RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM050E.rwl.conv LOG FILE PROCESSED: GERM050E.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 20 10 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: 043 1 Villingen-S. (D), EU-Pr. WIDTH_EARLY PCAB - 043 2 Germany Norway spruce 880 4802-821 1897 1994 - 043 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 043001 1901 1994 94 1.442 0.421 1.470 4.808 0.141 0.708 2 043002 1909 1994 86 1.521 0.571 1.353 5.245 0.170 0.752 3 043003 1899 1994 96 1.639 0.553 0.774 2.948 0.188 0.719 4 043004 1901 1994 94 1.470 0.553 1.465 4.427 0.140 0.827 5 043005 1897 1992 96 2.436 1.328 1.012 3.071 0.170 0.919 6 043006 1902 1992 91 1.707 1.071 1.653 5.077 0.197 0.879 7 043007 1900 1992 93 1.813 0.963 1.487 4.963 0.183 0.812 8 043008 1903 1992 90 2.592 1.016 1.359 5.056 0.186 0.763 9 043009 1903 1992 90 2.822 0.895 0.632 3.014 0.188 0.644 10 043010 1911 1992 82 3.318 1.041 0.795 3.353 0.242 0.519 11 043011 1900 1992 93 2.513 0.820 0.906 3.794 0.227 0.492 12 043012 1906 1992 87 1.791 0.881 1.016 3.528 0.190 0.794 13 043013 1899 1992 94 2.627 0.928 0.840 3.822 0.195 0.779 14 043014 1903 1992 90 1.847 0.935 0.820 2.988 0.183 0.890 15 043015 1899 1992 94 2.036 1.171 0.791 2.655 0.217 0.896 16 043016 1906 1992 87 2.304 1.022 0.385 2.475 0.208 0.815 17 043017 1899 1994 96 2.050 0.865 2.227 8.079 0.197 0.821 18 043018 1900 1994 95 2.310 0.790 2.163 8.494 0.179 0.702 19 043019 1899 1994 96 1.696 0.839 3.192 12.238 0.176 0.835 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 043020 1901 1994 94 1.798 0.827 3.069 12.383 0.171 0.760 NUMBER OF SERIES READ IN: 20 FROM 1897 TO 1994 98 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 92 2.087 0.875 1.371 5.121 0.187 0.766 STANDARD DEVIATION 3 0.509 0.222 0.770 2.940 0.025 0.114 MEDIAN (50TH QUANTILE) 93 1.941 0.888 1.184 4.125 0.187 0.786 INTERQUARTILE RANGE 4 0.773 0.214 0.763 2.118 0.023 0.118 MINIMUM VALUE 82 1.442 0.421 0.385 2.475 0.140 0.492 LOWER HINGE (25TH QUANTILE) 90 1.701 0.805 0.808 3.043 0.174 0.714 UPPER HINGE (75TH QUANTILE) 94 2.474 1.019 1.570 5.161 0.197 0.831 MAXIMUM VALUE 96 3.318 1.328 3.192 12.383 0.242 0.919 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.558 0.224 0.016 -0.228 2.219 0.035 0.947 MINIMUM CORRELATION: 0.035 SERIES 043012 AND 043018 87 YEARS MAXIMUM CORRELATION: 0.947 SERIES 043017 AND 043020 94 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 91.26 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 171. 190. 190. 190. 190. 190. 190. RBAR 0.474 0.522 0.423 0.369 0.370 0.401 0.470 SDEV 0.263 0.221 0.319 0.296 0.300 0.271 0.252 SERR 0.020 0.016 0.023 0.021 0.022 0.020 0.018 EPS 0.947 0.956 0.936 0.921 0.921 0.930 0.947 NSS 20.0 20.0 20.0 20.0 20.0 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 1897 1994 98 2.110 0.815 1.548 4.834 0.153 0.795 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.545 0.196 0.310 29 69 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.35 0.63 1.06 1.17 1.80 4.89 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.00 0.87 0.91 0.97 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 94. 4. 82. 90. 94. 96. |----------- 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 0.787 0.669 0.727 0.666 0.632 0.565 0.480 0.512 0.488 0.421 PACF 0.787 0.128 0.446 -0.077 0.199 -0.263 -0.005 0.086 0.010 0.036 95% C.L. 0.202 0.302 0.358 0.414 0.455 0.490 0.516 0.534 0.553 0.571 |------------------ 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 0.752 0.548 -0.074 0.449 |================== 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 043001 1 1.52382064 0.10192717 0.00000000 1.29063833 2 043002 1 2.68153000 0.22052963 0.00000000 1.39502418 3 043003 3 0.00000000 0.00000000 0.00020171 1.62917542 4 043004 1 1.98559356 0.10075259 0.00000000 1.27117181 5 043005 1 4.68068743 0.03541163 0.00000000 1.12881231 6 043006 1 4.09379911 0.06138359 0.00000000 0.99909276 7 043007 1 3.35525131 0.04424291 0.00000000 1.02829218 8 043008 1 3.63308954 0.06827868 0.00000000 2.02196813 9 043009 3 0.00000000 0.00000000 -0.02070231 3.76373291 10 043010 1 0.49697208 0.05312696 0.00000000 3.20852232 11 043011 1 1.61926579 0.02487245 0.00000000 1.88973820 12 043012 1 3.31067705 0.01806985 0.00000000 0.13752709 13 043013 1 2.85035658 0.02896200 0.00000000 1.66319668 14 043014 3 0.00000000 0.00000000 -0.02892398 3.16348553 15 043015 1 3.96383762 0.01873498 0.00000000 0.18902658 16 043016 1 3.31906152 0.02133911 0.00000000 0.81124544 17 043017 1 3.31852388 0.08084679 0.00000000 1.63996994 18 043018 1 4.47127581 0.21558787 0.00000000 2.11458468 19 043019 1 3.95819736 0.12734333 0.00000000 1.39192295 SERIES IDENT OPTION A B C D 20 043020 1 5.02868938 0.17116590 0.00000000 1.51121044 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 043001 1901 1994 94 1.000 0.203 0.705 3.766 0.139 0.480 2 043002 1909 1994 86 1.000 0.295 0.524 2.892 0.168 0.697 3 043003 1899 1994 96 1.000 0.338 0.788 2.982 0.186 0.712 4 043004 1901 1994 94 0.999 0.266 0.929 3.390 0.137 0.751 5 043005 1897 1992 96 1.003 0.293 1.179 5.831 0.168 0.726 6 043006 1902 1992 91 1.001 0.287 0.389 2.991 0.193 0.584 7 043007 1900 1992 93 1.000 0.263 0.323 2.272 0.180 0.606 8 043008 1903 1992 90 1.000 0.239 0.270 2.789 0.182 0.500 9 043009 1903 1992 90 0.999 0.245 0.432 3.479 0.185 0.460 10 043010 1911 1992 82 1.000 0.314 0.923 3.852 0.239 0.511 11 043011 1900 1992 93 1.000 0.277 0.735 3.798 0.225 0.285 12 043012 1906 1992 87 1.000 0.253 0.933 4.329 0.184 0.536 13 043013 1899 1992 94 1.000 0.226 0.060 3.350 0.193 0.493 14 043014 1903 1992 90 1.033 0.406 1.926 7.577 0.182 0.799 15 043015 1899 1992 94 1.010 0.388 0.653 3.747 0.215 0.794 16 043016 1906 1992 87 1.002 0.314 -0.012 3.030 0.205 0.687 17 043017 1899 1994 96 1.000 0.216 -0.238 3.107 0.194 0.372 18 043018 1900 1994 95 1.000 0.223 0.493 2.894 0.175 0.463 19 043019 1899 1994 96 1.000 0.211 0.384 3.188 0.173 0.426 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 043020 1901 1994 94 1.000 0.181 0.074 2.883 0.165 0.385 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 92 1.002 0.272 0.574 3.607 0.185 0.563 STANDARD DEVIATION 3 0.008 0.059 0.483 1.192 0.025 0.151 MEDIAN (50TH QUANTILE) 93 1.000 0.265 0.509 3.269 0.183 0.524 INTERQUARTILE RANGE 4 0.001 0.080 0.559 0.844 0.023 0.243 MINIMUM VALUE 82 0.999 0.181 -0.238 2.272 0.137 0.285 LOWER HINGE (25TH QUANTILE) 90 1.000 0.225 0.297 2.938 0.171 0.462 UPPER HINGE (75TH QUANTILE) 94 1.001 0.305 0.856 3.782 0.194 0.705 MAXIMUM VALUE 96 1.033 0.406 1.926 7.577 0.239 0.799 |------------------------ 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 043001 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 043002 -67 57 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 043003 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 043004 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 043005 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 043006 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 043007 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 043008 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 043009 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 043010 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 043011 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 043012 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 043013 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 043014 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 043015 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 043016 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 043017 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 043018 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 043019 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 043020 -67 62 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 043001 1901 1994 94 0.998 0.183 0.621 3.165 0.139 0.421 2 043002 1909 1994 86 0.996 0.261 0.188 3.091 0.168 0.633 3 043003 1899 1994 96 0.995 0.241 0.351 2.849 0.185 0.498 4 043004 1901 1994 94 0.998 0.192 0.400 2.746 0.136 0.560 5 043005 1897 1992 96 0.997 0.242 0.532 3.526 0.167 0.583 6 043006 1902 1992 91 0.998 0.281 0.670 3.380 0.192 0.551 7 043007 1900 1992 93 0.996 0.230 0.355 2.519 0.179 0.470 8 043008 1903 1992 90 0.999 0.233 0.307 2.889 0.182 0.466 9 043009 1903 1992 90 0.999 0.237 0.290 3.187 0.185 0.438 10 043010 1911 1992 82 0.996 0.259 -0.052 2.512 0.239 0.317 11 043011 1900 1992 93 0.998 0.265 0.674 3.957 0.225 0.236 12 043012 1906 1992 87 0.999 0.247 0.898 4.069 0.184 0.514 13 043013 1899 1992 94 0.998 0.208 -0.140 3.061 0.192 0.370 14 043014 1903 1992 90 0.991 0.250 0.557 3.175 0.180 0.598 15 043015 1899 1992 94 0.983 0.248 -0.303 3.810 0.214 0.514 16 043016 1906 1992 87 0.992 0.248 -0.625 3.469 0.205 0.465 17 043017 1899 1994 96 0.999 0.200 -0.451 3.475 0.194 0.266 18 043018 1900 1994 95 0.999 0.202 0.977 5.174 0.175 0.345 19 043019 1899 1994 96 0.999 0.201 0.622 3.789 0.173 0.370 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 043020 1901 1994 94 0.999 0.167 0.067 3.104 0.165 0.283 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 92 0.996 0.230 0.297 3.347 0.184 0.445 STANDARD DEVIATION 3 0.004 0.031 0.435 0.616 0.025 0.116 MEDIAN (50TH QUANTILE) 93 0.998 0.239 0.353 3.181 0.183 0.465 INTERQUARTILE RANGE 4 0.003 0.048 0.614 0.683 0.023 0.174 MINIMUM VALUE 82 0.983 0.167 -0.625 2.512 0.136 0.236 LOWER HINGE (25TH QUANTILE) 90 0.996 0.201 0.008 2.975 0.171 0.358 UPPER HINGE (75TH QUANTILE) 94 0.999 0.249 0.621 3.658 0.193 0.532 MAXIMUM VALUE 96 0.999 0.281 0.977 5.174 0.239 0.633 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.408 0.155 0.011 0.363 3.449 0.017 0.886 MINIMUM CORRELATION: 0.017 SERIES 043001 AND 043015 92 YEARS MAXIMUM CORRELATION: 0.886 SERIES 043005 AND 043008 90 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 91.26 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 171. 190. 190. 190. 190. 190. 190. RBAR 0.458 0.533 0.461 0.410 0.390 0.426 0.448 SDEV 0.265 0.199 0.254 0.286 0.291 0.248 0.251 SERR 0.020 0.014 0.018 0.021 0.021 0.018 0.018 EPS 0.944 0.958 0.945 0.933 0.927 0.937 0.942 NSS 20.0 20.0 20.0 20.0 20.0 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 1897 1994 98 0.985 0.157 0.157 3.001 0.145 0.397 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.361 0.138 0.031 35 63 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.12 0.36 1.00 1.02 1.38 5.87 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 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 0.393 0.120 0.085 -0.071 -0.083 -0.192 -0.267 -0.112 -0.143 -0.163 PACF 0.393 -0.041 0.062 -0.145 -0.005 -0.187 -0.135 0.051 -0.123 -0.087 95% C.L. 0.202 0.231 0.234 0.235 0.236 0.237 0.243 0.255 0.257 0.260 |------------------ 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 0.157 0.394 |======================= 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 0.377 0.110 0.103 -0.020 -0.112 -0.229 -0.259 -0.102 -0.169 -0.143 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 0.377 2 0.391 -0.037 3 0.394 -0.071 0.087 4 0.403 -0.078 0.127 -0.101 5 0.394 -0.068 0.120 -0.067 -0.085 6 0.378 -0.080 0.143 -0.080 -0.010 -0.191 7 0.355 -0.082 0.133 -0.062 -0.019 -0.145 -0.121 8 0.362 -0.073 0.134 -0.059 -0.027 -0.140 -0.143 0.061 9 0.371 -0.094 0.113 -0.063 -0.036 -0.120 -0.154 0.115 -0.151 10 0.367 -0.091 0.109 -0.066 -0.037 -0.121 -0.151 0.113 -0.141 -0.027 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) 658.09 645.10 646.96 648.22 649.22 650.51 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 648.89 649.44 651.08 650.82 652.74 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 0.377 R-SQUARED DUE TO POOLED AUTOREGRESSION: 14.19 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 116.53 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.377 0.142 0.053 0.020 0.008 0.003 0.001 0.000 0.000 0.0001 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 043001 1 0.197 0.441 2 043002 1 0.426 0.653 3 043003 1 0.273 0.509 4 043004 1 0.319 0.565 5 043005 1 0.356 0.591 6 043006 1 0.315 0.552 7 043007 1 0.229 0.471 8 043008 1 0.229 0.473 9 043009 1 0.219 0.454 10 043010 1 0.115 0.318 11 043011 1 0.074 0.248 12 043012 1 0.275 0.523 13 043013 1 0.158 0.381 14 043014 1 0.371 0.602 15 043015 1 0.274 0.523 16 043016 1 0.246 0.474 17 043017 1 0.083 0.276 18 043018 1 0.126 0.347 19 043019 1 0.146 0.382 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 043020 1 0.084 0.284 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.226 0.453 STANDARD DEVIATION 0 0.103 0.117 MEDIAN 1 0.229 0.472 INTERQUARTILE RANGE 0 0.159 0.174 MINIMUM VALUE 1 0.074 0.248 LOWER HINGE 1 0.136 0.364 UPPER HINGE 1 0.295 0.538 MAXIMUM VALUE 1 0.426 0.653 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 043001 1901 1994 94 1.000 0.164 0.908 5.069 0.158 0.039 2 043002 1909 1994 86 1.000 0.198 -0.063 4.019 0.224 0.006 3 043003 1899 1994 96 1.000 0.206 0.387 3.204 0.239 -0.079 4 043004 1901 1994 94 1.000 0.158 0.457 3.402 0.181 0.006 5 043005 1897 1992 96 1.000 0.195 0.616 4.625 0.216 -0.056 6 043006 1902 1992 91 1.000 0.234 0.475 4.508 0.264 -0.068 7 043007 1900 1992 93 1.000 0.203 0.490 3.971 0.230 -0.047 8 043008 1903 1992 90 1.000 0.206 0.482 3.406 0.226 -0.032 9 043009 1903 1992 90 1.000 0.211 0.323 3.397 0.217 0.072 10 043010 1911 1992 82 1.000 0.246 0.216 2.904 0.279 -0.039 11 043011 1900 1992 93 1.000 0.256 0.710 3.886 0.240 0.016 12 043012 1906 1992 87 1.000 0.210 0.912 3.417 0.223 0.022 13 043013 1899 1992 94 1.000 0.191 -0.373 3.176 0.219 0.040 14 043014 1903 1992 90 1.000 0.199 0.414 2.784 0.213 0.062 15 043015 1899 1992 94 1.000 0.211 -0.606 5.202 0.250 0.002 16 043016 1906 1992 87 1.000 0.217 -0.896 5.119 0.244 0.076 17 043017 1899 1994 96 1.000 0.192 -0.225 3.321 0.210 0.013 18 043018 1900 1994 95 1.000 0.190 1.066 5.845 0.205 0.027 19 043019 1899 1994 96 1.000 0.185 0.754 4.153 0.192 -0.014 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 043020 1901 1994 94 1.000 0.160 0.224 3.309 0.181 0.017 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 92 1.000 0.202 0.314 3.936 0.221 0.003 STANDARD DEVIATION 3 0.000 0.025 0.517 0.864 0.029 0.045 MEDIAN (50TH QUANTILE) 93 1.000 0.201 0.436 3.652 0.221 0.010 INTERQUARTILE RANGE 4 0.000 0.021 0.587 1.251 0.032 0.069 MINIMUM VALUE 82 1.000 0.158 -0.896 2.784 0.158 -0.079 LOWER HINGE (25TH QUANTILE) 90 1.000 0.190 0.076 3.315 0.207 -0.036 UPPER HINGE (75TH QUANTILE) 94 1.000 0.211 0.663 4.566 0.239 0.033 MAXIMUM VALUE 96 1.000 0.256 1.066 5.845 0.279 0.076 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.455 0.122 0.009 0.716 3.757 0.198 0.866 MINIMUM CORRELATION: 0.198 SERIES 043001 AND 043018 94 YEARS MAXIMUM CORRELATION: 0.866 SERIES 043005 AND 043008 90 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 91.26 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 171. 190. 190. 190. 190. 190. 190. RBAR 0.416 0.459 0.509 0.532 0.447 0.380 0.473 SDEV 0.232 0.189 0.179 0.168 0.201 0.238 0.202 SERR 0.018 0.014 0.013 0.012 0.015 0.017 0.015 EPS 0.934 0.944 0.954 0.958 0.942 0.924 0.947 NSS 20.0 20.0 20.0 20.0 20.0 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 1897 1994 98 0.994 0.141 0.349 3.423 0.164 -0.017 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.374 0.125 0.015 39 59 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.49 1.00 1.05 1.53 5.91 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.86 0.92 0.99 |----------- 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 -0.017 -0.097 0.090 -0.063 -0.007 -0.113 -0.215 0.062 -0.071 -0.104 PACF -0.017 -0.097 0.088 -0.071 0.009 -0.137 -0.212 0.026 -0.101 -0.086 95% C.L. 0.202 0.202 0.204 0.206 0.206 0.206 0.209 0.218 0.218 0.219 |------------------ 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 -0.002 -0.096 0.088 -0.062 -0.010 -0.117 -0.216 0.057 -0.071 -0.105 PACF -0.002 -0.096 0.088 -0.073 0.008 -0.141 -0.209 0.027 -0.103 -0.085 95% C.L. 0.202 0.202 0.204 0.205 0.206 0.206 0.209 0.218 0.218 0.219 |----------------- 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 0.009 -0.002 |========================= 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 1897 1994 98 0.994 0.150 0.264 3.130 0.142 0.354 |------------ 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 0.351 0.065 0.068 -0.057 -0.093 -0.205 -0.260 -0.083 -0.127 -0.128 PACF 0.351 -0.066 0.077 -0.119 -0.035 -0.193 -0.136 0.056 -0.135 -0.050 95% C.L. 0.202 0.226 0.226 0.227 0.228 0.229 0.237 0.248 0.249 0.252 |------------------- 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 0.127 0.352 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.27 MINUTES