RUN: CANA FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: cana044l.rwl LOG FILE PROCESSED: cana044l.rwl_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: 811 1 Willow Lake WIDTH_LATE PCMA - 811 2 Canada Black Spruce 620 6210-11908 1850 1988 - 811 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 811441 MISSING VALUES FOUND: 1 IN 1 GAPS / 1884 1884 / -------------------------------------------------------------------- 11 811491 MISSING VALUES FOUND: 1 IN 1 GAPS / 1958 1958 / -------------------------------------------------------------------- 14 811511 MISSING VALUES FOUND: 5 IN 1 GAPS / 1977 1981 / -------------------------------------------------------------------- 15 811512 MISSING VALUES FOUND: 5 IN 1 GAPS / 1970 1974 / -------------------------------------------------------------------- 18 811531 MISSING VALUES FOUND: 5 IN 1 GAPS / 1896 1900 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 811411 1890 1988 99 0.177 0.100 1.009 3.413 0.256 0.753 2 811412 1898 1988 91 0.194 0.093 1.041 3.802 0.325 0.623 3 811421 1950 1988 39 0.186 0.078 1.543 5.023 0.267 0.505 4 811422 1951 1988 38 0.264 0.088 2.104 8.307 0.277 0.384 5 811441 1830 1987 158 0.126 0.067 2.468 12.964 0.223 0.478 6 811442 1830 1987 158 0.102 0.067 1.602 6.069 0.253 0.728 7 811451 1857 1987 131 0.166 0.098 1.455 5.075 0.290 0.547 8 811452 1864 1942 79 0.122 0.054 1.858 6.194 0.216 0.642 9 811481 1870 1958 89 0.149 0.035 1.122 4.013 0.185 0.394 10 811482 1869 1986 118 0.111 0.132 5.126 31.062 0.318 0.389 11 811491 1911 1988 78 0.155 0.083 1.126 3.742 0.321 0.640 12 811492 1921 1988 68 0.106 0.088 1.768 5.396 0.242 0.840 13 811501 1932 1988 57 0.155 0.086 0.937 3.483 0.242 0.773 14 811511 1878 1988 111 0.120 0.066 1.602 6.010 0.248 0.742 15 811512 1877 1988 112 0.136 0.079 0.623 2.184 0.227 0.843 16 811521 1853 1988 136 0.109 0.093 1.259 3.683 0.258 0.847 17 811522 1895 1988 94 0.105 0.066 1.242 3.818 0.257 0.821 18 811531 1875 1988 114 0.078 0.069 3.389 16.014 0.263 0.826 19 811532 1886 1969 84 0.114 0.040 0.480 3.485 0.197 0.666 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 811541 1919 1988 70 0.193 0.059 0.104 2.275 0.272 0.424 21 811542 1923 1988 66 0.157 0.040 1.082 4.634 0.227 0.294 22 811551 1901 1988 88 0.182 0.080 1.621 6.353 0.277 0.494 23 811552 1910 1988 79 0.142 0.044 0.521 3.089 0.184 0.685 NUMBER OF SERIES READ IN: 23 FROM 1830 TO 1988 159 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 93 0.146 0.074 1.525 6.526 0.253 0.623 STANDARD DEVIATION 32 0.042 0.023 1.051 6.254 0.039 0.174 MEDIAN (50TH QUANTILE) 89 0.142 0.078 1.259 4.634 0.256 0.642 INTERQUARTILE RANGE 34 0.059 0.025 0.669 2.548 0.048 0.277 MINIMUM VALUE 38 0.078 0.035 0.104 2.184 0.184 0.294 LOWER HINGE (25TH QUANTILE) 73 0.113 0.063 1.025 3.584 0.227 0.486 UPPER HINGE (75TH QUANTILE) 108 0.171 0.088 1.694 6.131 0.274 0.763 MAXIMUM VALUE 158 0.264 0.132 5.126 31.062 0.325 0.847 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 245 0.412 0.227 0.015 -0.519 2.830 -0.256 0.854 MINIMUM CORRELATION: -0.256 SERIES 811481 AND 811501 27 YEARS MAXIMUM CORRELATION: 0.854 SERIES 811492 AND 811521 68 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 96.84 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 44.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1855. 1890. 1915. 1940. CORR 1. 10. 66. 105. RBAR 0.877 0.383 0.203 0.434 SDEV 0.000 0.249 0.219 0.158 SERR 0.000 0.079 0.027 0.015 EPS 0.966 0.876 0.813 0.940 NSS 3.9 11.4 17.0 20.3 |======================== 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 1830 1988 159 0.146 0.060 1.541 7.391 0.179 0.640 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.188 0.088 0.045 62 97 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.87 1.00 1.11 1.98 22.16 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.96 0.12 0.58 0.88 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 89. 39. 38. 74. 113. 158. |----------- 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 0.636 0.531 0.469 0.492 0.521 0.445 0.328 0.285 0.275 0.262 PACF 0.636 0.211 0.120 0.200 0.188 -0.018 -0.131 -0.034 -0.008 -0.021 95% C.L. 0.159 0.213 0.244 0.266 0.288 0.311 0.326 0.335 0.341 0.346 |------------------ 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 5 0.508 0.391 0.132 0.019 0.104 0.206 |================== 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 811411 3 0.00000000 0.00000000 -0.00199691 0.27641106 2 811412 1 0.25275660 0.04662595 0.00000000 0.13703872 3 811421 1 0.24158585 0.20490880 0.00000000 0.15866779 4 811422 3 0.00000000 0.00000000 0.00191596 0.22711237 5 811441 3 0.00000000 0.00000000 -0.00091897 0.19958287 6 811442 3 0.00000000 0.00000000 -0.00114469 0.19347094 7 811451 1 0.26343775 0.01558527 0.00000000 0.05477507 8 811452 1 0.21368656 0.10104532 0.00000000 0.09646824 9 811481 3 0.00000000 0.00000000 -0.00045914 0.16998723 10 811482 1 0.25906360 0.02052948 0.00000000 0.01498549 11 811491 3 0.00000000 0.00000000 -0.00264959 0.25892210 12 811492 1 0.32720244 0.05756356 0.00000000 0.02629581 13 811501 1 0.27330026 0.08088187 0.00000000 0.09873893 14 811511 1 0.20162770 0.02954893 0.00000000 0.05803227 15 811512 3 0.00000000 0.00000000 -0.00212507 0.25200930 16 811521 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 811522 3 0.00000000 0.00000000 -0.00196315 0.19846259 18 811531 1 0.35616860 0.11671016 0.00000000 0.05278526 19 811532 3 0.00000000 0.00000000 -0.00121606 0.16537292 SERIES IDENT OPTION A B C D 20 811541 1 0.12843265 0.02477758 0.00000000 0.13277465 21 811542 1 0.07889383 0.26246983 0.00000000 0.15313852 22 811551 3 0.00000000 0.00000000 -0.00007080 0.18496865 23 811552 3 0.00000000 0.00000000 -0.00126996 0.19307692 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 811411 1890 1988 99 0.985 0.404 0.826 3.406 0.255 0.607 2 811412 1898 1988 91 1.000 0.370 1.085 4.972 0.322 0.434 3 811421 1950 1988 39 1.000 0.364 2.775 11.808 0.258 0.399 4 811422 1951 1988 38 1.001 0.311 1.370 5.263 0.271 0.318 5 811441 1830 1987 158 0.996 0.329 2.464 15.873 0.227 0.225 6 811442 1830 1987 158 1.070 0.468 2.292 10.968 0.253 0.577 7 811451 1857 1987 131 0.998 0.456 2.185 9.155 0.288 0.366 8 811452 1864 1942 79 1.000 0.262 1.210 5.056 0.215 0.335 9 811481 1870 1958 89 1.000 0.216 1.002 3.969 0.183 0.305 10 811482 1869 1986 118 1.015 0.700 3.773 20.111 0.317 0.313 11 811491 1911 1988 78 1.021 0.387 1.222 4.921 0.317 0.299 12 811492 1921 1988 68 0.995 0.235 0.682 3.580 0.242 0.178 13 811501 1932 1988 57 0.999 0.471 2.548 10.188 0.238 0.718 14 811511 1878 1988 111 0.999 0.368 1.621 5.990 0.250 0.446 15 811512 1877 1988 112 1.117 0.602 2.763 11.299 0.230 0.796 16 811521 1853 1988 136 1.005 0.323 1.180 6.056 0.260 0.388 17 811522 1895 1988 94 1.080 0.465 1.706 6.414 0.258 0.571 18 811531 1875 1988 114 1.001 0.415 1.639 7.633 0.265 0.488 19 811532 1886 1969 84 0.995 0.233 0.638 3.896 0.196 0.342 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 811541 1919 1988 70 1.000 0.284 0.602 2.866 0.268 0.276 21 811542 1923 1988 66 1.000 0.250 1.243 5.521 0.224 0.263 22 811551 1901 1988 88 1.000 0.439 1.662 6.659 0.274 0.485 23 811552 1910 1988 79 0.999 0.228 0.575 2.910 0.184 0.475 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.012 0.373 1.611 7.327 0.252 0.418 STANDARD DEVIATION 32 0.032 0.122 0.843 4.358 0.038 0.156 MEDIAN (50TH QUANTILE) 89 1.000 0.368 1.370 5.990 0.255 0.388 INTERQUARTILE RANGE 39 0.004 0.174 1.196 5.226 0.041 0.177 MINIMUM VALUE 38 0.985 0.216 0.575 2.866 0.183 0.178 LOWER HINGE (25TH QUANTILE) 74 0.999 0.273 1.043 4.445 0.229 0.309 UPPER HINGE (75TH QUANTILE) 113 1.003 0.447 2.239 9.672 0.269 0.487 MAXIMUM VALUE 158 1.117 0.700 3.773 20.111 0.322 0.796 |------------------------ 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 811411 -67 66 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 811412 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 811421 -67 26 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 811422 -67 25 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 811441 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 811442 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 811451 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 811452 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 811481 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 811482 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 811491 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 811492 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 811501 -67 38 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 811511 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 811512 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 811521 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 811522 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 811531 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 811532 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 811541 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 811542 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 811551 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 811552 -67 52 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 811411 1890 1988 99 0.983 0.272 0.548 3.242 0.254 0.314 2 811412 1898 1988 91 0.997 0.356 1.055 5.012 0.322 0.394 3 811421 1950 1988 39 0.995 0.280 1.826 7.049 0.260 0.165 4 811422 1951 1988 38 0.996 0.265 1.050 4.159 0.271 0.119 5 811441 1830 1987 158 0.999 0.324 2.489 15.715 0.228 0.198 6 811442 1830 1987 158 0.996 0.307 0.869 4.802 0.253 0.307 7 811451 1857 1987 131 0.997 0.419 1.889 7.712 0.289 0.310 8 811452 1864 1942 79 0.998 0.226 1.155 5.075 0.215 0.130 9 811481 1870 1958 89 0.999 0.201 0.909 3.926 0.184 0.233 10 811482 1869 1986 118 0.993 0.618 3.770 22.317 0.316 0.255 11 811491 1911 1988 78 0.995 0.340 1.859 8.502 0.317 0.072 12 811492 1921 1988 68 0.998 0.223 0.685 3.733 0.242 0.076 13 811501 1932 1988 57 0.986 0.280 0.739 4.171 0.239 0.362 14 811511 1878 1988 111 0.997 0.341 1.460 5.200 0.250 0.384 15 811512 1877 1988 112 0.989 0.243 0.330 2.758 0.227 0.318 16 811521 1853 1988 136 0.997 0.307 1.215 6.739 0.259 0.353 17 811522 1895 1988 94 0.991 0.255 1.035 4.440 0.256 0.086 18 811531 1875 1988 114 0.996 0.365 3.947 26.195 0.266 0.110 19 811532 1886 1969 84 0.998 0.212 0.922 4.159 0.196 0.172 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 811541 1919 1988 70 0.999 0.279 0.548 2.792 0.268 0.254 21 811542 1923 1988 66 0.999 0.242 1.000 4.625 0.224 0.239 22 811551 1901 1988 88 0.990 0.371 1.618 7.015 0.277 0.284 23 811552 1910 1988 79 0.998 0.216 0.496 2.693 0.183 0.417 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 0.995 0.302 1.366 7.045 0.252 0.241 STANDARD DEVIATION 32 0.004 0.090 0.946 6.114 0.038 0.109 MEDIAN (50TH QUANTILE) 89 0.997 0.280 1.050 4.802 0.254 0.254 INTERQUARTILE RANGE 39 0.005 0.098 0.918 2.989 0.042 0.168 MINIMUM VALUE 38 0.983 0.201 0.330 2.693 0.183 0.072 LOWER HINGE (25TH QUANTILE) 74 0.994 0.243 0.804 4.043 0.227 0.148 UPPER HINGE (75TH QUANTILE) 113 0.998 0.340 1.722 7.032 0.269 0.316 MAXIMUM VALUE 158 0.999 0.618 3.947 26.195 0.322 0.417 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 245 0.155 0.163 0.010 0.359 2.780 -0.234 0.588 MINIMUM CORRELATION: -0.234 SERIES 811522 AND 811552 79 YEARS MAXIMUM CORRELATION: 0.588 SERIES 811482 AND 811501 55 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 96.84 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 44.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1855. 1890. 1915. 1940. CORR 1. 10. 66. 105. RBAR 0.829 0.157 0.180 0.120 SDEV 0.000 0.234 0.171 0.186 SERR 0.000 0.074 0.021 0.018 EPS 0.950 0.679 0.789 0.735 NSS 3.9 11.4 17.0 20.3 |======================== 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 1830 1988 159 0.969 0.231 1.204 7.697 0.198 0.247 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.425 0.172 0.040 53 106 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.55 1.28 1.01 1.07 2.35 25.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.12 0.78 0.88 1.00 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.246 0.123 0.088 0.086 0.089 0.010 -0.113 -0.150 -0.129 -0.102 PACF 0.246 0.066 0.046 0.051 0.052 -0.037 -0.135 -0.115 -0.069 -0.036 95% C.L. 0.159 0.168 0.170 0.171 0.172 0.174 0.174 0.175 0.179 0.181 |------------------ 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 0.066 0.248 |======================= 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 0.323 0.137 0.150 0.024 -0.169 -0.116 -0.053 -0.168 -0.096 0.024 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 0.323 2 0.311 0.037 3 0.307 0.004 0.106 4 0.314 0.004 0.126 -0.064 5 0.302 0.029 0.127 -0.002 -0.197 6 0.297 0.029 0.130 -0.001 -0.190 -0.024 7 0.297 0.033 0.130 -0.004 -0.190 -0.030 0.021 8 0.300 0.029 0.107 -0.004 -0.175 -0.026 0.056 -0.119 9 0.301 0.029 0.107 -0.003 -0.175 -0.027 0.056 -0.121 0.007 10 0.300 0.034 0.105 -0.002 -0.167 -0.027 0.050 -0.122 -0.007 0.048 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) 1051.99 1036.44 1038.23 1038.42 1039.77 1035.47 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1037.38 1039.31 1039.06 1041.05 1042.69 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 0.323 R-SQUARED DUE TO POOLED AUTOREGRESSION: 10.45 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 111.67 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.323 0.105 0.034 0.011 0.004 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 811411 1 0.106 0.314 2 811412 1 0.166 0.398 3 811421 1 0.046 0.167 4 811422 1 0.058 0.121 5 811441 1 0.051 0.200 6 811442 1 0.105 0.312 7 811451 1 0.098 0.313 8 811452 1 0.018 0.132 9 811481 1 0.062 0.234 10 811482 1 0.069 0.259 11 811491 1 0.010 0.073 12 811492 1 0.023 0.076 13 811501 1 0.139 0.365 14 811511 1 0.149 0.384 15 811512 1 0.154 0.323 16 811521 1 0.128 0.355 17 811522 1 0.013 0.087 18 811531 1 0.013 0.111 19 811532 1 0.062 0.180 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 811541 1 0.153 0.256 21 811542 1 0.075 0.240 22 811551 1 0.089 0.287 23 811552 1 0.189 0.424 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.086 0.244 STANDARD DEVIATION 0 0.055 0.110 MEDIAN 1 0.075 0.256 INTERQUARTILE RANGE 0 0.085 0.169 MINIMUM VALUE 1 0.010 0.073 LOWER HINGE 1 0.049 0.150 UPPER HINGE 1 0.133 0.318 MAXIMUM VALUE 1 0.189 0.424 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 811411 1890 1988 99 1.000 0.258 0.631 3.502 0.294 -0.028 2 811412 1898 1988 91 1.000 0.327 0.789 3.642 0.371 0.039 3 811421 1950 1988 39 1.000 0.276 1.957 7.666 0.276 0.023 4 811422 1951 1988 38 1.000 0.263 1.039 4.350 0.286 0.026 5 811441 1830 1987 158 1.000 0.318 2.456 15.812 0.257 -0.022 6 811442 1830 1987 158 1.000 0.291 0.978 4.800 0.297 -0.025 7 811451 1857 1987 131 1.000 0.398 2.153 9.368 0.336 -0.007 8 811452 1864 1942 79 1.000 0.224 1.192 5.378 0.229 0.000 9 811481 1870 1958 89 1.000 0.195 0.828 3.850 0.212 -0.021 10 811482 1869 1986 118 1.000 0.597 4.623 29.356 0.347 -0.007 11 811491 1911 1988 78 1.000 0.339 1.859 8.469 0.330 0.005 12 811492 1921 1988 68 1.000 0.223 0.646 3.646 0.248 0.009 13 811501 1932 1988 57 1.000 0.260 0.557 3.300 0.284 0.025 14 811511 1878 1988 111 1.000 0.315 1.180 5.080 0.320 -0.015 15 811512 1877 1988 112 1.000 0.230 0.090 2.673 0.274 -0.072 16 811521 1853 1988 136 1.000 0.287 0.954 5.776 0.301 -0.013 17 811522 1895 1988 94 1.000 0.254 1.004 4.211 0.267 -0.007 18 811531 1875 1988 114 1.000 0.362 3.986 26.965 0.284 -0.002 19 811532 1886 1969 84 1.000 0.209 1.038 4.569 0.214 -0.029 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 811541 1919 1988 70 1.000 0.270 0.407 2.603 0.294 0.078 21 811542 1923 1988 66 1.000 0.235 1.072 4.716 0.241 0.033 22 811551 1901 1988 88 1.000 0.355 1.771 7.794 0.309 -0.023 23 811552 1910 1988 79 1.000 0.195 0.550 2.697 0.235 -0.050 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.291 1.381 7.401 0.283 -0.004 STANDARD DEVIATION 32 0.000 0.087 1.095 7.182 0.042 0.032 MEDIAN (50TH QUANTILE) 89 1.000 0.270 1.038 4.716 0.284 -0.007 INTERQUARTILE RANGE 39 0.000 0.090 1.098 4.086 0.052 0.038 MINIMUM VALUE 38 1.000 0.195 0.090 2.603 0.212 -0.072 LOWER HINGE (25TH QUANTILE) 74 1.000 0.233 0.717 3.644 0.253 -0.022 UPPER HINGE (75TH QUANTILE) 113 1.000 0.322 1.815 7.730 0.305 0.016 MAXIMUM VALUE 158 1.000 0.597 4.623 29.356 0.371 0.078 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 245 0.154 0.157 0.010 0.325 2.659 -0.259 0.552 MINIMUM CORRELATION: -0.259 SERIES 811522 AND 811552 79 YEARS MAXIMUM CORRELATION: 0.552 SERIES 811421 AND 811551 39 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 96.84 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 44.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1855. 1890. 1915. 1940. CORR 1. 10. 66. 105. RBAR 0.826 0.187 0.193 0.124 SDEV 0.000 0.259 0.162 0.174 SERR 0.000 0.082 0.020 0.017 EPS 0.949 0.725 0.802 0.742 NSS 3.9 11.4 17.0 20.3 |======================== 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 1830 1988 159 0.973 0.217 1.285 8.272 0.221 -0.012 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.461 0.186 0.019 48 111 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.63 1.63 1.02 1.19 2.82 21.11 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.12 0.65 0.88 1.00 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.012 0.057 0.051 0.051 0.093 0.004 -0.091 -0.102 -0.075 -0.072 PACF -0.012 0.057 0.053 0.049 0.090 -0.001 -0.108 -0.121 -0.084 -0.067 95% C.L. 0.159 0.159 0.159 0.160 0.160 0.161 0.161 0.163 0.164 0.165 |------------------ 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 0.001 0.057 0.053 0.053 0.094 0.004 -0.093 -0.104 -0.078 -0.074 PACF 0.001 0.057 0.053 0.050 0.089 -0.003 -0.109 -0.121 -0.083 -0.066 95% C.L. 0.159 0.159 0.159 0.160 0.160 0.161 0.161 0.163 0.164 0.165 |----------------- 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 0.003 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 1830 1988 159 0.974 0.232 1.066 7.747 0.183 0.351 |------------ 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 0.349 0.186 0.130 0.114 0.110 0.004 -0.121 -0.163 -0.153 -0.144 PACF 0.349 0.073 0.050 0.051 0.049 -0.074 -0.145 -0.107 -0.062 -0.050 95% C.L. 0.159 0.177 0.182 0.184 0.186 0.187 0.187 0.189 0.193 0.196 |------------------- 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 0.129 0.352 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.00 MINUTES