RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: MONG007E.rwl.conv LOG FILE PROCESSED: MONG007E.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 WIDTH_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 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 / -------------------------------------------------------------------- 14 113102 MISSING VALUES FOUND: 2 IN 2 GAPS / 1671 1671 / 1830 1830 / -------------------------------------------------------------------- 16 113112 MISSING VALUES FOUND: 1 IN 1 GAPS / 1677 1677 / -------------------------------------------------------------------- 21 113191 MISSING VALUES FOUND: 5 IN 2 GAPS / 1735 1736 / 1786 1788 / -------------------------------------------------------------------- 22 113192 MISSING VALUES FOUND: 7 IN 1 GAPS / 1882 1888 / -------------------------------------------------------------------- 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: 3 IN 1 GAPS / 1682 1684 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 113011 1751 1956 206 0.793 0.483 1.377 4.826 0.321 0.748 2 113012 1736 1936 201 0.539 0.318 1.762 7.144 0.358 0.726 3 113021 1784 1982 199 0.724 0.344 0.367 2.512 0.363 0.678 4 113022 1766 1981 216 0.693 0.379 0.767 3.114 0.375 0.631 5 113051 1730 1959 230 0.705 0.489 1.309 3.942 0.327 0.789 6 113052 1751 1959 209 0.718 0.476 1.126 3.347 0.340 0.762 7 113061 1751 1995 245 0.587 0.367 1.548 6.213 0.413 0.693 8 113062 1751 1995 245 0.541 0.299 1.323 5.793 0.404 0.638 9 113071 1755 1850 96 0.897 0.578 0.828 3.039 0.473 0.570 10 113072 1758 1973 216 0.707 0.442 0.977 3.734 0.437 0.709 11 113091 1755 1994 240 0.449 0.264 2.402 13.039 0.432 0.626 12 113092 1754 1994 241 0.518 0.278 1.162 5.720 0.433 0.592 13 113101 1613 1994 382 0.463 0.296 1.006 3.712 0.413 0.744 14 113102 1612 1994 383 0.431 0.298 1.174 4.150 0.439 0.749 15 113111 1601 1995 395 0.331 0.313 2.968 15.412 0.495 0.657 16 113112 1601 1994 394 0.259 0.262 3.978 24.180 0.510 0.698 17 113121 1760 1924 165 0.377 0.216 0.978 4.050 0.434 0.568 18 113122 1761 1958 198 0.327 0.282 2.409 10.627 0.492 0.655 19 113181 1752 1959 208 0.830 0.512 1.284 4.312 0.333 0.782 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 0.975 0.557 0.711 2.794 0.354 0.730 21 113191 1570 1963 394 0.424 0.290 1.832 8.351 0.413 0.723 22 113192 1570 1964 395 0.411 0.298 1.112 3.773 0.444 0.777 23 113201 1792 1944 153 0.826 0.366 0.629 3.056 0.231 0.810 24 113202 1772 1954 183 0.840 0.340 0.327 2.930 0.310 0.558 25 113211 1661 1951 291 0.672 0.325 0.539 2.906 0.320 0.714 26 113212 1655 1958 304 0.577 0.292 0.548 3.259 0.340 0.749 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 252 0.601 0.360 1.325 5.998 0.393 0.695 STANDARD DEVIATION 85 0.196 0.099 0.839 4.939 0.068 0.073 MEDIAN (50TH QUANTILE) 221 0.582 0.321 1.144 3.996 0.409 0.711 INTERQUARTILE RANGE 100 0.293 0.150 0.781 3.099 0.098 0.111 MINIMUM VALUE 96 0.259 0.216 0.327 2.512 0.231 0.558 LOWER HINGE (25TH QUANTILE) 201 0.431 0.292 0.767 3.114 0.340 0.638 UPPER HINGE (75TH QUANTILE) 301 0.724 0.442 1.548 6.213 0.437 0.749 MAXIMUM VALUE 395 0.975 0.578 3.978 24.180 0.510 0.810 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.520 0.219 0.012 -0.737 2.809 -0.057 0.916 MINIMUM CORRELATION: -0.057 SERIES 113071 AND 113202 79 YEARS MAXIMUM CORRELATION: 0.916 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 0.750 0.791 0.651 0.585 0.600 0.748 0.624 0.497 0.600 0.528 SDEV 0.000 0.133 0.221 0.266 0.277 0.119 0.180 0.191 0.286 0.188 SERR 0.000 0.054 0.057 0.058 0.052 0.022 0.030 0.015 0.017 0.011 EPS 0.902 0.956 0.928 0.917 0.923 0.965 0.965 0.959 0.975 0.967 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 0.525 0.526 0.708 0.645 0.530 SDEV 0.186 0.216 0.100 0.116 0.174 SERR 0.011 0.012 0.006 0.008 0.026 EPS 0.966 0.965 0.984 0.977 0.953 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 0.536 0.272 0.867 3.904 0.343 0.659 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.745 0.434 0.043 79 347 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 1.07 1.01 1.09 2.16 9999.00 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.09 0.41 0.84 0.93 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 0.657 0.486 0.482 0.408 0.408 0.335 0.310 0.319 0.246 0.192 PACF 0.657 0.094 0.233 0.000 0.154 -0.077 0.086 0.030 -0.049 -0.052 95% C.L. 0.097 0.132 0.148 0.162 0.172 0.180 0.186 0.191 0.196 0.199 |------------------ 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 0.468 0.574 -0.044 0.232 |================== 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 1 1.40374196 0.02436272 0.00000000 0.51818925 2 113012 1 0.70087290 0.00853600 0.00000000 0.20524722 3 113021 3 0.00000000 0.00000000 0.00147796 0.55877501 4 113022 3 0.00000000 0.00000000 0.00112916 0.56869626 5 113051 1 1.08270168 0.00579103 0.00000000 0.10981978 6 113052 1 1.49890983 0.02251881 0.00000000 0.40555787 7 113061 1 0.75411052 0.02667368 0.00000000 0.47369465 8 113062 1 0.92211080 0.07975283 0.00000000 0.49568614 9 113071 3 0.00000000 0.00000000 -0.01297307 1.52658987 10 113072 1 0.59100407 0.01681564 0.00000000 0.55019677 11 113091 1 1.03919435 0.07802474 0.00000000 0.39580929 12 113092 1 0.46649784 0.02935751 0.00000000 0.45338222 13 113101 3 0.00000000 0.00000000 -0.00089595 0.63495117 14 113102 3 0.00000000 0.00000000 -0.00135429 0.69114906 15 113111 1 1.42921567 0.04859474 0.00000000 0.25824934 16 113112 1 1.38608146 0.05535721 0.00000000 0.19797115 17 113121 1 0.53377157 0.00985881 0.00000000 0.11477614 18 113122 1 0.75566924 0.01877512 0.00000000 0.13015462 19 113181 1 1.35962319 0.02348372 0.00000000 0.55705786 SERIES IDENT OPTION A B C D 20 113182 1 1.29779029 0.02043495 0.00000000 0.67553562 21 113191 1 0.53370482 0.00614757 0.00000000 0.22383636 22 113192 3 0.00000000 0.00000000 -0.00145493 0.69372869 23 113201 3 0.00000000 0.00000000 -0.00334761 1.08156943 24 113202 3 0.00000000 0.00000000 0.00052110 0.78620112 25 113211 3 0.00000000 0.00000000 0.00029380 0.63438487 26 113212 3 0.00000000 0.00000000 0.00090944 0.43531826 |-------------------- 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 0.438 0.766 3.463 0.319 0.594 2 113012 1736 1936 201 1.001 0.440 0.546 3.411 0.357 0.589 3 113021 1784 1982 199 1.003 0.503 0.611 3.028 0.361 0.683 4 113022 1766 1981 216 1.001 0.549 0.839 3.275 0.377 0.581 5 113051 1730 1959 230 1.004 0.561 0.943 3.880 0.322 0.744 6 113052 1751 1959 209 1.001 0.447 0.638 3.466 0.339 0.533 7 113061 1751 1995 245 0.999 0.513 0.643 3.489 0.411 0.628 8 113062 1751 1995 245 1.000 0.472 0.456 3.292 0.403 0.589 9 113071 1755 1850 96 1.013 0.506 0.295 2.331 0.469 0.510 10 113072 1758 1973 216 1.000 0.569 0.691 3.386 0.436 0.681 11 113091 1755 1994 240 1.000 0.430 0.241 3.477 0.431 0.412 12 113092 1754 1994 241 1.000 0.470 0.393 3.283 0.432 0.517 13 113101 1613 1994 382 0.993 0.560 0.780 3.616 0.412 0.700 14 113102 1612 1994 383 1.000 0.540 0.701 3.872 0.437 0.636 15 113111 1601 1995 395 1.002 0.688 1.739 9.805 0.494 0.610 16 113112 1601 1994 394 1.003 0.565 0.396 2.658 0.509 0.525 17 113121 1760 1924 165 1.000 0.456 0.252 2.897 0.431 0.487 18 113122 1761 1958 198 1.007 0.517 0.414 2.862 0.490 0.431 19 113181 1752 1959 208 1.000 0.447 0.239 2.432 0.332 0.687 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.491 0.667 3.313 0.352 0.677 21 113191 1570 1963 394 1.000 0.536 0.566 3.404 0.411 0.643 22 113192 1570 1964 395 1.009 0.597 0.850 3.918 0.442 0.679 23 113201 1792 1944 153 0.998 0.382 0.364 3.168 0.231 0.735 24 113202 1772 1954 183 1.000 0.412 0.410 2.961 0.310 0.562 25 113211 1661 1951 291 1.000 0.483 0.533 2.813 0.314 0.733 26 113212 1655 1958 304 0.998 0.497 0.539 2.952 0.339 0.716 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.001 0.503 0.597 3.479 0.391 0.611 STANDARD DEVIATION 86 0.004 0.066 0.306 1.354 0.067 0.093 MEDIAN (50TH QUANTILE) 223 1.000 0.500 0.556 3.302 0.407 0.619 INTERQUARTILE RANGE 103 0.002 0.101 0.305 0.525 0.097 0.150 MINIMUM VALUE 96 0.993 0.382 0.239 2.331 0.231 0.412 LOWER HINGE (25TH QUANTILE) 201 1.000 0.447 0.396 2.952 0.339 0.533 UPPER HINGE (75TH QUANTILE) 304 1.002 0.549 0.701 3.477 0.436 0.683 MAXIMUM VALUE 395 1.013 0.688 1.739 9.805 0.509 0.744 |------------------------ 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 0.433 0.733 3.404 0.319 0.591 2 113012 1736 1936 201 0.996 0.424 0.468 3.332 0.357 0.570 3 113021 1784 1982 199 0.995 0.451 0.389 2.686 0.361 0.613 4 113022 1766 1981 216 0.992 0.507 0.643 2.880 0.377 0.584 5 113051 1730 1959 230 0.978 0.476 0.716 3.578 0.322 0.679 6 113052 1751 1959 209 0.994 0.422 0.446 3.011 0.339 0.494 7 113061 1751 1995 245 0.995 0.483 0.588 3.502 0.411 0.549 8 113062 1751 1995 245 0.994 0.434 0.419 3.756 0.403 0.472 9 113071 1755 1850 96 0.982 0.444 0.292 2.609 0.469 0.363 10 113072 1758 1973 216 0.994 0.564 0.819 3.941 0.436 0.672 11 113091 1755 1994 240 0.998 0.421 0.277 3.463 0.431 0.354 12 113092 1754 1994 241 0.997 0.458 0.352 3.175 0.432 0.469 13 113101 1613 1994 382 0.989 0.502 0.605 3.538 0.412 0.598 14 113102 1612 1994 383 0.992 0.515 0.620 3.719 0.437 0.597 15 113111 1601 1995 395 0.995 0.640 1.074 4.528 0.494 0.603 16 113112 1601 1994 394 0.997 0.553 0.377 2.623 0.509 0.499 17 113121 1760 1924 165 0.996 0.446 0.236 3.029 0.431 0.460 18 113122 1761 1958 198 0.996 0.480 0.230 2.782 0.489 0.366 19 113181 1752 1959 208 0.996 0.436 0.289 2.798 0.332 0.662 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 0.997 0.476 0.551 3.065 0.352 0.657 21 113191 1570 1963 394 0.989 0.506 0.447 3.344 0.411 0.616 22 113192 1570 1964 395 0.985 0.539 0.552 2.981 0.442 0.631 23 113201 1792 1944 153 0.990 0.335 0.173 2.827 0.230 0.651 24 113202 1772 1954 183 0.989 0.377 0.430 2.932 0.309 0.487 25 113211 1661 1951 291 0.993 0.420 0.198 2.534 0.314 0.650 26 113212 1655 1958 304 0.995 0.461 0.339 2.594 0.339 0.653 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 0.993 0.469 0.472 3.178 0.391 0.559 STANDARD DEVIATION 86 0.005 0.062 0.214 0.487 0.068 0.099 MEDIAN (50TH QUANTILE) 223 0.995 0.460 0.438 3.047 0.407 0.594 INTERQUARTILE RANGE 103 0.006 0.072 0.313 0.704 0.097 0.162 MINIMUM VALUE 96 0.978 0.335 0.173 2.534 0.230 0.354 LOWER HINGE (25TH QUANTILE) 201 0.990 0.433 0.292 2.798 0.339 0.487 UPPER HINGE (75TH QUANTILE) 304 0.996 0.506 0.605 3.502 0.436 0.650 MAXIMUM VALUE 395 0.999 0.640 1.074 4.528 0.509 0.679 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.538 0.144 0.008 -0.271 2.641 0.164 0.871 MINIMUM CORRELATION: 0.164 SERIES 113192 AND 113211 291 YEARS MAXIMUM CORRELATION: 0.871 SERIES 113181 AND 113182 203 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 0.769 0.880 0.670 0.575 0.623 0.770 0.606 0.486 0.582 0.582 SDEV 0.000 0.059 0.144 0.302 0.246 0.098 0.205 0.213 0.214 0.133 SERR 0.000 0.024 0.037 0.066 0.047 0.018 0.034 0.017 0.013 0.008 EPS 0.911 0.977 0.933 0.914 0.930 0.969 0.962 0.958 0.973 0.973 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 0.538 0.536 0.704 0.641 0.554 SDEV 0.199 0.212 0.100 0.126 0.149 SERR 0.012 0.012 0.006 0.009 0.022 EPS 0.967 0.967 0.983 0.977 0.957 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 0.967 0.403 0.142 2.642 0.346 0.566 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.567 0.218 0.091 108 318 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.68 1.00 1.07 1.76 30.06 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.46 0.85 0.94 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 0.565 0.317 0.275 0.216 0.173 0.059 0.059 0.052 -0.006 -0.072 PACF 0.565 -0.003 0.142 0.010 0.037 -0.114 0.068 -0.025 -0.043 -0.084 95% C.L. 0.097 0.124 0.131 0.137 0.140 0.142 0.142 0.142 0.143 0.143 |------------------ 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 0.319 0.565 |======================= 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 0.585 0.330 0.281 0.256 0.195 0.112 0.145 0.075 -0.008 -0.107 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 0.585 2 0.595 -0.018 3 0.598 -0.104 0.145 4 0.589 -0.098 0.110 0.059 5 0.589 -0.098 0.110 0.058 0.001 6 0.589 -0.095 0.114 0.054 0.027 -0.045 7 0.594 -0.098 0.109 0.041 0.037 -0.109 0.109 8 0.606 -0.110 0.113 0.046 0.050 -0.120 0.176 -0.111 9 0.601 -0.101 0.107 0.049 0.052 -0.114 0.170 -0.081 -0.050 10 0.594 -0.113 0.131 0.033 0.059 -0.108 0.185 -0.095 0.034 -0.140 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) 4157.87 3981.55 3983.41 3976.40 3976.92 3978.92 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 3980.07 3976.94 3973.61 3974.55 3968.10 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 0.585 R-SQUARED DUE TO POOLED AUTOREGRESSION: 34.20 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 151.98 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.585 0.342 0.200 0.117 0.068 0.040 0.023 0.014 0.008 0.0047 0.003 0.002 0.001 0.001 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 0.352 0.593 2 113012 1 0.331 0.572 3 113021 1 0.377 0.614 4 113022 1 0.349 0.586 5 113051 1 0.467 0.680 6 113052 1 0.246 0.495 7 113061 1 0.306 0.550 8 113062 1 0.224 0.473 9 113071 1 0.137 0.364 10 113072 1 0.453 0.672 11 113091 1 0.131 0.354 12 113092 1 0.221 0.470 13 113101 1 0.363 0.602 14 113102 1 0.361 0.600 15 113111 1 0.386 0.621 16 113112 1 0.255 0.502 17 113121 1 0.215 0.460 18 113122 1 0.144 0.370 19 113181 1 0.447 0.664 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 113182 1 0.442 0.660 21 113191 1 0.388 0.617 22 113192 1 0.417 0.632 23 113201 1 0.452 0.661 24 113202 1 0.322 0.491 25 113211 1 0.428 0.653 26 113212 1 0.435 0.659 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.333 0.562 STANDARD DEVIATION 0 0.105 0.100 MEDIAN 1 0.356 0.596 INTERQUARTILE RANGE 0 0.182 0.162 MINIMUM VALUE 1 0.131 0.354 LOWER HINGE 1 0.246 0.491 UPPER HINGE 1 0.428 0.653 MAXIMUM VALUE 1 0.467 0.680 |------------------- 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 0.349 0.355 3.373 0.394 -0.011 2 113012 1736 1936 201 1.000 0.348 0.189 3.162 0.424 -0.036 3 113021 1784 1982 199 1.000 0.356 0.061 2.770 0.431 -0.004 4 113022 1766 1981 216 1.000 0.410 0.521 3.454 0.465 -0.052 5 113051 1730 1959 230 1.001 0.347 0.119 3.221 0.419 -0.059 6 113052 1751 1959 209 1.001 0.365 0.012 3.401 0.421 -0.007 7 113061 1751 1995 245 1.001 0.399 0.101 3.287 0.472 -0.034 8 113062 1751 1995 245 1.000 0.381 -0.231 3.282 0.470 -0.004 9 113071 1755 1850 96 1.000 0.414 0.229 2.704 0.496 -0.024 10 113072 1758 1973 216 1.001 0.415 0.210 3.451 0.520 -0.013 11 113091 1755 1994 240 1.001 0.391 0.062 3.223 0.485 -0.022 12 113092 1754 1994 241 1.001 0.403 0.111 3.506 0.480 0.021 13 113101 1613 1994 382 1.000 0.400 0.481 4.017 0.456 0.017 14 113102 1612 1994 383 1.000 0.412 0.327 3.214 0.498 -0.022 15 113111 1601 1995 395 1.003 0.493 0.659 4.539 0.555 0.032 16 113112 1601 1994 394 1.001 0.476 0.397 3.070 0.562 -0.028 17 113121 1760 1924 165 1.000 0.395 0.037 3.045 0.486 0.031 18 113122 1761 1958 198 1.000 0.446 0.218 3.202 0.520 0.037 19 113181 1752 1959 208 1.000 0.326 0.036 3.085 0.394 -0.070 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.358 0.188 3.179 0.427 -0.068 21 113191 1570 1963 394 1.001 0.395 0.219 3.794 0.472 -0.065 22 113192 1570 1964 395 1.001 0.415 0.313 3.169 0.496 -0.096 23 113201 1792 1944 153 1.000 0.250 0.166 3.798 0.286 -0.118 24 113202 1772 1954 183 1.000 0.328 0.367 3.241 0.390 -0.158 25 113211 1661 1951 291 1.000 0.318 -0.004 3.426 0.378 -0.040 26 113212 1655 1958 304 1.001 0.343 -0.146 3.691 0.409 -0.013 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.382 0.192 3.358 0.454 -0.031 STANDARD DEVIATION 86 0.001 0.051 0.201 0.380 0.060 0.046 MEDIAN (50TH QUANTILE) 223 1.000 0.393 0.189 3.261 0.467 -0.023 INTERQUARTILE RANGE 103 0.001 0.065 0.267 0.286 0.077 0.055 MINIMUM VALUE 96 1.000 0.250 -0.231 2.704 0.286 -0.158 LOWER HINGE (25TH QUANTILE) 201 1.000 0.348 0.061 3.169 0.419 -0.059 UPPER HINGE (75TH QUANTILE) 304 1.001 0.412 0.327 3.454 0.496 -0.004 MAXIMUM VALUE 395 1.003 0.493 0.659 4.539 0.562 0.037 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.527 0.106 0.006 0.073 2.874 0.276 0.855 MINIMUM CORRELATION: 0.276 SERIES 113011 AND 113192 206 YEARS MAXIMUM CORRELATION: 0.855 SERIES 113111 AND 113112 394 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 0.725 0.802 0.698 0.645 0.604 0.643 0.504 0.486 0.562 0.606 SDEV 0.000 0.085 0.118 0.144 0.176 0.124 0.191 0.156 0.145 0.107 SERR 0.000 0.035 0.030 0.031 0.033 0.023 0.032 0.013 0.009 0.006 EPS 0.890 0.958 0.941 0.935 0.924 0.943 0.943 0.957 0.970 0.975 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 0.559 0.520 0.548 0.530 0.553 SDEV 0.141 0.161 0.133 0.148 0.157 SERR 0.008 0.009 0.008 0.010 0.023 EPS 0.970 0.964 0.968 0.964 0.957 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 0.990 0.326 0.017 2.834 0.383 0.011 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.363 0.137 0.110 104 322 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 1.08 1.01 1.07 2.15 48.51 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.41 0.85 0.95 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 0.011 -0.119 0.067 0.063 0.099 -0.071 0.031 0.046 0.020 -0.107 PACF 0.011 -0.119 0.070 0.047 0.116 -0.068 0.053 0.009 0.030 -0.118 95% C.L. 0.097 0.097 0.098 0.099 0.099 0.100 0.100 0.101 0.101 0.101 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.022 0.021 -0.121 0.072 |---------- 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 0.001 -0.120 0.067 0.061 0.099 -0.072 0.032 0.046 0.021 -0.107 PACF 0.001 -0.120 0.069 0.047 0.117 -0.067 0.052 0.010 0.032 -0.118 95% C.L. 0.097 0.097 0.098 0.099 0.099 0.100 0.100 0.101 0.101 0.101 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.015 0.001 |========================= 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 0.990 0.396 0.155 2.635 0.325 0.569 |------------ 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 0.568 0.302 0.263 0.225 0.181 0.075 0.076 0.062 0.012 -0.058 PACF 0.568 -0.030 0.154 0.028 0.035 -0.095 0.071 -0.036 -0.026 -0.090 95% C.L. 0.097 0.124 0.131 0.136 0.139 0.141 0.142 0.142 0.142 0.142 |------------------- 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 0.323 0.568 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.50 MINUTES