RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: MONG007N.rwl.conv LOG FILE PROCESSED: MONG007N.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_MINIMUM 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 / -------------------------------------------------------------------- 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: 3 IN 3 GAPS / 1641 1641 / 1735 1735 / 1872 1872 / -------------------------------------------------------------------- 14 113102 MISSING VALUES FOUND: 5 IN 5 GAPS / 1617 1617 / 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: 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 0.236 0.050 -0.119 4.270 0.106 0.770 2 113012 1736 1936 201 0.248 0.047 0.900 3.568 0.097 0.757 3 113021 1784 1982 199 0.283 0.039 0.840 4.323 0.105 0.373 4 113022 1766 1981 216 0.280 0.035 1.339 7.985 0.103 0.250 5 113051 1730 1959 230 0.272 0.060 0.695 3.545 0.098 0.832 6 113052 1751 1959 209 0.261 0.042 -0.075 3.029 0.094 0.699 7 113061 1751 1995 245 0.283 0.052 0.945 4.644 0.101 0.671 8 113062 1751 1995 245 0.286 0.049 1.286 5.714 0.099 0.566 9 113071 1755 1850 96 0.288 0.053 0.753 3.369 0.140 0.495 10 113072 1758 1973 216 0.276 0.047 0.854 4.960 0.113 0.505 11 113091 1755 1994 240 0.267 0.047 1.124 5.651 0.120 0.532 12 113092 1754 1994 241 0.298 0.050 0.672 3.958 0.104 0.546 13 113101 1613 1994 382 0.277 0.055 1.112 5.257 0.095 0.748 14 113102 1612 1994 383 0.275 0.066 0.945 5.674 0.098 0.827 15 113111 1601 1995 395 0.302 0.053 1.013 4.781 0.123 0.415 16 113112 1601 1994 394 0.324 0.055 0.955 4.471 0.128 0.406 17 113121 1760 1924 165 0.285 0.038 0.289 3.988 0.101 0.463 18 113122 1761 1958 198 0.288 0.057 -0.191 3.506 0.113 0.675 19 113181 1752 1959 208 0.254 0.035 0.577 3.755 0.108 0.441 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 0.264 0.042 0.909 3.375 0.090 0.708 21 113191 1570 1963 394 0.279 0.050 1.165 4.419 0.105 0.623 22 113192 1570 1964 395 0.307 0.045 0.649 4.147 0.108 0.457 23 113201 1792 1944 153 0.266 0.048 0.532 3.358 0.108 0.667 24 113202 1772 1954 183 0.263 0.038 0.929 4.206 0.093 0.599 25 113211 1661 1951 291 0.264 0.035 0.659 4.303 0.098 0.482 26 113212 1655 1958 304 0.269 0.048 1.389 8.641 0.112 0.492 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 251 0.277 0.048 0.775 4.573 0.106 0.577 STANDARD DEVIATION 84 0.019 0.008 0.419 1.333 0.012 0.151 MEDIAN (50TH QUANTILE) 221 0.277 0.048 0.877 4.287 0.104 0.556 INTERQUARTILE RANGE 100 0.021 0.011 0.364 1.392 0.014 0.236 MINIMUM VALUE 96 0.236 0.035 -0.191 3.029 0.090 0.250 LOWER HINGE (25TH QUANTILE) 201 0.264 0.042 0.649 3.568 0.098 0.463 UPPER HINGE (75TH QUANTILE) 301 0.286 0.053 1.013 4.960 0.112 0.699 MAXIMUM VALUE 391 0.324 0.066 1.389 8.641 0.140 0.832 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.413 0.197 0.011 -0.331 2.476 -0.131 0.831 MINIMUM CORRELATION: -0.131 SERIES 113192 AND 113201 153 YEARS MAXIMUM CORRELATION: 0.831 SERIES 113012 AND 113051 201 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 0.433 0.468 0.470 0.411 0.392 0.506 0.572 0.370 0.361 0.366 SDEV 0.000 0.171 0.172 0.193 0.143 0.109 0.142 0.197 0.196 0.192 SERR 0.000 0.070 0.044 0.042 0.027 0.021 0.024 0.016 0.012 0.011 EPS 0.701 0.834 0.859 0.846 0.838 0.905 0.956 0.933 0.936 0.937 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 0.363 0.392 0.334 0.397 0.333 SDEV 0.157 0.154 0.150 0.162 0.305 SERR 0.009 0.009 0.009 0.011 0.045 EPS 0.935 0.942 0.926 0.940 0.899 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 0.294 0.047 0.574 3.131 0.068 0.804 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.147 0.045 0.022 129 297 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 1.16 1.00 1.10 2.25 144.80 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.11 0.54 0.85 0.96 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 0.802 0.755 0.737 0.741 0.707 0.698 0.684 0.674 0.680 0.663 PACF 0.802 0.312 0.218 0.212 0.047 0.087 0.051 0.043 0.101 0.017 95% C.L. 0.097 0.147 0.179 0.206 0.230 0.249 0.267 0.283 0.298 0.312 |------------------ 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 0.725 0.428 0.143 0.119 0.233 |================== 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 -0.00046952 0.28461474 2 113012 1 0.15506245 0.02057433 0.00000000 0.21184024 3 113021 1 0.03939975 0.03928517 0.00000000 0.27873716 4 113022 1 0.05207730 0.00993524 0.00000000 0.25871190 5 113051 1 0.20042825 0.01146335 0.00000000 0.20198169 6 113052 3 0.00000000 0.00000000 -0.00052735 0.31613773 7 113061 1 0.30595186 0.00241113 0.00000000 0.05245368 8 113062 1 0.12510113 0.01279202 0.00000000 0.24765629 9 113071 1 0.13621798 0.05024452 0.00000000 0.26060092 10 113072 3 0.00000000 0.00000000 -0.00051318 0.33207420 11 113091 1 0.12040371 0.01223763 0.00000000 0.22824834 12 113092 1 0.19255747 0.00387335 0.00000000 0.17263278 13 113101 1 0.17948462 0.01126071 0.00000000 0.23702416 14 113102 1 0.34237218 0.00213359 0.00000000 0.04132493 15 113111 1 0.12474885 0.00693498 0.00000000 0.25975648 16 113112 1 0.11443346 0.00830722 0.00000000 0.29120943 17 113121 1 0.08655245 0.06816332 0.00000000 0.27808324 18 113122 3 0.00000000 0.00000000 -0.00070006 0.35687822 19 113181 1 0.08370878 0.03252426 0.00000000 0.24163890 SERIES IDENT OPTION A B C D 20 113182 1 0.13757947 0.02679111 0.00000000 0.23996705 21 113191 1 0.12859370 0.01086204 0.00000000 0.25012890 22 113192 1 0.08288773 0.01324196 0.00000000 0.29154888 23 113201 1 0.15494579 0.01741311 0.00000000 0.21396852 24 113202 1 0.09907118 0.02714094 0.00000000 0.24349666 25 113211 1 0.05199151 0.01636749 0.00000000 0.25297955 26 113212 1 0.11398690 0.00792454 0.00000000 0.22641815 |-------------------- 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 0.178 -0.398 3.403 0.106 0.688 2 113012 1736 1936 201 1.000 0.108 0.632 4.327 0.097 0.244 3 113021 1784 1982 199 1.000 0.133 0.907 4.354 0.107 0.317 4 113022 1766 1981 216 1.000 0.115 1.715 11.028 0.103 0.139 5 113051 1730 1959 230 1.000 0.123 0.451 4.612 0.097 0.402 6 113052 1751 1959 209 1.000 0.109 0.162 5.227 0.094 0.320 7 113061 1751 1995 245 1.000 0.116 1.447 6.917 0.101 0.256 8 113062 1751 1995 245 1.000 0.126 1.144 7.702 0.099 0.259 9 113071 1755 1850 96 1.000 0.141 0.094 2.828 0.139 0.222 10 113072 1758 1973 216 1.000 0.125 1.218 7.193 0.113 0.113 11 113091 1755 1994 240 1.000 0.132 1.079 5.846 0.120 0.202 12 113092 1754 1994 241 1.000 0.126 0.984 5.511 0.104 0.227 13 113101 1613 1994 382 1.000 0.123 0.538 5.336 0.097 0.390 14 113102 1612 1994 383 1.000 0.134 1.589 10.462 0.100 0.391 15 113111 1601 1995 395 1.000 0.144 1.844 8.916 0.123 0.107 16 113112 1601 1994 394 1.000 0.146 1.376 5.839 0.128 0.229 17 113121 1760 1924 165 1.000 0.122 0.273 5.172 0.101 0.326 18 113122 1761 1958 198 0.999 0.154 1.614 12.848 0.112 0.325 19 113181 1752 1959 208 1.000 0.120 0.543 3.699 0.107 0.243 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.100 0.619 4.127 0.090 0.242 21 113191 1570 1963 394 1.000 0.138 1.515 8.069 0.106 0.322 22 113192 1570 1964 395 1.000 0.138 1.423 7.549 0.108 0.350 23 113201 1792 1944 153 1.000 0.114 0.299 5.673 0.109 0.165 24 113202 1772 1954 183 1.000 0.112 0.753 3.914 0.094 0.381 25 113211 1661 1951 291 1.000 0.123 0.609 4.406 0.097 0.398 26 113212 1655 1958 304 1.000 0.141 1.690 10.754 0.111 0.258 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.129 0.928 6.374 0.106 0.289 STANDARD DEVIATION 86 0.000 0.017 0.596 2.634 0.011 0.119 MEDIAN (50TH QUANTILE) 223 1.000 0.125 0.946 5.592 0.105 0.258 INTERQUARTILE RANGE 103 0.000 0.022 0.910 3.348 0.014 0.122 MINIMUM VALUE 96 0.999 0.100 -0.398 2.828 0.090 0.107 LOWER HINGE (25TH QUANTILE) 201 1.000 0.116 0.538 4.354 0.097 0.227 UPPER HINGE (75TH QUANTILE) 304 1.000 0.138 1.447 7.702 0.111 0.350 MAXIMUM VALUE 395 1.000 0.178 1.844 12.848 0.139 0.688 |------------------------ 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 0.997 0.138 -0.258 5.347 0.106 0.413 2 113012 1736 1936 201 1.000 0.106 0.579 4.159 0.097 0.221 3 113021 1784 1982 199 0.999 0.118 1.029 5.276 0.107 0.125 4 113022 1766 1981 216 1.000 0.113 1.826 11.881 0.103 0.113 5 113051 1730 1959 230 0.999 0.110 0.554 4.414 0.098 0.268 6 113052 1751 1959 209 1.000 0.108 0.188 5.137 0.094 0.309 7 113061 1751 1995 245 1.000 0.111 1.613 7.773 0.101 0.192 8 113062 1751 1995 245 1.000 0.123 1.290 8.620 0.099 0.221 9 113071 1755 1850 96 1.000 0.136 -0.025 2.925 0.140 0.177 10 113072 1758 1973 216 1.000 0.123 1.432 8.222 0.113 0.082 11 113091 1755 1994 240 1.000 0.126 1.252 6.992 0.120 0.124 12 113092 1754 1994 241 1.000 0.119 1.405 7.456 0.104 0.130 13 113101 1613 1994 382 0.999 0.110 0.952 6.685 0.097 0.236 14 113102 1612 1994 383 0.999 0.128 1.743 11.450 0.100 0.338 15 113111 1601 1995 395 1.000 0.142 1.889 9.120 0.123 0.087 16 113112 1601 1994 394 1.000 0.144 1.368 5.701 0.128 0.207 17 113121 1760 1924 165 1.000 0.119 0.428 5.595 0.101 0.294 18 113122 1761 1958 198 0.999 0.149 2.231 17.517 0.112 0.257 19 113181 1752 1959 208 1.000 0.118 0.687 3.846 0.107 0.213 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.100 0.706 4.300 0.090 0.228 21 113191 1570 1963 394 1.000 0.136 1.556 8.150 0.106 0.306 22 113192 1570 1964 395 0.999 0.131 1.377 7.489 0.108 0.288 23 113201 1792 1944 153 1.000 0.111 0.317 5.767 0.109 0.123 24 113202 1772 1954 183 1.000 0.110 0.794 3.968 0.094 0.361 25 113211 1661 1951 291 1.000 0.118 0.629 4.576 0.097 0.349 26 113212 1655 1958 304 1.000 0.134 1.645 10.665 0.111 0.187 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.122 1.046 7.040 0.106 0.225 STANDARD DEVIATION 86 0.001 0.013 0.638 3.205 0.011 0.090 MEDIAN (50TH QUANTILE) 223 1.000 0.119 1.141 6.226 0.105 0.221 INTERQUARTILE RANGE 103 0.000 0.022 0.977 3.645 0.014 0.164 MINIMUM VALUE 96 0.997 0.100 -0.258 2.925 0.090 0.082 LOWER HINGE (25TH QUANTILE) 201 0.999 0.111 0.579 4.576 0.098 0.130 UPPER HINGE (75TH QUANTILE) 304 1.000 0.134 1.556 8.222 0.111 0.294 MAXIMUM VALUE 395 1.000 0.149 2.231 17.517 0.140 0.413 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.343 0.109 0.006 0.032 3.265 -0.012 0.676 MINIMUM CORRELATION: -0.012 SERIES 113011 AND 113102 206 YEARS MAXIMUM CORRELATION: 0.676 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 0.370 0.497 0.398 0.399 0.379 0.500 0.503 0.314 0.381 0.360 SDEV 0.000 0.159 0.168 0.176 0.155 0.122 0.163 0.186 0.184 0.179 SERR 0.000 0.065 0.043 0.038 0.029 0.023 0.027 0.015 0.011 0.010 EPS 0.643 0.849 0.820 0.839 0.830 0.903 0.943 0.916 0.941 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 0.376 0.380 0.328 0.408 0.343 SDEV 0.151 0.153 0.146 0.148 0.192 SERR 0.009 0.009 0.009 0.010 0.029 EPS 0.939 0.939 0.924 0.942 0.903 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 0.996 0.078 1.357 6.336 0.066 0.267 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.384 0.176 -0.090 144 282 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 1.27 1.01 1.11 2.38 39.66 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.54 0.85 0.95 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 0.267 0.079 0.020 0.040 -0.027 -0.026 -0.068 -0.096 -0.035 -0.104 PACF 0.267 0.008 -0.003 0.037 -0.051 -0.010 -0.059 -0.070 0.017 -0.101 95% C.L. 0.097 0.104 0.104 0.104 0.104 0.104 0.104 0.105 0.106 0.106 |------------------ 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 0.072 0.267 |======================= 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 0.214 0.020 -0.015 -0.008 -0.031 0.035 -0.035 -0.075 0.026 -0.054 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 0.214 2 0.219 -0.027 3 0.219 -0.024 -0.014 4 0.219 -0.024 -0.014 -0.001 5 0.219 -0.024 -0.015 0.006 -0.031 6 0.220 -0.024 -0.014 0.007 -0.042 0.050 7 0.223 -0.027 -0.013 0.006 -0.043 0.062 -0.056 8 0.220 -0.023 -0.016 0.006 -0.044 0.061 -0.042 -0.060 9 0.223 -0.020 -0.020 0.009 -0.044 0.062 -0.041 -0.073 0.060 10 0.228 -0.026 -0.023 0.014 -0.048 0.062 -0.043 -0.074 0.078 -0.080 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) 2840.25 2822.36 2824.06 2825.98 2827.98 2829.57 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2830.50 2831.18 2831.67 2832.13 2831.42 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 0.214 R-SQUARED DUE TO POOLED AUTOREGRESSION: 4.56 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 104.78 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.214 0.046 0.010 0.002 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 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 0.216 0.428 2 113012 1 0.062 0.222 3 113021 1 0.016 0.125 4 113022 1 0.019 0.114 5 113051 1 0.074 0.271 6 113052 1 0.097 0.309 7 113061 1 0.037 0.192 8 113062 1 0.054 0.221 9 113071 1 0.041 0.177 10 113072 1 0.009 0.082 11 113091 1 0.025 0.124 12 113092 1 0.022 0.130 13 113101 1 0.061 0.236 14 113102 1 0.121 0.339 15 113111 1 0.013 0.088 16 113112 1 0.049 0.209 17 113121 1 0.093 0.298 18 113122 1 0.089 0.298 19 113181 1 0.051 0.214 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 113182 1 0.057 0.229 21 113191 1 0.104 0.307 22 113192 1 0.108 0.289 23 113201 1 0.016 0.124 24 113202 1 0.133 0.364 25 113211 1 0.168 0.350 26 113212 1 0.046 0.189 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.068 0.228 STANDARD DEVIATION 0 0.051 0.093 MEDIAN 1 0.056 0.222 INTERQUARTILE RANGE 0 0.072 0.168 MINIMUM VALUE 1 0.009 0.082 LOWER HINGE 1 0.025 0.130 UPPER HINGE 1 0.097 0.298 MAXIMUM VALUE 1 0.216 0.428 |------------------- 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 0.125 -0.262 6.457 0.129 -0.077 2 113012 1736 1936 201 1.000 0.104 0.683 4.189 0.107 -0.024 3 113021 1784 1982 199 1.000 0.117 1.090 5.599 0.114 0.000 4 113022 1766 1981 216 1.000 0.113 1.917 12.806 0.110 -0.009 5 113051 1730 1959 230 1.000 0.106 0.560 5.071 0.110 0.003 6 113052 1751 1959 209 1.000 0.103 0.395 5.795 0.109 0.012 7 113061 1751 1995 245 1.000 0.109 1.570 7.677 0.109 0.001 8 113062 1751 1995 245 1.000 0.120 1.294 9.314 0.108 0.017 9 113071 1755 1850 96 1.000 0.134 -0.093 2.983 0.152 -0.017 10 113072 1758 1973 216 1.000 0.123 1.460 8.622 0.118 0.004 11 113091 1755 1994 240 1.000 0.125 1.225 7.029 0.130 -0.012 12 113092 1754 1994 241 1.000 0.118 1.428 7.786 0.112 -0.009 13 113101 1613 1994 382 1.000 0.107 0.863 6.847 0.110 -0.018 14 113102 1612 1994 383 1.000 0.121 1.288 9.939 0.122 -0.027 15 113111 1601 1995 395 1.000 0.142 1.891 9.240 0.130 -0.006 16 113112 1601 1994 394 1.000 0.141 1.394 5.929 0.143 -0.017 17 113121 1760 1924 165 1.000 0.114 0.769 6.134 0.119 -0.020 18 113122 1761 1958 198 1.000 0.143 2.339 18.090 0.129 0.038 19 113181 1752 1959 208 1.000 0.115 0.622 4.022 0.120 -0.014 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 113182 1757 1963 207 1.000 0.097 0.824 5.113 0.101 -0.017 21 113191 1570 1963 394 1.000 0.130 1.642 8.935 0.125 -0.032 22 113192 1570 1964 395 1.000 0.126 1.351 7.566 0.126 -0.047 23 113201 1792 1944 153 1.000 0.110 0.363 5.981 0.115 0.005 24 113202 1772 1954 183 1.000 0.102 0.761 3.782 0.111 -0.002 25 113211 1661 1951 291 1.000 0.110 0.575 4.883 0.118 -0.079 26 113212 1655 1958 304 1.000 0.131 1.873 12.167 0.122 -0.021 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 254 1.000 0.119 1.070 7.383 0.119 -0.014 STANDARD DEVIATION 86 0.000 0.013 0.634 3.274 0.012 0.025 MEDIAN (50TH QUANTILE) 223 1.000 0.118 1.157 6.652 0.118 -0.013 INTERQUARTILE RANGE 103 0.000 0.016 0.838 3.822 0.017 0.022 MINIMUM VALUE 96 1.000 0.097 -0.262 2.983 0.101 -0.079 LOWER HINGE (25TH QUANTILE) 201 1.000 0.109 0.622 5.113 0.110 -0.021 UPPER HINGE (75TH QUANTILE) 304 1.000 0.126 1.460 8.935 0.126 0.001 MAXIMUM VALUE 395 1.000 0.143 2.339 18.090 0.152 0.038 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 325 0.346 0.105 0.006 0.287 3.245 0.051 0.671 MINIMUM CORRELATION: 0.051 SERIES 113022 AND 113102 216 YEARS MAXIMUM CORRELATION: 0.671 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 0.392 0.504 0.402 0.409 0.365 0.466 0.489 0.316 0.400 0.384 SDEV 0.000 0.149 0.164 0.195 0.186 0.132 0.143 0.166 0.163 0.168 SERR 0.000 0.061 0.042 0.043 0.035 0.025 0.024 0.013 0.010 0.010 EPS 0.664 0.853 0.822 0.845 0.821 0.890 0.940 0.917 0.945 0.942 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 0.353 0.358 0.323 0.389 0.331 SDEV 0.158 0.162 0.142 0.146 0.175 SERR 0.009 0.009 0.009 0.010 0.026 EPS 0.933 0.933 0.922 0.938 0.898 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 0.074 1.399 6.681 0.073 0.031 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.365 0.168 -0.085 149 277 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 1.13 1.00 1.11 2.24 8.74 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.10 0.43 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 0.031 0.009 -0.013 0.044 -0.038 0.003 -0.034 -0.080 -0.002 -0.081 PACF 0.031 0.008 -0.013 0.045 -0.041 0.004 -0.033 -0.082 0.007 -0.084 95% C.L. 0.097 0.097 0.097 0.097 0.097 0.097 0.097 0.097 0.098 0.098 |------------------ 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 0.000 0.008 -0.014 0.046 -0.040 0.005 -0.032 -0.079 0.003 -0.080 PACF 0.000 0.008 -0.014 0.046 -0.040 0.004 -0.030 -0.083 0.007 -0.083 95% C.L. 0.097 0.097 0.097 0.097 0.097 0.097 0.097 0.097 0.098 0.098 |----------------- 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 0.000 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 1570 1995 426 0.997 0.075 1.397 6.562 0.067 0.214 |------------ 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 0.214 0.052 0.004 0.036 -0.031 -0.011 -0.050 -0.090 -0.035 -0.093 PACF 0.214 0.006 -0.009 0.039 -0.049 0.003 -0.047 -0.076 0.006 -0.090 95% C.L. 0.097 0.101 0.101 0.101 0.102 0.102 0.102 0.102 0.103 0.103 |------------------- 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 0.046 0.214 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.28 MINUTES