RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN025N.rwl.conv LOG FILE PROCESSED: FRAN025N.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: 482 1 Miraules Refuge DENSITY_MINIMUM ABAL - 482 2 France silver fir, European fir 1720 4228-224 1831 1977 - 482 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 482041 MISSING VALUES FOUND: 6 IN 1 GAPS / 1900 1905 / -------------------------------------------------------------------- 11 482061 MISSING VALUES FOUND: 7 IN 1 GAPS / 1913 1919 / -------------------------------------------------------------------- 12 482062 MISSING VALUES FOUND: 5 IN 1 GAPS / 1899 1903 / -------------------------------------------------------------------- 15 482081 MISSING VALUES FOUND: 5 IN 1 GAPS / 1860 1864 / -------------------------------------------------------------------- 16 482082 MISSING VALUES FOUND: 5 IN 1 GAPS / 1961 1965 / -------------------------------------------------------------------- 18 482092 MISSING VALUES FOUND: 5 IN 1 GAPS / 1905 1909 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 0.267 0.035 2.589 11.166 0.059 0.711 2 482012 1846 1977 132 0.260 0.023 0.914 3.505 0.064 0.525 3 482021 1891 1977 87 0.243 0.024 -0.110 2.772 0.071 0.594 4 482022 1889 1977 89 0.248 0.026 0.318 4.049 0.080 0.562 5 482031 1849 1977 129 0.280 0.051 1.701 5.245 0.064 0.900 6 482032 1863 1977 115 0.261 0.020 0.355 2.774 0.055 0.575 7 482041 1831 1977 147 0.253 0.026 1.676 7.084 0.047 0.757 8 482042 1855 1977 123 0.252 0.030 1.690 5.714 0.051 0.829 9 482051 1883 1977 95 0.234 0.021 1.008 3.990 0.068 0.545 10 482052 1888 1977 90 0.244 0.023 1.018 4.439 0.063 0.627 11 482061 1836 1977 142 0.255 0.028 1.646 7.082 0.052 0.744 12 482062 1842 1977 136 0.236 0.019 0.685 3.283 0.058 0.547 13 482071 1879 1977 99 0.287 0.029 3.377 20.360 0.062 0.432 14 482072 1875 1977 103 0.281 0.039 2.726 13.165 0.076 0.551 15 482081 1853 1977 125 0.237 0.029 2.802 11.575 0.053 0.775 16 482082 1849 1977 129 0.234 0.018 0.498 3.337 0.053 0.565 17 482091 1846 1977 132 0.283 0.029 1.782 7.229 0.061 0.658 18 482092 1852 1977 126 0.283 0.028 2.217 9.018 0.058 0.709 19 482101 1838 1977 140 0.286 0.031 1.348 6.203 0.059 0.681 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.281 0.026 1.217 5.164 0.060 0.590 21 482111 1896 1977 82 0.256 0.018 0.259 2.906 0.064 0.288 22 482112 1889 1977 89 0.262 0.024 0.695 4.006 0.070 0.528 23 482121 1861 1977 117 0.254 0.020 0.319 2.766 0.049 0.662 24 482122 1842 1977 136 0.252 0.022 0.760 3.514 0.052 0.627 NUMBER OF SERIES READ IN: 24 FROM 1831 TO 1977 147 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 117 0.260 0.027 1.312 6.264 0.060 0.624 STANDARD DEVIATION 19 0.018 0.007 0.928 4.222 0.008 0.130 MEDIAN (50TH QUANTILE) 122 0.255 0.026 1.118 4.802 0.059 0.610 INTERQUARTILE RANGE 36 0.035 0.007 1.149 3.735 0.011 0.161 MINIMUM VALUE 82 0.234 0.018 -0.110 2.766 0.047 0.288 LOWER HINGE (25TH QUANTILE) 97 0.246 0.022 0.592 3.421 0.053 0.549 UPPER HINGE (75TH QUANTILE) 133 0.281 0.029 1.741 7.156 0.064 0.710 MAXIMUM VALUE 141 0.287 0.051 3.377 20.360 0.080 0.900 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.303 0.255 0.015 -0.150 2.343 -0.328 0.827 MINIMUM CORRELATION: -0.328 SERIES 482011 AND 482052 90 YEARS MAXIMUM CORRELATION: 0.827 SERIES 482071 AND 482072 99 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.448 0.331 0.453 SDEV 0.208 0.259 0.175 SERR 0.019 0.017 0.011 EPS 0.944 0.922 0.952 NSS 20.6 23.9 24.0 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1831 1977 147 0.266 0.029 2.126 7.158 0.045 0.807 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.376 0.133 -0.009 41 106 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 1.04 1.00 1.07 2.10 9.17 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.11 0.00 0.84 0.95 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 126. 39. 82. 97. 136. 147. |----------- 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 0.718 0.635 0.607 0.549 0.513 0.505 0.448 0.396 0.347 PACF 0.802 0.211 0.035 0.135 -0.014 0.033 0.109 -0.094 -0.048 -0.018 95% C.L. 0.165 0.249 0.300 0.335 0.364 0.386 0.404 0.421 0.433 0.443 |------------------ 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 2 0.734 0.591 0.297 |================== 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 482011 1 0.21501656 0.14671220 0.00000000 0.25756660 2 482012 1 0.06865114 0.07485375 0.00000000 0.25308195 3 482021 1 0.05467796 0.03950629 0.00000000 0.22754969 4 482022 1 0.04666585 0.06087601 0.00000000 0.23932397 5 482031 1 0.15058433 0.02689495 0.00000000 0.23882276 6 482032 1 0.05886922 0.01465891 0.00000000 0.23306446 7 482041 1 0.11176982 0.08102222 0.00000000 0.24447356 8 482042 1 0.13314387 0.08329523 0.00000000 0.23940864 9 482051 1 0.08616176 0.15729073 0.00000000 0.22835967 10 482052 3 0.00000000 0.00000000 -0.00041314 0.26268664 11 482061 1 0.13314335 0.11101043 0.00000000 0.24641179 12 482062 1 0.06157082 0.06901477 0.00000000 0.22936755 13 482071 1 0.06068007 0.06669255 0.00000000 0.27769053 14 482072 1 0.11047681 0.04741858 0.00000000 0.25905129 15 482081 1 0.15707113 0.12330614 0.00000000 0.22880809 16 482082 3 0.00000000 0.00000000 -0.00017670 0.24471308 17 482091 1 0.09065109 0.03546352 0.00000000 0.26463801 18 482092 1 0.10994770 0.09703520 0.00000000 0.27431506 19 482101 1 0.20350243 0.29514819 0.00000000 0.28205189 SERIES IDENT OPTION A B C D 20 482102 3 0.00000000 0.00000000 0.00001548 0.28022850 21 482111 3 0.00000000 0.00000000 0.00010100 0.25141823 22 482112 3 0.00000000 0.00000000 0.00042969 0.24246170 23 482121 3 0.00000000 0.00000000 -0.00022352 0.26677719 24 482122 1 0.02267410 0.06689381 0.00000000 0.24964920 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.000 0.072 0.217 3.121 0.057 0.394 2 482012 1846 1977 132 1.000 0.072 0.986 4.356 0.064 0.292 3 482021 1891 1977 87 1.000 0.081 -0.377 2.907 0.071 0.358 4 482022 1889 1977 89 1.000 0.094 0.028 2.782 0.079 0.443 5 482031 1849 1977 129 1.000 0.109 0.788 4.297 0.064 0.699 6 482032 1863 1977 115 1.000 0.057 0.417 3.363 0.054 0.229 7 482041 1831 1977 147 1.000 0.065 0.485 4.241 0.046 0.537 8 482042 1855 1977 123 1.000 0.062 -0.175 2.878 0.051 0.423 9 482051 1883 1977 95 1.000 0.071 0.584 3.480 0.068 0.293 10 482052 1888 1977 90 1.000 0.080 0.899 4.637 0.063 0.508 11 482061 1836 1977 142 1.000 0.067 0.060 2.633 0.051 0.524 12 482062 1842 1977 136 1.000 0.063 0.233 2.978 0.057 0.275 13 482071 1879 1977 99 1.000 0.083 1.955 10.547 0.061 0.267 14 482072 1875 1977 103 1.000 0.091 1.235 5.872 0.075 0.233 15 482081 1853 1977 125 1.000 0.060 0.448 2.909 0.053 0.321 16 482082 1849 1977 129 1.000 0.072 0.368 3.012 0.052 0.503 17 482091 1846 1977 132 1.000 0.065 0.674 3.996 0.061 0.180 18 482092 1852 1977 126 1.000 0.067 0.872 5.762 0.057 0.330 19 482101 1838 1977 140 1.000 0.088 0.432 3.329 0.059 0.596 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.092 1.254 5.354 0.059 0.585 21 482111 1896 1977 82 1.000 0.068 0.340 3.268 0.063 0.266 22 482112 1889 1977 89 1.000 0.081 0.786 4.286 0.069 0.371 23 482121 1861 1977 117 1.000 0.071 0.289 2.655 0.049 0.606 24 482122 1842 1977 136 1.000 0.086 0.753 3.210 0.052 0.609 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.076 0.565 3.995 0.060 0.410 STANDARD DEVIATION 20 0.000 0.013 0.503 1.693 0.008 0.147 MEDIAN (50TH QUANTILE) 125 1.000 0.072 0.467 3.346 0.059 0.382 INTERQUARTILE RANGE 39 0.000 0.019 0.569 1.383 0.011 0.248 MINIMUM VALUE 82 1.000 0.057 -0.377 2.633 0.046 0.180 LOWER HINGE (25TH QUANTILE) 97 1.000 0.066 0.261 2.944 0.052 0.283 UPPER HINGE (75TH QUANTILE) 136 1.000 0.085 0.830 4.326 0.064 0.531 MAXIMUM VALUE 147 1.000 0.109 1.955 10.547 0.079 0.699 |------------------------ 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 482011 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 482012 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 482021 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 482022 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 482031 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 482032 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 482041 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 482042 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 482051 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 482052 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 482061 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 482062 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 482071 -67 66 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 482072 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 482081 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 482082 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 482091 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 482092 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 482101 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 482102 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 482111 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 482112 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 482121 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 482122 -67 91 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 482011 1838 1977 140 1.000 0.066 0.301 3.540 0.058 0.282 2 482012 1846 1977 132 1.000 0.066 0.871 3.934 0.064 0.169 3 482021 1891 1977 87 1.000 0.065 -0.133 3.688 0.071 -0.007 4 482022 1889 1977 89 1.000 0.079 0.247 3.123 0.079 0.214 5 482031 1849 1977 129 0.999 0.096 0.601 4.626 0.064 0.620 6 482032 1863 1977 115 1.000 0.055 0.504 3.304 0.054 0.180 7 482041 1831 1977 147 1.000 0.058 0.149 3.610 0.047 0.441 8 482042 1855 1977 123 1.000 0.055 -0.053 2.585 0.051 0.266 9 482051 1883 1977 95 1.000 0.066 0.447 3.258 0.068 0.190 10 482052 1888 1977 90 1.000 0.071 0.769 4.301 0.062 0.380 11 482061 1836 1977 142 1.000 0.054 0.469 3.531 0.051 0.280 12 482062 1842 1977 136 1.000 0.059 -0.049 3.373 0.057 0.156 13 482071 1879 1977 99 1.000 0.083 2.014 10.927 0.061 0.259 14 482072 1875 1977 103 1.000 0.086 1.465 7.119 0.076 0.155 15 482081 1853 1977 125 1.000 0.058 0.415 2.892 0.053 0.291 16 482082 1849 1977 129 1.000 0.065 0.365 3.426 0.052 0.389 17 482091 1846 1977 132 1.000 0.062 0.649 4.286 0.061 0.109 18 482092 1852 1977 126 1.000 0.063 0.709 6.147 0.057 0.245 19 482101 1838 1977 140 0.999 0.066 0.803 3.620 0.059 0.304 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.072 0.280 3.671 0.059 0.396 21 482111 1896 1977 82 1.000 0.067 0.343 3.125 0.063 0.242 22 482112 1889 1977 89 1.000 0.077 0.575 3.494 0.069 0.312 23 482121 1861 1977 117 0.999 0.051 0.385 2.972 0.049 0.257 24 482122 1842 1977 136 0.999 0.067 1.000 4.473 0.053 0.376 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.067 0.547 4.126 0.060 0.271 STANDARD DEVIATION 20 0.000 0.011 0.473 1.763 0.008 0.126 MEDIAN (50TH QUANTILE) 125 1.000 0.066 0.458 3.575 0.059 0.263 INTERQUARTILE RANGE 39 0.000 0.013 0.449 1.012 0.011 0.159 MINIMUM VALUE 82 0.999 0.051 -0.133 2.585 0.047 -0.007 LOWER HINGE (25TH QUANTILE) 97 1.000 0.059 0.290 3.281 0.053 0.185 UPPER HINGE (75TH QUANTILE) 136 1.000 0.072 0.739 4.294 0.064 0.344 MAXIMUM VALUE 147 1.000 0.096 2.014 10.927 0.079 0.620 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.375 0.143 0.009 -0.216 3.069 -0.072 0.805 MINIMUM CORRELATION: -0.072 SERIES 482011 AND 482052 90 YEARS MAXIMUM CORRELATION: 0.805 SERIES 482071 AND 482072 99 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.362 0.424 0.507 SDEV 0.161 0.185 0.156 SERR 0.015 0.012 0.009 EPS 0.921 0.946 0.961 NSS 20.6 23.9 24.0 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1831 1977 147 0.997 0.044 0.443 3.776 0.044 0.158 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.117 0.047 0.002 52 95 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.49 1.00 1.06 1.55 8.72 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.87 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 0.157 0.155 0.111 0.126 -0.080 -0.087 -0.007 -0.176 -0.126 -0.066 PACF 0.157 0.133 0.073 0.085 -0.138 -0.102 0.028 -0.158 -0.051 0.009 95% C.L. 0.165 0.169 0.173 0.175 0.177 0.178 0.179 0.179 0.184 0.186 |------------------ 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 0.048 0.136 0.136 |======================= POOLED AUTOREGRESSION ANALYSIS =======================| POOLED AUTOCORRELATIONS: LAG T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.152 0.187 0.087 0.105 -0.020 -0.152 -0.030 -0.121 -0.125 -0.156 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 0.152 2 0.127 0.168 3 0.120 0.163 0.040 4 0.118 0.153 0.032 0.061 5 0.121 0.155 0.042 0.068 -0.065 6 0.110 0.168 0.050 0.097 -0.042 -0.184 7 0.112 0.168 0.049 0.096 -0.044 -0.185 0.013 8 0.113 0.155 0.046 0.103 -0.041 -0.173 0.021 -0.071 9 0.107 0.157 0.032 0.100 -0.033 -0.170 0.033 -0.063 -0.079 10 0.101 0.152 0.035 0.087 -0.035 -0.162 0.036 -0.051 -0.071 -0.077 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) 685.04 683.59 681.39 683.16 684.62 686.00 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 682.95 684.92 686.17 687.25 688.38 SELECTED AUTOREGRESSION ORDER: 2 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 0.127 0.168 R-SQUARED DUE TO POOLED AUTOREGRESSION: 5.07 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 105.34 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.127 0.184 0.045 0.036 0.012 0.008 0.003 0.002 0.001 0.0004 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 482011 2 0.110 0.250 0.119 2 482012 2 0.075 0.134 0.215 3 482021 2 0.171 -0.005 0.269 4 482022 2 0.114 0.169 0.221 5 482031 2 0.432 0.497 0.209 6 482032 2 0.036 0.179 0.034 7 482041 2 0.226 0.366 0.175 8 482042 2 0.108 0.223 0.187 9 482051 2 0.142 0.133 0.299 10 482052 2 0.219 0.280 0.267 11 482061 2 0.152 0.240 0.145 12 482062 2 0.081 0.133 0.170 13 482071 2 0.078 0.288 -0.096 14 482072 2 0.033 0.151 0.030 15 482081 2 0.119 0.279 0.050 16 482082 2 0.198 0.333 0.148 17 482091 2 0.019 0.104 0.078 18 482092 2 0.079 0.258 -0.005 19 482101 2 0.117 0.257 0.155 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 482102 2 0.214 0.304 0.242 21 482111 2 0.085 0.242 0.029 22 482112 2 0.122 0.277 0.129 23 482121 2 0.096 0.215 0.168 24 482122 2 0.261 0.249 0.338 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.137 0.232 0.149 STANDARD DEVIATION 0 0.090 0.100 0.105 MEDIAN 2 0.116 0.246 0.161 INTERQUARTILE RANGE 0 0.104 0.120 0.154 MINIMUM VALUE 2 0.019 -0.005 -0.096 LOWER HINGE 2 0.080 0.160 0.064 UPPER HINGE 2 0.185 0.280 0.218 MAXIMUM VALUE 2 0.432 0.497 0.338 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.000 0.063 0.443 4.190 0.067 -0.013 2 482012 1846 1977 132 1.000 0.063 0.772 3.649 0.069 0.004 3 482021 1891 1977 87 1.000 0.062 -0.140 3.672 0.074 -0.087 4 482022 1889 1977 89 1.000 0.075 0.405 4.057 0.086 0.029 5 482031 1849 1977 129 1.000 0.072 0.336 3.223 0.082 -0.038 6 482032 1863 1977 115 1.000 0.054 0.574 3.306 0.060 0.004 7 482041 1831 1977 147 1.000 0.051 -0.051 4.492 0.058 -0.015 8 482042 1855 1977 123 1.000 0.051 -0.032 2.621 0.059 -0.005 9 482051 1883 1977 95 1.000 0.062 0.324 3.129 0.073 -0.045 10 482052 1888 1977 90 1.000 0.064 0.723 4.152 0.073 -0.034 11 482061 1836 1977 142 1.000 0.052 0.378 3.311 0.059 -0.035 12 482062 1842 1977 136 1.000 0.057 0.134 3.217 0.062 -0.019 13 482071 1879 1977 99 1.000 0.079 1.606 9.721 0.073 -0.004 14 482072 1875 1977 103 1.000 0.085 1.377 6.969 0.083 0.002 15 482081 1853 1977 125 1.000 0.056 0.237 3.034 0.063 -0.011 16 482082 1849 1977 129 1.000 0.059 0.457 3.665 0.065 -0.026 17 482091 1846 1977 132 1.000 0.061 0.649 4.347 0.064 -0.003 18 482092 1852 1977 126 1.000 0.061 0.512 5.486 0.064 -0.010 19 482101 1838 1977 140 1.000 0.062 0.787 3.491 0.067 -0.008 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.064 0.481 4.056 0.067 0.011 21 482111 1896 1977 82 1.000 0.065 0.319 3.378 0.072 0.012 22 482112 1889 1977 89 1.000 0.072 0.458 3.499 0.081 0.013 23 482121 1861 1977 117 1.000 0.049 0.384 2.879 0.056 -0.012 24 482122 1842 1977 136 1.000 0.058 0.866 4.768 0.063 -0.058 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.062 0.500 4.096 0.068 -0.015 STANDARD DEVIATION 20 0.000 0.009 0.401 1.515 0.008 0.025 MEDIAN (50TH QUANTILE) 125 1.000 0.062 0.450 3.657 0.067 -0.011 INTERQUARTILE RANGE 39 0.000 0.008 0.365 1.004 0.011 0.033 MINIMUM VALUE 82 1.000 0.049 -0.140 2.621 0.056 -0.087 LOWER HINGE (25TH QUANTILE) 97 1.000 0.056 0.321 3.265 0.063 -0.030 UPPER HINGE (75TH QUANTILE) 136 1.000 0.064 0.686 4.269 0.073 0.003 MAXIMUM VALUE 147 1.000 0.085 1.606 9.721 0.086 0.029 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.401 0.126 0.008 -0.159 3.143 0.015 0.794 MINIMUM CORRELATION: 0.015 SERIES 482052 AND 482071 90 YEARS MAXIMUM CORRELATION: 0.794 SERIES 482071 AND 482072 99 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.420 0.455 0.499 SDEV 0.124 0.154 0.137 SERR 0.011 0.010 0.008 EPS 0.937 0.952 0.960 NSS 20.6 23.9 24.0 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1831 1977 147 0.997 0.043 0.342 3.482 0.050 -0.113 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.240 0.080 -0.037 57 90 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.72 1.00 1.13 1.85 12.72 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.86 0.93 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 -0.112 -0.072 0.058 0.131 -0.127 -0.080 0.086 -0.128 -0.102 -0.008 PACF -0.112 -0.085 0.041 0.140 -0.091 -0.095 0.040 -0.135 -0.093 -0.044 95% C.L. 0.165 0.167 0.168 0.168 0.171 0.174 0.175 0.176 0.178 0.180 |------------------ 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 0.003 0.017 0.048 0.115 -0.113 -0.089 0.041 -0.144 -0.111 -0.037 PACF 0.003 0.017 0.048 0.115 -0.117 -0.097 0.037 -0.147 -0.081 -0.026 95% C.L. 0.165 0.165 0.165 0.165 0.168 0.170 0.171 0.171 0.174 0.176 |----------------- 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 2 0.003 0.003 0.017 |========================= 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 1831 1977 147 0.998 0.044 0.422 3.800 0.044 0.168 |------------ 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 0.167 0.220 0.088 0.123 -0.089 -0.100 -0.026 -0.178 -0.133 -0.103 PACF 0.167 0.198 0.028 0.069 -0.147 -0.120 0.040 -0.146 -0.063 -0.008 95% C.L. 0.165 0.170 0.177 0.178 0.181 0.182 0.183 0.183 0.188 0.191 |------------------- 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 2 0.068 0.134 0.200 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.27 MINUTES