.082 0.764 5.598 0.057 0.574 5 737030 1863 1983 121 1.000 0.058 0.302 3.076 0.061 0.110 6 737041 1684 1983 300 1.000 0.054 0.162 5.075 0.047 0.369 7 737042 1654 1983 330 1.000 0.084 1.493 7.311 0.048 0.700 8 737051 1801 1983 183 1.000 0.054 0.051 2.947 0.047 0.353 9 737052 1801 1983 183 0.999 0.061 0.464 3.485 0.055 0.325 10 737060 1876 1983 108 1.000 0.087 1.005 4.215 0.058 0.561 11 737071 1859 1983 125 1.000 0.054 -0.175 2.813 0.055 0.205 12 737072 1835 1983 149 1.000 0.058 0.152 3.021 0.045 0.544 13 737081 1735 1983 249 0.999 0.085 1.734 11.291 0.050 0.659 14 737082 1725 1983 259 0.999 0.076 0.299 3.181 0.051 0.616 15 737091 1750 1983 234 1.000 0.070 0.109 3.432 0.055 0.507 16 737092 1762 1983 222 1.000 0.061 -0.038 3.247 0.046 0.499 17 737101 1851 1983 133 1.000 0.059 0.930 5.094 0.061 0.023 18 737102 1788 1983 196 1.000 0.069 -0.266 4.078 0.053 0.499 19 737111 1792 1983 192 1.000 0.068 -0.559 6.212 0.056 0.372 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 737112 1775 1983 209 1.000 0.056 0.160 3.412 0.045 0.389 21 737121 1713 1983 271 1.000 0.062 0.000 3.723 0.045 0.541 22 737122 1725 1983 259 1.000 0.057 0.162 2.696 0.050 0.358 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 217 1.000 0.070 0.397 4.318 0.054 0.441 STANDARD DEVIATION 64 0.000 0.017 0.571 1.961 0.008 0.179 MEDIAN (50TH QUANTILE) 223 1.000 0.063 0.163 3.576 0.054 0.499 INTERQUARTILE RANGE 76 0.000 0.024 0.836 1.895 0.011 0.221 MINIMUM VALUE 108 0.998 0.054 -0.559 2.696 0.045 0.023 LOWER HINGE (25TH QUANTILE) 183 1.000 0.058 0.051 3.181 0.047 0.353 UPPER HINGE (75TH QUANTILE) 259 1.000 0.082 0.887 5.075 0.058 0.574 MAXIMUM VALUE 330 1.000 0.125 1.734 11.291 0.081 0.700 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.211 0.114 0.008 -0.156 2.931 -0.084 0.501 MINIMUM CORRELATION: -0.084 SERIES 737012 AND 737092 200 YEARS MAXIMUM CORRELATION: 0.501 SERIES 737081 AND 737082 249 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.95 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1679. 1710. 1735. 1760. 1785. 1810. 1835. 1860. 1885. 1910. CORR 1. 3. 6. 28. 55. 78. 136. 153. 190. 231. RBAR -0.259 -0.030 0.173 0.212 0.165 0.217 0.258 0.197 0.237 0.211 SDEV 0.000 0.246 0.273 0.208 0.211 0.179 0.196 0.238 0.167 0.184 SERR 0.000 0.142 0.111 0.039 0.028 0.020 0.017 0.019 0.012 0.012 EPS -1.114 -0.156 0.606 0.741 0.732 0.818 0.860 0.829 0.870 0.855 NSS 2.6 4.6 7.4 10.7 13.8 16.2 17.7 19.8 21.6 22.0 YEAR 1935. CORR 231. RBAR 0.227 SDEV 0.181 SERR 0.012 EPS 0.866 NSS 22.0 |======================== 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 1654 1983 330 0.996 0.038 0.198 3.009 0.033 0.383 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.272 0.194 -0.130 88 242 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.40 1.04 1.00 1.13 2.17 24.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.13 0.69 0.87 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 0.382 0.392 0.382 0.349 0.272 0.128 0.168 0.125 0.082 0.073 PACF 0.382 0.288 0.211 0.130 0.013 -0.156 -0.006 0.001 -0.003 0.028 95% C.L. 0.110 0.125 0.139 0.151 0.161 0.166 0.168 0.170 0.171 0.171 |------------------ 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 4 0.270 0.183 0.200 0.185 0.136 |======================= 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 0.370 0.383 0.379 0.320 0.282 0.119 0.166 0.066 0.072 0.046 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 0.370 2 0.264 0.285 3 0.202 0.228 0.217 4 0.180 0.205 0.197 0.101 5 0.176 0.196 0.188 0.093 0.046 6 0.183 0.210 0.217 0.123 0.073 -0.156 7 0.183 0.210 0.217 0.124 0.074 -0.155 -0.002 8 0.182 0.198 0.223 0.134 0.091 -0.139 0.012 -0.080 9 0.184 0.197 0.225 0.132 0.089 -0.142 0.009 -0.083 0.016 10 0.183 0.199 0.225 0.134 0.088 -0.144 0.006 -0.086 0.013 0.013 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) 1547.39 1500.91 1474.95 1460.98 1459.59 1460.89 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1454.78 1456.78 1456.65 1458.57 1460.51 SELECTED AUTOREGRESSION ORDER: 4 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 0.180 0.205 0.197 0.101 R-SQUARED DUE TO POOLED AUTOREGRESSION: 25.20 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 133.68 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 4) PROCESS OUT TO ORDER 50: 1.0000 0.180 0.237 0.277 0.235 0.164 0.156 0.136 0.112 0.095 0.0827 0.070 0.060 0.051 0.044 0.037 0.032 0.027 0.023 0.020 0.0168 0.014 0.012 0.010 0.009 0.008 0.006 0.006 0.005 0.004 0.0034 0.003 0.003 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.0007 0.001 0.001 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 737011 4 0.400 0.386 0.239 0.104 0.007 2 737012 4 0.447 0.507 0.058 0.148 0.053 3 737021 4 0.170 0.153 0.156 0.147 0.144 4 737022 4 0.386 0.401 0.254 0.076 -0.028 5 737030 4 0.032 0.097 0.118 0.002 0.058 6 737041 4 0.157 0.327 0.096 -0.022 0.095 7 737042 4 0.514 0.562 0.122 0.115 -0.024 8 737051 4 0.155 0.292 0.106 0.035 0.092 9 737052 4 0.172 0.283 0.171 -0.074 0.064 10 737060 4 0.342 0.463 0.192 -0.048 0.043 11 737071 4 0.112 0.171 -0.017 0.227 0.095 12 737072 4 0.396 0.314 0.180 0.195 0.074 13 737081 4 0.534 0.392 0.414 -0.001 -0.008 14 737082 4 0.478 0.359 0.334 0.061 0.035 15 737091 4 0.299 0.385 0.136 0.123 0.016 16 737092 4 0.323 0.326 0.188 0.173 0.011 17 737101 4 0.023 0.029 -0.049 0.129 0.008 18 737102 4 0.334 0.359 0.153 0.175 0.013 19 737111 4 0.184 0.280 0.112 0.118 0.071 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 737112 4 0.203 0.311 0.097 0.129 0.047 21 737121 4 0.373 0.341 0.169 0.169 0.065 22 737122 4 0.244 0.215 0.301 0.168 -0.095 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 4 0.285 0.316 0.160 0.098 0.038 STANDARD DEVIATION 0 0.150 0.127 0.106 0.083 0.052 MEDIAN 4 0.311 0.327 0.154 0.121 0.045 INTERQUARTILE RANGE 0 0.226 0.105 0.086 0.133 0.063 MINIMUM VALUE 4 0.023 0.029 -0.049 -0.074 -0.095 LOWER HINGE 4 0.170 0.280 0.106 0.035 0.008 UPPER HINGE 4 0.396 0.386 0.192 0.168 0.071 MAXIMUM VALUE 4 0.534 0.562 0.414 0.227 0.144 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 737011 1654 1983 330 1.000 0.074 0.794 4.689 0.077 0.000 2 737012 1696 1961 266 1.000 0.093 0.404 3.284 0.104 -0.005 3 737021 1745 1983 239 1.000 0.058 -0.191 3.442 0.065 -0.012 4 737022 1759 1983 225 1.000 0.064 0.761 6.629 0.070 0.001 5 737030 1863 1983 121 1.000 0.057 0.425 3.251 0.064 -0.003 6 737041 1684 1983 300 1.000 0.050 0.195 5.097 0.056 0.005 7 737042 1654 1983 330 1.000 0.058 1.028 6.592 0.063 -0.002 8 737051 1801 1983 183 1.000 0.049 0.147 3.086 0.054 0.004 9 737052 1801 1983 183 1.000 0.057 0.548 3.745 0.064 -0.012 10 737060 1876 1983 108 1.000 0.070 0.927 4.696 0.074 -0.001 11 737071 1859 1983 125 1.000 0.051 -0.193 2.519 0.059 -0.001 12 737072 1835 1983 149 1.000 0.045 0.083 2.482 0.053 0.008 13 737081 1735 1983 249 1.000 0.058 1.459 12.122 0.061 0.002 14 737082 1725 1983 259 1.000 0.055 0.226 3.460 0.061 0.000 15 737091 1750 1983 234 1.000 0.059 0.281 3.597 0.066 0.000 16 737092 1762 1983 222 1.000 0.050 -0.172 3.503 0.055 -0.001 17 737101 1851 1983 133 1.000 0.058 0.953 5.332 0.062 0.000 18 737102 1788 1983 196 1.000 0.056 -0.522 3.937 0.063 -0.022 19 737111 1792 1983 192 1.000 0.062 -1.010 10.467 0.065 0.003 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 737112 1775 1983 209 1.000 0.050 0.176 3.260 0.054 0.004 21 737121 1713 1983 271 1.000 0.050 0.145 3.363 0.055 -0.001 22 737122 1725 1983 259 1.000 0.050 0.241 3.551 0.055 0.005 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 217 1.000 0.058 0.305 4.641 0.064 -0.001 STANDARD DEVIATION 64 0.000 0.010 0.555 2.439 0.011 0.007 MEDIAN (50TH QUANTILE) 223 1.000 0.057 0.234 3.574 0.062 0.000 INTERQUARTILE RANGE 76 0.000 0.008 0.678 1.814 0.010 0.005 MINIMUM VALUE 108 1.000 0.045 -1.010 2.482 0.053 -0.022 LOWER HINGE (25TH QUANTILE) 183 1.000 0.050 0.083 3.284 0.055 -0.002 UPPER HINGE (75TH QUANTILE) 259 1.000 0.059 0.761 5.097 0.065 0.003 MAXIMUM VALUE 330 1.000 0.093 1.459 12.122 0.104 0.008 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.227 0.109 0.007 -0.279 3.229 -0.107 0.505 MINIMUM CORRELATION: -0.107 SERIES 737060 AND 737111 108 YEARS MAXIMUM CORRELATION: 0.505 SERIES 737121 AND 737122 259 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.95 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1679. 1710. 1735. 1760. 1785. 1810. 1835. 1860. 1885. 1910. CORR 1. 3. 6. 28. 55. 78. 136. 153. 190. 231. RBAR -0.016 0.000 0.036 0.238 0.187 0.168 0.251 0.237 0.204 0.209 SDEV 0.000 0.137 0.158 0.189 0.144 0.170 0.164 0.144 0.154 0.150 SERR 0.000 0.079 0.064 0.036 0.019 0.019 0.014 0.012 0.011 0.010 EPS -0.041 -0.002 0.218 0.769 0.761 0.765 0.855 0.860 0.847 0.853 NSS 2.6 4.6 7.4 10.7 13.8 16.2 17.7 19.8 21.6 22.0 YEAR 1935. CORR 231. RBAR 0.221 SDEV 0.150 SERR 0.010 EPS 0.862 NSS 22.0 |======================== 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 1654 1983 330 0.999 0.033 0.273 3.156 0.040 -0.144 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.212 0.149 -0.100 95 235 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.55 1.00 1.09 1.65 28.21 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.12 0.72 0.88 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 -0.143 -0.014 0.027 0.052 0.063 -0.107 0.036 0.027 0.004 0.022 PACF -0.143 -0.036 0.020 0.060 0.083 -0.087 0.007 0.023 0.010 0.032 95% C.L. 0.110 0.112 0.112 0.112 0.113 0.113 0.114 0.115 0.115 0.115 |------------------ 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 0.022 -0.144 |---------- 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 -0.004 0.003 0.004 0.008 0.067 -0.098 0.026 0.030 0.013 0.022 PACF -0.004 0.003 0.004 0.008 0.067 -0.098 0.026 0.030 0.012 0.019 95% C.L. 0.110 0.110 0.110 0.110 0.110 0.111 0.112 0.112 0.112 0.112 |----------------- 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 4 0.005 -0.004 0.003 0.004 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 1654 1983 330 0.999 0.038 0.151 2.898 0.034 0.362 |------------ 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 0.361 0.375 0.366 0.306 0.268 0.133 0.171 0.128 0.080 0.058 PACF 0.361 0.282 0.208 0.094 0.043 -0.117 0.010 0.001 -0.018 -0.019 95% C.L. 0.110 0.124 0.137 0.148 0.156 0.161 0.162 0.165 0.166 0.166 |------------------- 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 4 0.244 0.182 0.206 0.189 0.096 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.26 MINUTES