RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: MONG007I.rwl.conv LOG FILE PROCESSED: MONG007I.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: 113 1 Turgen-charchira mountai DENSITY_EARLY LADA - 113 2 Mongolia Larch 2000 4942-9133 1570 1995 - 113 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 113011 MISSING VALUES FOUND: 24 IN 1 GAPS / 1931 1954 / -------------------------------------------------------------------- 3 113021 MISSING VALUES FOUND: 7 IN 1 GAPS / 1824 1830 / -------------------------------------------------------------------- 4 113022 MISSING VALUES FOUND: 1 IN 1 GAPS / 1816 1816 / -------------------------------------------------------------------- 5 113051 MISSING VALUES FOUND: 3 IN 2 GAPS / 1776 1777 / 1858 1858 / -------------------------------------------------------------------- 8 113062 MISSING VALUES FOUND: 1 IN 1 GAPS / 1872 1872 / -------------------------------------------------------------------- 10 113072 MISSING VALUES FOUND: 1 IN 1 GAPS / 1951 1951 / -------------------------------------------------------------------- 11 113091 MISSING VALUES FOUND: 1 IN 1 GAPS / 1821 1821 / -------------------------------------------------------------------- 13 113101 MISSING VALUES FOUND: 6 IN 4 GAPS / 1620 1622 / 1641 1641 / 1735 1735 / 1872 1872 / -------------------------------------------------------------------- 14 113102 MISSING VALUES FOUND: 8 IN 6 GAPS / 1617 1617 / 1652 1654 / 1671 1671 / 1735 1735 / / 1830 1830 / 1872 1872 / -------------------------------------------------------------------- 15 113111 MISSING VALUES FOUND: 4 IN 3 GAPS / 1715 1715 / 1749 1750 / 1821 1821 / -------------------------------------------------------------------- 16 113112 MISSING VALUES FOUND: 6 IN 4 GAPS / 1677 1677 / 1715 1715 / 1749 1750 / 1821 1822 / -------------------------------------------------------------------- 17 113121 MISSING VALUES FOUND: 1 IN 1 GAPS / 1900 1900 / -------------------------------------------------------------------- 18 113122 MISSING VALUES FOUND: 3 IN 3 GAPS / 1900 1900 / 1911 1911 / 1950 1950 / -------------------------------------------------------------------- 21 113191 MISSING VALUES FOUND: 6 IN 3 GAPS / 1735 1736 / 1786 1788 / 1886 1886 / -------------------------------------------------------------------- 22 113192 MISSING VALUES FOUND: 12 IN 5 GAPS / 1735 1736 / 1817 1817 / 1879 1879 / 1882 1888 / / 1910 1910 / -------------------------------------------------------------------- 23 113201 MISSING VALUES FOUND: 3 IN 1 GAPS / 1822 1824 / -------------------------------------------------------------------- 24 113202 MISSING VALUES FOUND: 3 IN 1 GAPS / 1822 1824 / -------------------------------------------------------------------- 25 113211 MISSING VALUES FOUND: 8 IN 2 GAPS / 1802 1807 / 1850 1851 / -------------------------------------------------------------------- 26 113212 MISSING VALUES FOUND: 8 IN 2 GAPS / 1682 1684 / 1793 1797 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 3.248 0.435 0.550 5.567 0.069 0.765 2 113012 1736 1936 201 3.223 0.476 1.012 3.654 0.070 0.779 3 113021 1784 1982 199 3.633 0.389 0.502 4.919 0.075 0.481 4 113022 1766 1981 216 3.672 0.337 0.709 4.592 0.074 0.330 5 113051 1730 1959 230 3.482 0.592 0.429 3.192 0.075 0.832 6 113052 1751 1959 209 3.381 0.468 0.026 2.727 0.071 0.755 7 113061 1751 1995 245 3.613 0.509 0.874 4.358 0.070 0.724 8 113062 1751 1995 245 3.633 0.474 1.389 5.605 0.067 0.648 9 113071 1755 1850 96 3.692 0.502 0.928 3.762 0.076 0.714 10 113072 1758 1973 216 3.559 0.472 0.492 4.099 0.071 0.664 11 113091 1755 1994 240 3.507 0.464 0.780 5.066 0.088 0.597 12 113092 1754 1994 241 3.871 0.467 0.254 3.301 0.080 0.592 13 113101 1613 1994 382 3.567 0.540 0.983 5.266 0.062 0.773 14 113102 1612 1994 383 3.487 0.672 0.397 3.057 0.065 0.865 15 113111 1601 1995 395 3.853 0.499 0.600 3.367 0.074 0.639 16 113112 1601 1994 394 4.042 0.484 0.774 4.016 0.075 0.577 17 113121 1760 1924 165 3.700 0.320 -0.414 4.548 0.064 0.499 18 113122 1761 1958 198 3.662 0.530 -0.342 3.216 0.080 0.731 19 113181 1752 1959 208 3.322 0.341 0.635 3.856 0.072 0.559 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 3.437 0.403 0.956 3.508 0.065 0.752 21 113191 1570 1963 394 3.595 0.467 1.195 4.575 0.070 0.709 22 113192 1570 1964 395 3.898 0.425 0.310 3.185 0.072 0.568 23 113201 1792 1944 153 3.513 0.466 0.510 3.366 0.061 0.765 24 113202 1772 1954 183 3.534 0.304 0.504 4.494 0.063 0.430 25 113211 1661 1951 291 3.553 0.350 0.346 3.737 0.070 0.534 26 113212 1655 1958 304 3.594 0.435 0.498 4.693 0.076 0.604 NUMBER OF SERIES READ IN: 26 FROM 1570 TO 1995 426 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 250 3.587 0.455 0.573 4.066 0.071 0.650 STANDARD DEVIATION 84 0.192 0.084 0.414 0.814 0.006 0.130 MEDIAN (50TH QUANTILE) 221 3.581 0.467 0.530 3.936 0.071 0.656 INTERQUARTILE RANGE 101 0.186 0.096 0.477 1.226 0.008 0.187 MINIMUM VALUE 96 3.223 0.304 -0.414 2.727 0.061 0.330 LOWER HINGE (25TH QUANTILE) 195 3.487 0.403 0.397 3.366 0.067 0.568 UPPER HINGE (75TH QUANTILE) 296 3.672 0.499 0.874 4.592 0.075 0.755 MAXIMUM VALUE 391 4.042 0.672 1.389 5.605 0.088 0.865 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.444 0.217 0.012 -0.533 2.781 -0.203 0.850 MINIMUM CORRELATION: -0.203 SERIES 113192 AND 113201 153 YEARS MAXIMUM CORRELATION: 0.850 SERIES 113051 AND 113052 209 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 46.97 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1595. 1630. 1655. 1680. 1705. 1730. 1755. 1780. 1805. 1830. CORR 1. 6. 15. 21. 28. 28. 36. 153. 276. 300. RBAR 0.530 0.369 0.440 0.396 0.389 0.493 0.483 0.429 0.343 0.333 SDEV 0.000 0.241 0.147 0.193 0.197 0.107 0.157 0.191 0.201 0.226 SERR 0.000 0.098 0.038 0.042 0.037 0.020 0.026 0.015 0.012 0.013 EPS 0.775 0.769 0.844 0.838 0.836 0.900 0.939 0.947 0.931 0.928 NSS 3.1 5.7 6.9 7.9 8.0 9.3 16.4 23.8 25.7 25.9 YEAR 1855. 1880. 1905. 1930. 1955. CORR 300. 300. 276. 210. 45. RBAR 0.423 0.466 0.359 0.388 0.338 SDEV 0.177 0.161 0.176 0.176 0.319 SERR 0.010 0.009 0.011 0.012 0.048 EPS 0.949 0.956 0.933 0.938 0.901 NSS 25.4 25.0 24.9 23.8 17.8 |======================== 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 1570 1995 426 3.764 0.466 0.420 2.760 0.049 0.845 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.014 -0.004 0.369 117 309 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.76 1.01 1.10 1.86 24.50 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.52 0.85 0.95 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 223. 103. 96. 201. 304. 395. |----------- 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 0.843 0.814 0.801 0.784 0.770 0.765 0.746 0.728 0.743 0.735 PACF 0.843 0.356 0.235 0.134 0.094 0.104 0.027 0.003 0.133 0.054 95% C.L. 0.097 0.151 0.188 0.217 0.242 0.264 0.284 0.302 0.318 0.334 |------------------ 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 6 0.785 0.401 0.163 0.146 0.079 0.061 0.099 |================== 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 113011 3 0.00000000 0.00000000 -0.00467858 3.64452147 2 113012 1 1.59794545 0.01949004 0.00000000 2.82685208 3 113021 1 0.45280525 0.04181382 0.00000000 3.58486128 4 113022 3 0.00000000 0.00000000 -0.00184236 3.87131763 5 113051 1 2.43782878 0.00550448 0.00000000 2.10988545 6 113052 3 0.00000000 0.00000000 -0.00630485 4.04349279 7 113061 1 3.04495978 0.00245962 0.00000000 1.32860565 8 113062 1 1.26231372 0.01291069 0.00000000 3.25042725 9 113071 1 1.52050960 0.04308355 0.00000000 3.33839107 10 113072 3 0.00000000 0.00000000 -0.00575309 4.18340540 11 113091 1 1.26222122 0.01064705 0.00000000 3.05590343 12 113092 1 3.68732119 0.00149493 0.00000000 0.77782017 13 113101 1 1.84037602 0.00884335 0.00000000 3.06149960 14 113102 3 0.00000000 0.00000000 -0.00544680 4.54795456 15 113111 1 1.54312634 0.00489554 0.00000000 3.17315912 16 113112 1 1.23515832 0.00750948 0.00000000 3.64931536 17 113121 1 0.61880016 0.07440940 0.00000000 3.65058208 18 113122 3 0.00000000 0.00000000 -0.00682674 4.33647156 19 113181 1 0.86366957 0.02058049 0.00000000 3.12548685 SERIES IDENT OPTION A B C D 20 113182 1 1.33738148 0.02318488 0.00000000 3.16432214 21 113191 1 1.22607434 0.00953907 0.00000000 3.27824688 22 113192 1 0.90917295 0.00907144 0.00000000 3.65098906 23 113201 1 1.78510869 0.01032494 0.00000000 2.63295150 24 113202 3 0.00000000 0.00000000 -0.00293761 3.80905509 25 113211 1 0.30877435 0.01502235 0.00000000 3.48340750 26 113212 1 1.10052383 0.00532268 0.00000000 3.05266237 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 1.000 0.121 0.012 2.875 0.068 0.742 2 113012 1736 1936 201 1.000 0.078 0.595 3.747 0.070 0.271 3 113021 1784 1982 199 1.000 0.103 0.576 5.317 0.077 0.432 4 113022 1766 1981 216 1.000 0.086 0.813 5.384 0.074 0.233 5 113051 1730 1959 230 1.000 0.094 0.457 3.800 0.075 0.447 6 113052 1751 1959 209 1.000 0.083 0.709 5.353 0.071 0.300 7 113061 1751 1995 245 1.000 0.085 1.232 6.753 0.070 0.326 8 113062 1751 1995 245 1.000 0.093 1.298 7.265 0.068 0.352 9 113071 1755 1850 96 1.000 0.087 -0.305 3.317 0.075 0.393 10 113072 1758 1973 216 1.000 0.085 0.997 7.082 0.071 0.240 11 113091 1755 1994 240 1.000 0.095 0.216 4.270 0.088 0.264 12 113092 1754 1994 241 1.000 0.087 0.102 4.406 0.080 0.247 13 113101 1613 1994 382 1.000 0.087 0.341 3.738 0.062 0.515 14 113102 1612 1994 383 1.000 0.090 0.697 6.334 0.066 0.433 15 113111 1601 1995 395 1.000 0.088 1.408 7.882 0.074 0.218 16 113112 1601 1994 394 1.000 0.091 1.269 6.451 0.076 0.303 17 113121 1760 1924 165 1.000 0.081 -0.503 5.056 0.063 0.428 18 113122 1761 1958 198 1.000 0.103 1.127 9.638 0.079 0.379 19 113181 1752 1959 208 1.000 0.080 0.440 3.743 0.072 0.285 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.068 0.407 3.822 0.065 0.221 21 113191 1570 1963 394 1.000 0.093 0.696 4.856 0.071 0.433 22 113192 1570 1964 395 1.000 0.093 0.956 6.042 0.072 0.400 23 113201 1792 1944 153 1.000 0.071 0.467 4.549 0.061 0.282 24 113202 1772 1954 183 1.000 0.074 0.507 4.118 0.062 0.285 25 113211 1661 1951 291 1.000 0.095 0.335 3.601 0.069 0.509 26 113212 1655 1958 304 1.000 0.100 0.753 5.475 0.075 0.439 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.089 0.600 5.188 0.071 0.361 STANDARD DEVIATION 86 0.000 0.011 0.476 1.622 0.006 0.119 MEDIAN (50TH QUANTILE) 223 1.000 0.088 0.585 4.956 0.071 0.339 INTERQUARTILE RANGE 103 0.000 0.011 0.614 2.534 0.008 0.162 MINIMUM VALUE 96 1.000 0.068 -0.503 2.875 0.061 0.218 LOWER HINGE (25TH QUANTILE) 201 1.000 0.083 0.341 3.800 0.068 0.271 UPPER HINGE (75TH QUANTILE) 304 1.000 0.094 0.956 6.334 0.075 0.433 MAXIMUM VALUE 395 1.000 0.121 1.408 9.638 0.088 0.742 |------------------------ 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 113011 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 113012 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 113021 -67 133 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 113022 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 113051 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 113052 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 113061 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 113062 -67 164 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 113071 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 113072 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 113091 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 113092 -67 161 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 113101 -67 255 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 113102 -67 256 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 113111 -67 264 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 113112 -67 263 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 113121 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 113122 -67 132 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 113181 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 113182 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 113191 -67 263 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 113192 -67 264 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 113201 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 113202 -67 122 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 113211 -67 194 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 113212 -67 203 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 113011 1751 1956 206 0.999 0.097 0.025 3.294 0.068 0.596 2 113012 1736 1936 201 1.000 0.077 0.563 3.670 0.070 0.253 3 113021 1784 1982 199 1.000 0.090 0.510 5.424 0.076 0.248 4 113022 1766 1981 216 1.000 0.083 0.937 5.911 0.074 0.177 5 113051 1730 1959 230 1.000 0.086 0.412 3.491 0.075 0.359 6 113052 1751 1959 209 1.000 0.082 0.771 5.520 0.071 0.285 7 113061 1751 1995 245 1.000 0.082 1.383 7.336 0.070 0.278 8 113062 1751 1995 245 1.000 0.092 1.384 7.921 0.068 0.327 9 113071 1755 1850 96 1.000 0.085 -0.411 3.560 0.075 0.357 10 113072 1758 1973 216 1.000 0.084 1.240 8.150 0.071 0.203 11 113091 1755 1994 240 1.000 0.090 0.252 5.360 0.088 0.182 12 113092 1754 1994 241 1.000 0.084 0.215 5.268 0.080 0.186 13 113101 1613 1994 382 1.000 0.077 0.666 4.245 0.062 0.377 14 113102 1612 1994 383 1.000 0.085 0.859 7.709 0.066 0.366 15 113111 1601 1995 395 1.000 0.087 1.421 8.066 0.074 0.200 16 113112 1601 1994 394 1.000 0.090 1.220 6.368 0.076 0.285 17 113121 1760 1924 165 1.000 0.079 -0.259 4.972 0.063 0.384 18 113122 1761 1958 198 1.000 0.100 1.532 11.731 0.079 0.328 19 113181 1752 1959 208 1.000 0.079 0.496 3.659 0.072 0.263 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.068 0.415 3.763 0.065 0.212 21 113191 1570 1963 394 1.000 0.093 0.692 4.868 0.071 0.428 22 113192 1570 1964 395 1.000 0.088 0.906 6.132 0.072 0.332 23 113201 1792 1944 153 1.000 0.069 0.485 4.759 0.061 0.245 24 113202 1772 1954 183 1.000 0.071 0.536 3.930 0.062 0.242 25 113211 1661 1951 291 1.000 0.089 0.321 3.636 0.069 0.439 26 113212 1655 1958 304 1.000 0.094 0.744 5.198 0.075 0.368 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.085 0.666 5.536 0.071 0.305 STANDARD DEVIATION 86 0.000 0.008 0.503 1.992 0.006 0.097 MEDIAN (50TH QUANTILE) 223 1.000 0.085 0.614 5.233 0.071 0.285 INTERQUARTILE RANGE 103 0.000 0.011 0.525 2.605 0.008 0.124 MINIMUM VALUE 96 0.999 0.068 -0.411 3.294 0.061 0.177 LOWER HINGE (25TH QUANTILE) 201 1.000 0.079 0.412 3.763 0.068 0.242 UPPER HINGE (75TH QUANTILE) 304 1.000 0.090 0.937 6.368 0.075 0.366 MAXIMUM VALUE 395 1.000 0.100 1.532 11.731 0.088 0.596 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.346 0.135 0.007 -0.240 3.208 -0.067 0.690 MINIMUM CORRELATION: -0.067 SERIES 113011 AND 113101 206 YEARS MAXIMUM CORRELATION: 0.690 SERIES 113091 AND 113092 240 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 46.97 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1595. 1630. 1655. 1680. 1705. 1730. 1755. 1780. 1805. 1830. CORR 1. 6. 15. 21. 28. 28. 36. 153. 276. 300. RBAR 0.535 0.369 0.362 0.394 0.360 0.460 0.422 0.340 0.352 0.345 SDEV 0.000 0.217 0.175 0.176 0.197 0.106 0.167 0.204 0.197 0.193 SERR 0.000 0.089 0.045 0.038 0.037 0.020 0.028 0.016 0.012 0.011 EPS 0.779 0.769 0.796 0.837 0.818 0.888 0.923 0.925 0.933 0.932 NSS 3.1 5.7 6.9 7.9 8.0 9.3 16.4 23.8 25.7 25.9 YEAR 1855. 1880. 1905. 1930. 1955. CORR 300. 300. 276. 210. 45. RBAR 0.436 0.441 0.369 0.389 0.345 SDEV 0.174 0.154 0.176 0.177 0.198 SERR 0.010 0.009 0.011 0.012 0.029 EPS 0.952 0.952 0.936 0.938 0.904 NSS 25.4 25.0 24.9 23.8 17.8 |======================== 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 1570 1995 426 0.997 0.055 0.514 3.486 0.050 0.287 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.197 0.094 -0.032 137 289 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.39 0.98 1.00 1.14 2.12 2277.44 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.10 0.38 0.86 0.96 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 0.287 0.147 0.074 0.044 -0.005 -0.008 -0.094 -0.143 -0.042 -0.080 PACF 0.287 0.070 0.016 0.011 -0.030 -0.005 -0.097 -0.102 0.043 -0.055 95% C.L. 0.097 0.105 0.106 0.107 0.107 0.107 0.107 0.108 0.110 0.110 |------------------ 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 2 0.088 0.269 0.070 |======================= 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 0.289 0.104 0.022 0.004 -0.034 0.029 -0.109 -0.137 0.012 -0.033 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 0.289 2 0.283 0.022 3 0.283 0.027 -0.016 4 0.283 0.027 -0.016 0.000 5 0.283 0.026 -0.015 0.010 -0.038 6 0.285 0.026 -0.014 0.009 -0.053 0.053 7 0.292 0.018 -0.013 0.007 -0.049 0.093 -0.139 8 0.281 0.026 -0.017 0.008 -0.050 0.094 -0.115 -0.083 9 0.289 0.038 -0.026 0.013 -0.051 0.096 -0.117 -0.111 0.100 10 0.295 0.031 -0.033 0.018 -0.054 0.097 -0.119 -0.109 0.117 -0.058 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) 2529.59 2494.37 2496.15 2498.05 2500.05 2501.44 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2502.24 2495.94 2494.99 2492.72 2493.27 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 0.289 R-SQUARED DUE TO POOLED AUTOREGRESSION: 8.37 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 109.13 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.289 0.084 0.024 0.007 0.002 0.001 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 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 113011 1 0.402 0.607 2 113012 1 0.066 0.254 3 113021 1 0.062 0.249 4 113022 1 0.043 0.181 5 113051 1 0.132 0.363 6 113052 1 0.082 0.286 7 113061 1 0.082 0.279 8 113062 1 0.108 0.329 9 113071 1 0.132 0.358 10 113072 1 0.041 0.203 11 113091 1 0.035 0.183 12 113092 1 0.043 0.186 13 113101 1 0.158 0.377 14 113102 1 0.170 0.366 15 113111 1 0.050 0.201 16 113112 1 0.111 0.287 17 113121 1 0.171 0.389 18 113122 1 0.138 0.369 19 113181 1 0.073 0.265 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 113182 1 0.067 0.214 21 113191 1 0.204 0.429 22 113192 1 0.153 0.333 23 113201 1 0.065 0.249 24 113202 1 0.063 0.251 25 113211 1 0.224 0.439 26 113212 1 0.158 0.373 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.117 0.308 STANDARD DEVIATION 0 0.079 0.099 MEDIAN 1 0.095 0.286 INTERQUARTILE RANGE 0 0.094 0.120 MINIMUM VALUE 1 0.035 0.181 LOWER HINGE 1 0.063 0.249 UPPER HINGE 1 0.158 0.369 MAXIMUM VALUE 1 0.402 0.607 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 1.000 0.077 -0.017 3.268 0.091 -0.143 2 113012 1736 1936 201 1.000 0.075 0.576 3.917 0.079 -0.011 3 113021 1784 1982 199 1.000 0.087 0.563 6.232 0.085 0.003 4 113022 1766 1981 216 1.000 0.082 1.134 7.439 0.082 -0.019 5 113051 1730 1959 230 1.000 0.080 0.454 3.821 0.087 0.003 6 113052 1751 1959 209 1.000 0.079 0.879 6.182 0.084 0.002 7 113061 1751 1995 245 1.000 0.079 1.378 7.706 0.080 -0.016 8 113062 1751 1995 245 1.000 0.087 1.468 9.077 0.078 -0.001 9 113071 1755 1850 96 1.000 0.079 -0.782 4.813 0.090 -0.025 10 113072 1758 1973 216 1.000 0.082 1.340 9.433 0.077 -0.002 11 113091 1755 1994 240 1.000 0.089 0.210 5.618 0.096 -0.007 12 113092 1754 1994 241 1.000 0.082 0.225 5.448 0.087 -0.017 13 113101 1613 1994 382 1.000 0.071 0.638 5.352 0.076 -0.051 14 113102 1612 1994 383 1.000 0.079 0.646 8.646 0.082 -0.073 15 113111 1601 1995 395 1.000 0.085 1.426 8.095 0.084 -0.020 16 113112 1601 1994 394 1.000 0.086 1.312 7.116 0.089 -0.052 17 113121 1760 1924 165 1.000 0.073 0.462 5.268 0.078 -0.055 18 113122 1761 1958 198 1.000 0.093 1.741 11.608 0.094 0.023 19 113181 1752 1959 208 1.000 0.076 0.542 3.782 0.081 -0.014 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.066 0.523 3.897 0.072 -0.032 21 113191 1570 1963 394 1.000 0.084 0.763 5.659 0.087 -0.067 22 113192 1570 1964 395 1.000 0.083 0.819 6.318 0.087 -0.072 23 113201 1792 1944 153 1.000 0.067 0.645 4.945 0.067 0.016 24 113202 1772 1954 183 1.000 0.069 0.571 4.103 0.069 0.003 25 113211 1661 1951 291 1.000 0.080 0.256 4.102 0.085 -0.087 26 113212 1655 1958 304 1.000 0.087 1.197 7.539 0.091 -0.058 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.080 0.730 6.130 0.083 -0.030 STANDARD DEVIATION 86 0.000 0.007 0.548 2.094 0.007 0.038 MEDIAN (50TH QUANTILE) 223 1.000 0.080 0.642 5.638 0.084 -0.018 INTERQUARTILE RANGE 103 0.000 0.010 0.736 3.436 0.010 0.054 MINIMUM VALUE 96 1.000 0.066 -0.782 3.268 0.067 -0.143 LOWER HINGE (25TH QUANTILE) 201 1.000 0.076 0.462 4.103 0.078 -0.055 UPPER HINGE (75TH QUANTILE) 304 1.000 0.085 1.197 7.539 0.087 -0.001 MAXIMUM VALUE 395 1.000 0.093 1.741 11.608 0.096 0.023 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.353 0.122 0.007 0.098 3.135 0.017 0.711 MINIMUM CORRELATION: 0.017 SERIES 113071 AND 113102 96 YEARS MAXIMUM CORRELATION: 0.711 SERIES 113091 AND 113092 240 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 46.97 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1595. 1630. 1655. 1680. 1705. 1730. 1755. 1780. 1805. 1830. CORR 1. 6. 15. 21. 28. 28. 36. 153. 276. 300. RBAR 0.578 0.412 0.394 0.416 0.398 0.465 0.467 0.362 0.368 0.362 SDEV 0.000 0.199 0.166 0.193 0.213 0.120 0.128 0.175 0.173 0.175 SERR 0.000 0.081 0.043 0.042 0.040 0.023 0.021 0.014 0.010 0.010 EPS 0.808 0.800 0.817 0.849 0.841 0.890 0.935 0.931 0.937 0.936 NSS 3.1 5.7 6.9 7.9 8.0 9.3 16.4 23.8 25.7 25.9 YEAR 1855. 1880. 1905. 1930. 1955. CORR 300. 300. 276. 210. 45. RBAR 0.392 0.401 0.361 0.375 0.349 SDEV 0.191 0.168 0.162 0.175 0.176 SERR 0.011 0.010 0.010 0.012 0.026 EPS 0.942 0.944 0.934 0.935 0.905 NSS 25.4 25.0 24.9 23.8 17.8 |======================== 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 1570 1995 426 0.997 0.052 0.563 3.906 0.057 -0.047 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.175 0.078 -0.022 137 289 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.37 1.16 1.00 1.13 2.29 29.89 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.11 0.58 0.85 0.96 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 -0.046 0.048 0.012 0.027 -0.028 0.026 -0.056 -0.119 0.021 -0.039 PACF -0.046 0.046 0.017 0.026 -0.028 0.021 -0.052 -0.127 0.016 -0.027 95% C.L. 0.097 0.097 0.097 0.097 0.097 0.097 0.098 0.098 0.099 0.099 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.002 0.047 0.016 0.026 -0.026 0.023 -0.060 -0.122 0.014 -0.042 PACF 0.002 0.047 0.016 0.024 -0.028 0.021 -0.059 -0.124 0.021 -0.032 95% C.L. 0.097 0.097 0.097 0.097 0.097 0.097 0.097 0.098 0.099 0.099 |----------------- 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 0.002 0.002 |========================= 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 1570 1995 426 0.997 0.054 0.522 3.564 0.049 0.302 |------------ 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 0.301 0.134 0.056 0.033 -0.014 -0.006 -0.089 -0.138 -0.045 -0.078 PACF 0.301 0.047 0.004 0.011 -0.033 0.004 -0.093 -0.097 0.039 -0.061 95% C.L. 0.097 0.105 0.107 0.107 0.107 0.107 0.107 0.108 0.110 0.110 |------------------- 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 0.094 0.303 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.34 MINUTES