RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN025X.rwl.conv LOG FILE PROCESSED: FRAN025X.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_MAXIMUM 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 --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 0.893 0.059 -0.389 2.412 0.064 0.321 2 482012 1846 1977 132 0.871 0.070 -0.686 3.351 0.070 0.407 3 482021 1891 1977 87 0.907 0.049 -0.008 2.584 0.055 0.213 4 482022 1889 1977 89 0.894 0.050 -0.185 3.442 0.058 0.189 5 482031 1849 1977 129 0.883 0.074 -1.164 4.730 0.065 0.519 6 482032 1863 1977 115 0.871 0.064 -0.158 2.478 0.068 0.330 7 482041 1831 1977 147 0.861 0.067 -0.095 2.191 0.054 0.602 8 482042 1855 1977 123 0.821 0.083 0.152 2.241 0.073 0.627 9 482051 1883 1977 95 0.896 0.063 -0.129 2.464 0.062 0.416 10 482052 1888 1977 90 0.897 0.057 -0.923 3.907 0.066 0.222 11 482061 1836 1977 142 0.847 0.062 -0.504 2.986 0.064 0.414 12 482062 1842 1977 136 0.816 0.068 -0.024 2.217 0.072 0.415 13 482071 1879 1977 99 0.904 0.055 -0.633 3.046 0.070 0.089 14 482072 1875 1977 103 0.923 0.055 -0.774 3.370 0.071 -0.004 15 482081 1853 1977 125 0.865 0.071 -0.461 2.877 0.069 0.479 16 482082 1849 1977 129 0.884 0.063 -0.373 2.676 0.066 0.384 17 482091 1846 1977 132 0.871 0.065 -0.322 2.704 0.069 0.377 18 482092 1852 1977 126 0.888 0.050 -0.299 2.511 0.059 0.183 19 482101 1838 1977 140 0.910 0.055 -0.261 2.715 0.059 0.248 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.901 0.050 -0.234 2.738 0.054 0.275 21 482111 1896 1977 82 0.895 0.061 -0.359 2.730 0.073 0.218 22 482112 1889 1977 89 0.888 0.059 -0.163 2.447 0.066 0.255 23 482121 1861 1977 117 0.783 0.092 0.121 2.325 0.081 0.643 24 482122 1842 1977 136 0.726 0.119 -0.535 2.206 0.084 0.815 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 118 0.871 0.065 -0.350 2.806 0.066 0.360 STANDARD DEVIATION 20 0.045 0.015 0.321 0.603 0.008 0.190 MEDIAN (50TH QUANTILE) 125 0.886 0.062 -0.311 2.690 0.066 0.353 INTERQUARTILE RANGE 39 0.034 0.014 0.377 0.586 0.010 0.228 MINIMUM VALUE 82 0.726 0.049 -1.164 2.191 0.054 -0.004 LOWER HINGE (25TH QUANTILE) 97 0.863 0.055 -0.520 2.430 0.061 0.220 UPPER HINGE (75TH QUANTILE) 136 0.896 0.069 -0.143 3.016 0.070 0.447 MAXIMUM VALUE 147 0.923 0.119 0.152 4.730 0.084 0.815 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.521 0.166 0.010 -0.747 3.703 -0.042 0.865 MINIMUM CORRELATION: -0.042 SERIES 482031 AND 482122 129 YEARS MAXIMUM CORRELATION: 0.865 SERIES 482041 AND 482042 123 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 0.651 0.532 0.524 SDEV 0.107 0.165 0.179 SERR 0.010 0.011 0.011 EPS 0.975 0.965 0.964 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 0.881 0.046 -0.384 2.580 0.051 0.235 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.505 -0.194 0.226 65 82 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.67 0.78 1.01 1.35 2.13 5.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.85 0.93 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 0.233 0.410 0.264 0.214 0.246 0.138 0.137 0.042 0.167 -0.011 PACF 0.233 0.376 0.143 0.013 0.092 -0.010 -0.025 -0.081 0.121 -0.078 95% C.L. 0.165 0.174 0.198 0.208 0.214 0.221 0.223 0.226 0.226 0.229 |------------------ 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 0.216 0.085 0.364 0.154 |================== 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 0.06372543 0.06859473 0.00000000 0.88658971 2 482012 1 0.55542296 0.00190415 0.00000000 0.38036355 3 482021 1 0.04519908 0.02938931 0.00000000 0.89059889 4 482022 3 0.00000000 0.00000000 -0.00050443 0.91719359 5 482031 3 0.00000000 0.00000000 0.00037489 0.85896558 6 482032 1 0.55195796 0.00216123 0.00000000 0.38279873 7 482041 1 0.38427496 0.00404433 0.00000000 0.57168925 8 482042 1 0.24188395 0.02431249 0.00000000 0.74476296 9 482051 1 0.18661065 0.01358791 0.00000000 0.79212117 10 482052 3 0.00000000 0.00000000 -0.00099222 0.94181275 11 482061 1 0.08847170 0.03437833 0.00000000 0.82922369 12 482062 1 0.15726456 0.01158907 0.00000000 0.73682863 13 482071 3 0.00000000 0.00000000 0.00004242 0.90171719 14 482072 3 0.00000000 0.00000000 -0.00030686 0.93877214 15 482081 3 0.00000000 0.00000000 -0.00105690 0.93146449 16 482082 3 0.00000000 0.00000000 -0.00081088 0.93658310 17 482091 1 0.23187767 0.00647403 0.00000000 0.71560466 18 482092 3 0.00000000 0.00000000 -0.00038992 0.91293460 19 482101 3 0.00000000 0.00000000 0.00008668 0.90431756 SERIES IDENT OPTION A B C D 20 482102 1 0.05847446 0.00957932 0.00000000 0.86909169 21 482111 3 0.00000000 0.00000000 -0.00081595 0.92861789 22 482112 3 0.00000000 0.00000000 -0.00058870 0.91458118 23 482121 1 0.34406552 0.01271683 0.00000000 0.60485953 24 482122 1 0.60939127 0.00523878 0.00000000 0.29145035 |-------------------- 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 0.065 -0.364 2.494 0.063 0.293 2 482012 1846 1977 132 1.000 0.070 -0.477 3.316 0.069 0.189 3 482021 1891 1977 87 1.000 0.052 -0.108 2.489 0.054 0.152 4 482022 1889 1977 89 1.000 0.054 -0.191 3.186 0.058 0.125 5 482031 1849 1977 129 1.000 0.083 -0.908 4.051 0.064 0.505 6 482032 1863 1977 115 1.000 0.062 0.103 2.504 0.068 0.015 7 482041 1831 1977 147 1.000 0.053 0.016 2.896 0.054 0.086 8 482042 1855 1977 123 1.000 0.070 0.244 2.892 0.072 0.179 9 482051 1883 1977 95 1.000 0.056 -0.406 2.997 0.061 0.055 10 482052 1888 1977 90 1.000 0.057 -1.033 4.518 0.065 0.008 11 482061 1836 1977 142 1.000 0.069 -0.461 3.097 0.064 0.319 12 482062 1842 1977 136 1.000 0.071 -0.021 2.348 0.071 0.174 13 482071 1879 1977 99 1.000 0.061 -0.640 3.059 0.069 0.088 14 482072 1875 1977 103 1.000 0.059 -0.707 3.194 0.071 -0.031 15 482081 1853 1977 125 1.000 0.070 -0.205 2.343 0.068 0.235 16 482082 1849 1977 129 1.000 0.062 -0.267 2.642 0.065 0.179 17 482091 1846 1977 132 1.000 0.061 -0.368 2.817 0.068 0.049 18 482092 1852 1977 126 1.000 0.054 -0.201 2.399 0.058 0.114 19 482101 1838 1977 140 1.000 0.060 -0.295 2.711 0.059 0.243 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.053 -0.295 2.660 0.053 0.217 21 482111 1896 1977 82 1.000 0.065 -0.277 2.818 0.072 0.125 22 482112 1889 1977 89 1.000 0.064 -0.037 2.251 0.065 0.201 23 482121 1861 1977 117 1.000 0.069 0.001 3.122 0.080 -0.056 24 482122 1842 1977 136 1.000 0.118 0.082 3.919 0.083 0.559 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.065 -0.284 2.947 0.066 0.168 STANDARD DEVIATION 20 0.000 0.013 0.314 0.565 0.008 0.148 MEDIAN (50TH QUANTILE) 125 1.000 0.062 -0.272 2.855 0.065 0.163 INTERQUARTILE RANGE 39 0.000 0.012 0.405 0.656 0.010 0.155 MINIMUM VALUE 82 1.000 0.052 -1.033 2.251 0.053 -0.056 LOWER HINGE (25TH QUANTILE) 97 1.000 0.057 -0.434 2.499 0.060 0.070 UPPER HINGE (75TH QUANTILE) 136 1.000 0.069 -0.029 3.154 0.070 0.226 MAXIMUM VALUE 147 1.000 0.118 0.244 4.518 0.083 0.559 |------------------------ 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 0.063 -0.348 2.381 0.063 0.260 2 482012 1846 1977 132 1.000 0.067 -0.406 3.228 0.069 0.119 3 482021 1891 1977 87 1.000 0.051 -0.112 2.389 0.054 0.120 4 482022 1889 1977 89 1.000 0.053 -0.266 3.233 0.058 0.090 5 482031 1849 1977 129 1.000 0.074 -0.568 3.501 0.064 0.361 6 482032 1863 1977 115 1.000 0.061 0.131 2.552 0.068 -0.016 7 482041 1831 1977 147 1.000 0.052 0.092 2.942 0.054 0.051 8 482042 1855 1977 123 1.000 0.068 0.204 2.843 0.072 0.139 9 482051 1883 1977 95 1.000 0.055 -0.442 3.140 0.061 0.030 10 482052 1888 1977 90 1.000 0.056 -0.992 4.545 0.065 -0.037 11 482061 1836 1977 142 1.000 0.066 -0.407 2.943 0.064 0.241 12 482062 1842 1977 136 1.000 0.068 -0.022 2.365 0.071 0.106 13 482071 1879 1977 99 1.000 0.058 -0.581 2.797 0.069 -0.023 14 482072 1875 1977 103 1.000 0.056 -0.599 2.743 0.071 -0.138 15 482081 1853 1977 125 1.000 0.065 -0.104 2.467 0.068 0.101 16 482082 1849 1977 129 1.000 0.059 -0.255 2.857 0.065 0.095 17 482091 1846 1977 132 1.000 0.060 -0.381 2.806 0.068 0.028 18 482092 1852 1977 126 1.000 0.053 -0.144 2.473 0.058 0.057 19 482101 1838 1977 140 1.000 0.056 -0.339 2.780 0.059 0.143 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.052 -0.317 2.621 0.053 0.178 21 482111 1896 1977 82 1.000 0.057 -0.371 2.763 0.072 -0.128 22 482112 1889 1977 89 1.000 0.057 -0.090 2.641 0.065 -0.010 23 482121 1861 1977 117 1.000 0.067 0.011 3.052 0.080 -0.096 24 482122 1842 1977 136 0.998 0.092 -0.077 4.180 0.083 0.318 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.061 -0.266 2.927 0.066 0.083 STANDARD DEVIATION 20 0.000 0.009 0.273 0.533 0.008 0.129 MEDIAN (50TH QUANTILE) 125 1.000 0.059 -0.292 2.801 0.065 0.092 INTERQUARTILE RANGE 39 0.000 0.011 0.323 0.510 0.010 0.155 MINIMUM VALUE 82 0.998 0.051 -0.992 2.365 0.053 -0.138 LOWER HINGE (25TH QUANTILE) 97 1.000 0.056 -0.407 2.587 0.060 -0.013 UPPER HINGE (75TH QUANTILE) 136 1.000 0.066 -0.083 3.096 0.070 0.141 MAXIMUM VALUE 147 1.000 0.092 0.204 4.545 0.083 0.361 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.543 0.117 0.007 -0.520 3.082 0.183 0.842 MINIMUM CORRELATION: 0.183 SERIES 482012 AND 482052 90 YEARS MAXIMUM CORRELATION: 0.842 SERIES 482021 AND 482022 87 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 0.618 0.545 0.556 SDEV 0.111 0.157 0.163 SERR 0.010 0.010 0.010 EPS 0.971 0.966 0.968 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 0.999 0.045 -0.120 2.550 0.050 -0.043 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.159 -0.049 0.087 52 95 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 0.99 1.00 1.10 2.09 5.71 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 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 -0.043 0.213 0.026 0.003 0.062 -0.060 -0.010 -0.167 0.047 -0.190 PACF -0.043 0.211 0.045 -0.041 0.048 -0.052 -0.040 -0.157 0.054 -0.132 95% C.L. 0.165 0.165 0.173 0.173 0.173 0.173 0.174 0.174 0.178 0.179 |------------------ 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 0.050 -0.034 0.215 |======================= 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 -0.102 0.167 -0.025 -0.013 0.035 -0.071 -0.028 -0.185 0.069 -0.210 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 -0.102 2 -0.086 0.158 3 -0.087 0.159 0.006 4 -0.087 0.166 0.002 -0.042 5 -0.085 0.165 -0.004 -0.039 0.035 6 -0.083 0.163 -0.004 -0.030 0.030 -0.058 7 -0.086 0.165 -0.006 -0.030 0.039 -0.063 -0.054 8 -0.096 0.154 0.001 -0.035 0.038 -0.033 -0.069 -0.178 9 -0.086 0.157 0.003 -0.037 0.039 -0.034 -0.077 -0.173 0.054 10 -0.078 0.130 -0.009 -0.043 0.046 -0.040 -0.077 -0.148 0.040 -0.159 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) 720.03 720.49 718.75 720.75 722.48 724.31 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 725.80 727.38 724.65 726.23 724.46 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 -0.086 0.158 R-SQUARED DUE TO POOLED AUTOREGRESSION: 3.52 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 103.65 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 -0.086 0.166 -0.028 0.029 -0.007 0.005 -0.002 0.001 0.000 0.0002 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 0.136 0.191 0.265 2 482012 2 0.055 0.099 0.170 3 482021 2 0.041 0.102 0.163 4 482022 2 0.052 0.072 0.198 5 482031 2 0.192 0.274 0.255 6 482032 2 0.016 -0.015 0.121 7 482041 2 0.072 0.039 0.262 8 482042 2 0.107 0.098 0.299 9 482051 2 0.003 0.029 0.043 10 482052 2 0.015 -0.036 0.012 11 482061 2 0.161 0.164 0.323 12 482062 2 0.076 0.079 0.253 13 482071 2 0.048 -0.019 0.191 14 482072 2 0.048 -0.116 0.170 15 482081 2 0.100 0.072 0.290 16 482082 2 0.102 0.066 0.306 17 482091 2 0.041 0.022 0.200 18 482092 2 0.013 0.052 0.097 19 482101 2 0.037 0.125 0.125 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 482102 2 0.055 0.152 0.153 21 482111 2 0.022 -0.121 0.063 22 482112 2 0.004 -0.010 0.059 23 482121 2 0.027 -0.083 0.135 24 482122 2 0.142 0.273 0.145 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.065 0.063 0.179 STANDARD DEVIATION 0 0.052 0.104 0.089 MEDIAN 2 0.050 0.069 0.170 INTERQUARTILE RANGE 0 0.077 0.126 0.136 MINIMUM VALUE 2 0.003 -0.121 0.012 LOWER HINGE 2 0.025 -0.012 0.123 UPPER HINGE 2 0.101 0.114 0.259 MAXIMUM VALUE 2 0.192 0.274 0.323 |------------------- 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 0.059 -0.407 2.407 0.069 -0.012 2 482012 1846 1977 132 1.000 0.066 -0.507 3.450 0.072 -0.019 3 482021 1891 1977 87 1.000 0.050 -0.109 2.372 0.057 -0.004 4 482022 1889 1977 89 1.000 0.051 -0.274 3.169 0.058 -0.014 5 482031 1849 1977 129 1.000 0.066 -0.676 3.981 0.074 -0.013 6 482032 1863 1977 115 1.000 0.060 0.076 2.570 0.066 0.003 7 482041 1831 1977 147 1.000 0.050 0.028 3.249 0.054 0.008 8 482042 1855 1977 123 1.000 0.064 0.086 2.749 0.073 0.003 9 482051 1883 1977 95 1.000 0.055 -0.436 3.189 0.062 0.000 10 482052 1888 1977 90 1.000 0.056 -1.020 4.628 0.064 -0.001 11 482061 1836 1977 142 1.000 0.060 -0.567 3.631 0.067 -0.021 12 482062 1842 1977 136 1.000 0.066 -0.202 2.616 0.071 -0.009 13 482071 1879 1977 99 1.000 0.057 -0.659 3.158 0.067 -0.020 14 482072 1875 1977 103 1.000 0.055 -0.684 3.110 0.063 0.002 15 482081 1853 1977 125 1.000 0.061 -0.181 2.835 0.069 -0.026 16 482082 1849 1977 129 1.000 0.056 -0.189 3.023 0.065 0.004 17 482091 1846 1977 132 1.000 0.059 -0.478 3.107 0.067 -0.003 18 482092 1852 1977 126 1.000 0.052 -0.244 2.658 0.060 0.004 19 482101 1838 1977 140 1.000 0.055 -0.386 2.918 0.062 0.004 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.051 -0.343 2.843 0.058 -0.004 21 482111 1896 1977 82 1.000 0.057 -0.405 3.071 0.068 0.003 22 482112 1889 1977 89 1.000 0.057 -0.093 2.615 0.065 -0.001 23 482121 1861 1977 117 1.000 0.066 -0.066 3.085 0.074 0.000 24 482122 1842 1977 136 1.000 0.087 -0.052 4.314 0.094 -0.021 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.059 -0.325 3.115 0.067 -0.006 STANDARD DEVIATION 20 0.000 0.008 0.276 0.563 0.008 0.010 MEDIAN (50TH QUANTILE) 125 1.000 0.057 -0.309 3.078 0.066 -0.002 INTERQUARTILE RANGE 39 0.000 0.008 0.392 0.516 0.008 0.017 MINIMUM VALUE 82 1.000 0.050 -1.020 2.372 0.054 -0.026 LOWER HINGE (25TH QUANTILE) 97 1.000 0.055 -0.493 2.703 0.062 -0.014 UPPER HINGE (75TH QUANTILE) 136 1.000 0.063 -0.101 3.219 0.070 0.003 MAXIMUM VALUE 147 1.000 0.087 0.086 4.628 0.094 0.008 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.555 0.108 0.006 -0.484 3.455 0.182 0.831 MINIMUM CORRELATION: 0.182 SERIES 482012 AND 482052 90 YEARS MAXIMUM CORRELATION: 0.831 SERIES 482021 AND 482022 87 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 0.643 0.546 0.551 SDEV 0.083 0.166 0.156 SERR 0.008 0.011 0.009 EPS 0.974 0.966 0.967 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 1.000 0.043 -0.252 2.910 0.051 -0.133 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.194 -0.061 0.098 39 108 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 0.70 1.01 1.13 1.82 19.10 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.86 0.92 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 -0.133 0.016 0.009 -0.024 0.058 -0.044 -0.020 -0.131 0.099 -0.162 PACF -0.133 -0.002 0.012 -0.022 0.053 -0.030 -0.030 -0.142 0.069 -0.149 95% C.L. 0.165 0.168 0.168 0.168 0.168 0.169 0.169 0.169 0.172 0.173 |------------------ 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 1 0.018 -0.134 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.002 0.001 0.009 -0.015 0.051 -0.040 -0.044 -0.126 0.063 -0.169 PACF 0.002 0.001 0.009 -0.015 0.051 -0.041 -0.044 -0.128 0.067 -0.177 95% C.L. 0.165 0.165 0.165 0.165 0.165 0.165 0.166 0.166 0.169 0.169 |----------------- 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 0.000 0.002 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 1831 1977 147 1.000 0.044 -0.173 2.649 0.051 -0.097 |------------ 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 -0.097 0.161 -0.010 -0.003 0.051 -0.067 -0.008 -0.159 0.063 -0.183 PACF -0.097 0.153 0.019 -0.028 0.049 -0.056 -0.035 -0.149 0.048 -0.139 95% C.L. 0.165 0.166 0.171 0.171 0.171 0.171 0.172 0.172 0.176 0.176 |------------------- 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 0.034 -0.083 0.156 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.21 MINUTES