RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM048T.rwl.conv LOG FILE PROCESSED: GERM048T.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: 029 1 Silberberg (D), EU-Pr. DENSITY_LATE PCAB - 029 2 Germany Norway spruce 1320 4750-759 1871 1995 - 029 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 029011 1873 1995 123 6.749 0.789 -1.010 4.633 0.125 0.122 2 029013 1873 1995 123 6.437 0.742 -0.756 4.508 0.117 0.090 3 029015 1873 1995 123 6.910 0.781 -0.758 4.197 0.104 0.300 4 029017 1873 1995 123 6.762 0.704 -1.228 6.054 0.111 0.016 5 029021 1872 1995 124 7.152 0.800 -0.366 3.237 0.111 0.190 6 029023 1872 1995 124 6.939 0.718 -0.480 4.567 0.117 -0.040 7 029025 1872 1995 124 7.091 0.720 -0.589 4.691 0.107 -0.027 8 029027 1872 1995 124 6.597 0.738 -0.594 4.008 0.117 0.028 9 029031 1887 1995 109 6.308 0.850 -0.284 3.175 0.128 0.280 10 029033 1887 1995 109 6.504 0.770 -0.391 3.502 0.120 0.174 11 029035 1887 1995 109 6.596 0.742 -0.458 3.712 0.124 0.041 12 029037 1888 1995 108 6.277 0.633 -0.308 3.710 0.116 -0.034 13 029041 1879 1995 117 6.457 0.923 -0.566 3.536 0.166 -0.040 14 029043 1877 1995 119 6.596 0.804 -0.363 2.737 0.144 -0.032 15 029045 1877 1995 119 6.488 0.851 -0.729 3.741 0.149 0.037 16 029047 1881 1995 115 6.646 0.899 -0.237 2.605 0.131 0.221 17 029051 1871 1995 125 5.620 0.843 -0.715 3.542 0.184 -0.159 18 029053 1871 1995 125 5.649 0.876 -0.415 3.408 0.172 0.034 19 029055 1871 1995 125 5.960 0.822 -0.422 3.281 0.165 -0.077 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 029057 1871 1995 125 5.836 0.894 -0.230 3.142 0.175 -0.007 NUMBER OF SERIES READ IN: 20 FROM 1871 TO 1995 125 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 6.479 0.795 -0.545 3.799 0.134 0.056 STANDARD DEVIATION 6 0.437 0.076 0.261 0.802 0.025 0.123 MEDIAN (50TH QUANTILE) 123 6.550 0.794 -0.469 3.626 0.125 0.031 INTERQUARTILE RANGE 8 0.463 0.111 0.357 1.093 0.041 0.181 MINIMUM VALUE 108 5.620 0.633 -1.228 2.605 0.104 -0.159 LOWER HINGE (25TH QUANTILE) 116 6.293 0.740 -0.722 3.259 0.116 -0.033 UPPER HINGE (75TH QUANTILE) 124 6.756 0.851 -0.365 4.352 0.157 0.148 MAXIMUM VALUE 125 7.152 0.923 -0.230 6.054 0.184 0.300 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.676 0.109 0.008 -0.761 3.431 0.374 0.880 MINIMUM CORRELATION: 0.374 SERIES 029021 AND 029053 124 YEARS MAXIMUM CORRELATION: 0.880 SERIES 029011 AND 029017 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 93.06 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1896. 1930. 1955. CORR 6. 190. 190. RBAR 0.825 0.787 0.740 SDEV 0.053 0.082 0.083 SERR 0.022 0.006 0.006 EPS 0.988 0.987 0.983 NSS 17.9 20.0 20.0 |======================== 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 1871 1995 125 6.504 0.668 -0.811 4.470 0.116 -0.055 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.122 -0.030 0.823 29 96 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.23 1.00 1.07 1.30 2.01 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.69 0.87 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 123. 8. 108. 116. 124. 125. |----------- 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 -0.054 0.249 0.127 0.160 0.120 0.074 0.146 0.022 0.079 0.106 PACF -0.054 0.247 0.161 0.128 0.080 0.006 0.076 -0.024 -0.007 0.073 95% C.L. 0.179 0.179 0.190 0.193 0.197 0.199 0.200 0.204 0.204 0.205 |------------------ 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 0.105 -0.082 0.256 0.163 |================== 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 029011 3 0.00000000 0.00000000 0.00601314 6.37637234 2 029013 3 0.00000000 0.00000000 0.00490352 6.13346148 3 029015 3 0.00000000 0.00000000 0.00748746 6.44553375 4 029017 3 0.00000000 0.00000000 0.00420787 6.50147009 5 029021 3 0.00000000 0.00000000 0.00927515 6.57272243 6 029023 3 0.00000000 0.00000000 0.00368576 6.70859146 7 029025 3 0.00000000 0.00000000 0.00798779 6.59173107 8 029027 1 0.24149807 0.03773439 0.00000000 6.54635906 9 029031 3 0.00000000 0.00000000 -0.00596849 6.63643217 10 029033 3 0.00000000 0.00000000 0.00750644 6.09164095 11 029035 3 0.00000000 0.00000000 0.00344287 6.40688086 12 029037 3 0.00000000 0.00000000 -0.00056975 6.30855131 13 029041 3 0.00000000 0.00000000 0.00493549 6.16581488 14 029043 3 0.00000000 0.00000000 0.00275338 6.43051147 15 029045 3 0.00000000 0.00000000 0.00485031 6.19654465 16 029047 3 0.00000000 0.00000000 0.01156995 5.97459507 17 029051 3 0.00000000 0.00000000 -0.00244498 5.77395344 18 029053 1 1.59189522 0.01015167 0.00000000 4.75191164 19 029055 3 0.00000000 0.00000000 0.00431275 5.68837690 SERIES IDENT OPTION A B C D 20 029057 3 0.00000000 0.00000000 0.00811183 5.32511473 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 029011 1873 1995 123 1.000 0.113 -1.092 4.783 0.124 0.049 2 029013 1873 1995 123 1.000 0.112 -0.821 4.600 0.116 0.034 3 029015 1873 1995 123 1.000 0.107 -0.992 4.323 0.103 0.201 4 029017 1873 1995 123 1.000 0.102 -1.328 6.106 0.110 -0.039 5 029021 1872 1995 124 1.000 0.102 -0.507 3.625 0.110 0.025 6 029023 1872 1995 124 1.000 0.102 -0.545 4.655 0.116 -0.080 7 029025 1872 1995 124 1.000 0.093 -0.817 5.886 0.107 -0.219 8 029027 1872 1995 124 1.000 0.112 -0.552 4.003 0.116 0.022 9 029031 1887 1995 109 1.000 0.132 -0.264 3.053 0.127 0.263 10 029033 1887 1995 109 1.000 0.113 -0.403 3.575 0.119 0.077 11 029035 1887 1995 109 1.000 0.112 -0.430 3.538 0.123 0.012 12 029037 1888 1995 108 1.000 0.101 -0.309 3.721 0.115 -0.034 13 029041 1879 1995 117 1.000 0.141 -0.547 3.582 0.164 -0.073 14 029043 1877 1995 119 1.000 0.121 -0.472 2.778 0.142 -0.049 15 029045 1877 1995 119 1.000 0.129 -0.786 3.642 0.148 0.002 16 029047 1881 1995 115 1.000 0.122 -0.502 2.812 0.130 0.049 17 029051 1871 1995 125 1.000 0.149 -0.710 3.646 0.182 -0.167 18 029053 1871 1995 125 1.000 0.144 -0.593 3.669 0.170 -0.123 19 029055 1871 1995 125 1.000 0.135 -0.565 3.261 0.164 -0.118 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 029057 1871 1995 125 1.000 0.145 -0.317 3.265 0.174 -0.136 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.119 -0.628 3.926 0.133 -0.015 STANDARD DEVIATION 6 0.000 0.017 0.276 0.901 0.025 0.117 MEDIAN (50TH QUANTILE) 123 1.000 0.113 -0.550 3.644 0.124 -0.016 INTERQUARTILE RANGE 8 0.000 0.029 0.350 1.060 0.041 0.141 MINIMUM VALUE 108 1.000 0.093 -1.328 2.778 0.103 -0.219 LOWER HINGE (25TH QUANTILE) 116 1.000 0.104 -0.801 3.401 0.115 -0.099 UPPER HINGE (75TH QUANTILE) 124 1.000 0.133 -0.451 4.461 0.156 0.042 MAXIMUM VALUE 125 1.000 0.149 -0.264 6.106 0.182 0.263 |------------------------ 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 029011 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 029013 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 029015 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 029017 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 029021 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 029023 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 029025 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 029027 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 029031 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 029033 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 029035 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 029037 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 029041 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 029043 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 029045 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 029047 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 029051 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 029053 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 029055 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 029057 -67 83 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 029011 1873 1995 123 1.000 0.107 -0.992 4.554 0.124 -0.100 2 029013 1873 1995 123 1.000 0.106 -0.825 4.603 0.116 -0.118 3 029015 1873 1995 123 0.999 0.099 -0.946 4.323 0.103 0.023 4 029017 1873 1995 123 1.000 0.098 -1.276 6.108 0.110 -0.163 5 029021 1872 1995 124 1.000 0.098 -0.529 3.667 0.110 -0.058 6 029023 1872 1995 124 1.000 0.097 -0.623 4.922 0.116 -0.207 7 029025 1872 1995 124 1.000 0.093 -0.761 5.928 0.107 -0.232 8 029027 1872 1995 124 1.000 0.109 -0.484 4.273 0.116 -0.051 9 029031 1887 1995 109 0.999 0.105 -0.483 3.610 0.126 -0.166 10 029033 1887 1995 109 0.999 0.104 -0.407 3.475 0.119 -0.114 11 029035 1887 1995 109 0.999 0.101 -0.349 3.503 0.123 -0.219 12 029037 1888 1995 108 1.000 0.096 -0.435 3.462 0.115 -0.153 13 029041 1879 1995 117 1.000 0.137 -0.389 3.699 0.164 -0.175 14 029043 1877 1995 119 1.000 0.119 -0.448 2.829 0.142 -0.082 15 029045 1877 1995 119 1.000 0.123 -0.670 3.489 0.148 -0.122 16 029047 1881 1995 115 0.999 0.115 -0.452 2.908 0.130 -0.085 17 029051 1871 1995 125 1.000 0.148 -0.704 3.620 0.183 -0.188 18 029053 1871 1995 125 1.000 0.141 -0.657 3.741 0.170 -0.185 19 029055 1871 1995 125 1.000 0.132 -0.425 3.209 0.164 -0.191 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 029057 1871 1995 125 1.000 0.140 -0.298 3.285 0.174 -0.229 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.113 -0.608 3.960 0.133 -0.141 STANDARD DEVIATION 6 0.000 0.018 0.251 0.893 0.025 0.068 MEDIAN (50TH QUANTILE) 123 1.000 0.106 -0.506 3.643 0.123 -0.158 INTERQUARTILE RANGE 8 0.000 0.029 0.303 0.970 0.041 0.098 MINIMUM VALUE 108 0.999 0.093 -1.276 2.829 0.103 -0.232 LOWER HINGE (25TH QUANTILE) 116 0.999 0.098 -0.733 3.468 0.115 -0.190 UPPER HINGE (75TH QUANTILE) 124 1.000 0.128 -0.430 4.439 0.156 -0.092 MAXIMUM VALUE 125 1.000 0.148 -0.298 6.108 0.183 0.023 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.728 0.066 0.005 0.376 3.302 0.554 0.893 MINIMUM CORRELATION: 0.554 SERIES 029027 AND 029035 109 YEARS MAXIMUM CORRELATION: 0.893 SERIES 029051 AND 029057 125 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 93.06 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1896. 1930. 1955. CORR 6. 190. 190. RBAR 0.844 0.794 0.755 SDEV 0.040 0.068 0.078 SERR 0.016 0.005 0.006 EPS 0.990 0.987 0.984 NSS 17.9 20.0 20.0 |======================== 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 1871 1995 125 1.001 0.097 -0.878 4.496 0.116 -0.231 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.134 -0.021 0.081 27 98 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.08 0.32 1.00 1.04 1.35 2.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.73 0.86 0.92 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 -0.229 0.130 -0.006 0.023 -0.012 -0.049 0.052 -0.068 -0.012 0.039 PACF -0.229 0.082 0.043 0.021 -0.008 -0.062 0.032 -0.041 -0.043 0.042 95% C.L. 0.179 0.188 0.191 0.191 0.191 0.191 0.191 0.192 0.193 0.193 |------------------ 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 0.060 -0.231 |======================= 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 -0.247 0.136 -0.022 0.026 -0.008 -0.044 0.066 -0.067 -0.017 0.045 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 -0.247 2 -0.227 0.080 3 -0.230 0.087 0.031 4 -0.230 0.085 0.035 0.019 5 -0.230 0.085 0.035 0.019 0.000 6 -0.230 0.086 0.037 0.023 -0.012 -0.054 7 -0.228 0.087 0.036 0.021 -0.016 -0.043 0.048 8 -0.226 0.085 0.035 0.022 -0.015 -0.040 0.040 -0.034 9 -0.228 0.087 0.033 0.021 -0.014 -0.038 0.045 -0.046 -0.055 10 -0.226 0.089 0.031 0.023 -0.013 -0.039 0.043 -0.050 -0.045 0.044 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) 765.39 759.52 760.72 762.60 764.56 766.56 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 768.20 769.91 771.77 773.39 775.15 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 -0.247 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.10 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 106.50 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 -0.247 0.061 -0.015 0.004 -0.001 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 029011 1 0.017 -0.100 2 029013 1 0.029 -0.118 3 029015 1 0.053 0.024 4 029017 1 0.032 -0.164 5 029021 1 0.004 -0.058 6 029023 1 0.044 -0.208 7 029025 1 0.058 -0.237 8 029027 1 0.021 -0.051 9 029031 1 0.070 -0.169 10 029033 1 0.034 -0.114 11 029035 1 0.082 -0.221 12 029037 1 0.038 -0.155 13 029041 1 0.039 -0.175 14 029043 1 0.023 -0.084 15 029045 1 0.019 -0.123 16 029047 1 0.029 -0.085 17 029051 1 0.039 -0.189 18 029053 1 0.056 -0.185 19 029055 1 0.042 -0.192 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 029057 1 0.058 -0.231 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.039 -0.142 STANDARD DEVIATION 0 0.019 0.069 MEDIAN 1 0.038 -0.159 INTERQUARTILE RANGE 0 0.029 0.098 MINIMUM VALUE 1 0.004 -0.237 LOWER HINGE 1 0.026 -0.191 UPPER HINGE 1 0.055 -0.093 MAXIMUM VALUE 1 0.082 0.024 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 029011 1873 1995 123 1.000 0.106 -0.986 4.484 0.118 0.008 2 029013 1873 1995 123 1.000 0.105 -0.772 4.205 0.109 0.014 3 029015 1873 1995 123 1.000 0.098 -0.953 4.400 0.104 -0.005 4 029017 1873 1995 123 1.000 0.096 -1.192 5.468 0.102 0.012 5 029021 1872 1995 124 1.000 0.098 -0.490 3.457 0.106 0.001 6 029023 1872 1995 124 1.000 0.094 -0.422 4.160 0.103 0.003 7 029025 1872 1995 124 1.000 0.090 -0.530 4.693 0.093 0.008 8 029027 1872 1995 124 1.000 0.108 -0.437 4.062 0.112 0.006 9 029031 1887 1995 109 1.000 0.103 -0.304 3.434 0.112 0.036 10 029033 1887 1995 109 1.000 0.103 -0.344 3.266 0.111 0.017 11 029035 1887 1995 109 1.000 0.099 -0.232 3.255 0.106 0.040 12 029037 1888 1995 108 1.000 0.094 -0.300 3.291 0.104 0.017 13 029041 1879 1995 117 1.000 0.135 -0.199 3.385 0.147 0.016 14 029043 1877 1995 119 1.000 0.119 -0.378 2.784 0.136 0.008 15 029045 1877 1995 119 1.000 0.122 -0.639 3.451 0.139 0.006 16 029047 1881 1995 115 1.000 0.115 -0.420 2.785 0.123 0.012 17 029051 1871 1995 125 1.000 0.146 -0.685 3.429 0.162 0.011 18 029053 1871 1995 125 1.000 0.138 -0.585 3.572 0.152 0.027 19 029055 1871 1995 125 1.000 0.130 -0.442 3.262 0.148 0.014 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 029057 1871 1995 125 1.000 0.136 -0.260 2.814 0.153 0.017 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.112 -0.528 3.683 0.122 0.013 STANDARD DEVIATION 6 0.000 0.017 0.271 0.703 0.021 0.011 MEDIAN (50TH QUANTILE) 123 1.000 0.106 -0.440 3.442 0.112 0.012 INTERQUARTILE RANGE 8 0.000 0.028 0.337 0.918 0.038 0.010 MINIMUM VALUE 108 1.000 0.090 -1.192 2.784 0.093 -0.005 LOWER HINGE (25TH QUANTILE) 116 1.000 0.098 -0.662 3.264 0.105 0.007 UPPER HINGE (75TH QUANTILE) 124 1.000 0.126 -0.324 4.182 0.143 0.017 MAXIMUM VALUE 125 1.000 0.146 -0.199 5.468 0.162 0.040 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.705 0.074 0.005 0.080 3.436 0.460 0.873 MINIMUM CORRELATION: 0.460 SERIES 029025 AND 029035 109 YEARS MAXIMUM CORRELATION: 0.873 SERIES 029013 AND 029015 123 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 93.06 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1896. 1930. 1955. CORR 6. 190. 190. RBAR 0.804 0.774 0.741 SDEV 0.052 0.076 0.084 SERR 0.021 0.005 0.006 EPS 0.987 0.986 0.983 NSS 17.9 20.0 20.0 |======================== 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 1871 1995 125 1.001 0.095 -0.793 4.133 0.106 -0.085 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.123 -0.021 0.083 27 98 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.45 1.00 1.06 1.51 2.86 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.66 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 -0.085 0.101 0.014 0.028 -0.021 -0.045 0.033 -0.065 -0.020 0.042 PACF -0.085 0.095 0.030 0.022 -0.021 -0.055 0.028 -0.051 -0.032 0.051 95% C.L. 0.179 0.180 0.182 0.182 0.182 0.182 0.183 0.183 0.183 0.184 |------------------ 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 0.008 0.097 0.025 0.029 -0.022 -0.044 0.024 -0.065 -0.022 0.042 PACF 0.008 0.097 0.024 0.019 -0.027 -0.050 0.028 -0.056 -0.023 0.055 95% C.L. 0.179 0.179 0.181 0.181 0.181 0.181 0.181 0.181 0.182 0.182 |----------------- 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 0.010 0.008 |========================= 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 1871 1995 125 1.001 0.098 -0.875 4.570 0.118 -0.261 |------------ 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 -0.258 0.149 -0.021 0.033 -0.018 -0.047 0.046 -0.064 -0.013 0.036 PACF -0.258 0.088 0.040 0.025 -0.010 -0.064 0.024 -0.037 -0.046 0.038 95% C.L. 0.179 0.190 0.194 0.194 0.194 0.194 0.195 0.195 0.196 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 0.076 -0.261 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.23 MINUTES