RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM055I.rwl.conv LOG FILE PROCESSED: GERM055I.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: 054 1 Sirnitz NE (D), EU-Pr. DENSITY_EARLY PCAB - 054 2 Germany Norway spruce 940 4747-745 1867 1995 - 054 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 054101 1879 1995 117 3.197 0.245 0.370 3.205 0.063 0.452 2 054103 1878 1995 118 3.554 0.281 0.865 5.888 0.068 0.314 3 054105 1878 1995 118 3.229 0.237 0.474 4.206 0.064 0.325 4 054107 1878 1995 118 3.213 0.239 1.082 6.040 0.056 0.426 5 054111 1877 1995 119 3.273 0.283 -0.166 3.864 0.063 0.526 6 054113 1877 1995 119 3.156 0.300 0.689 5.039 0.066 0.381 7 054115 1878 1995 118 3.560 0.278 -0.585 3.936 0.051 0.666 8 054117 1877 1995 119 3.390 0.320 -0.653 3.615 0.059 0.670 9 054131 1877 1995 119 3.197 0.333 1.548 7.802 0.070 0.463 10 054133 1876 1995 120 3.214 0.304 1.128 4.558 0.074 0.439 11 054135 1876 1995 120 3.125 0.318 2.171 10.097 0.064 0.571 12 054137 1876 1995 120 2.883 0.297 1.977 9.676 0.071 0.561 13 054141 1879 1995 117 2.996 0.257 1.219 8.474 0.062 0.467 14 054143 1875 1995 121 3.017 0.208 0.211 2.666 0.059 0.441 15 054145 1873 1980 108 3.186 0.262 0.268 2.652 0.059 0.583 16 054147 1873 1995 123 3.112 0.218 0.374 3.509 0.050 0.590 17 054181 1870 1995 126 2.739 0.301 -0.103 3.419 0.070 0.670 18 054183 1868 1995 128 3.234 0.387 -0.116 2.856 0.065 0.729 19 054185 1867 1995 129 3.308 0.434 0.661 5.946 0.062 0.734 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 054187 1867 1995 129 3.220 0.327 1.840 11.132 0.058 0.585 NUMBER OF SERIES READ IN: 20 FROM 1867 TO 1995 129 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 3.190 0.291 0.663 5.429 0.063 0.530 STANDARD DEVIATION 4 0.194 0.055 0.816 2.647 0.006 0.126 MEDIAN (50TH QUANTILE) 119 3.205 0.290 0.568 4.382 0.063 0.543 INTERQUARTILE RANGE 4 0.134 0.068 1.120 3.457 0.008 0.188 MINIMUM VALUE 108 2.739 0.208 -0.653 2.652 0.050 0.314 LOWER HINGE (25TH QUANTILE) 118 3.119 0.251 0.054 3.464 0.059 0.440 UPPER HINGE (75TH QUANTILE) 122 3.253 0.319 1.173 6.921 0.067 0.628 MAXIMUM VALUE 129 3.560 0.434 2.171 11.132 0.074 0.734 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.332 0.243 0.018 0.027 2.671 -0.334 0.839 MINIMUM CORRELATION: -0.334 SERIES 054135 AND 054185 120 YEARS MAXIMUM CORRELATION: 0.839 SERIES 054183 AND 054185 128 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 91.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1877. 1890. 1900. 1910. 1920. 1930. 1940. 1950. 1960. 1970. CORR 1. 190. 190. 190. 190. 190. 190. 190. 190. 190. RBAR 0.982 0.383 0.327 0.414 0.542 0.480 0.547 0.547 0.347 0.380 SDEV 0.000 0.285 0.260 0.245 0.185 0.210 0.188 0.153 0.254 0.262 SERR 0.000 0.021 0.019 0.018 0.013 0.015 0.014 0.011 0.018 0.019 EPS 0.998 0.925 0.907 0.934 0.959 0.949 0.960 0.960 0.914 0.925 NSS 12.1 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1980. CORR 171. RBAR 0.425 SDEV 0.234 SERR 0.018 EPS 0.935 NSS 19.5 |======================== 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 1867 1995 129 3.198 0.276 3.488 25.358 0.048 0.494 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.053 -0.022 0.375 21 108 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.14 0.35 1.00 1.02 1.37 15.18 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.68 0.87 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 119. 4. 108. 118. 122. 129. |----------- 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 0.491 0.240 0.104 -0.038 -0.113 -0.089 -0.012 -0.049 0.012 0.164 PACF 0.491 0.000 -0.018 -0.108 -0.068 0.018 0.068 -0.083 0.059 0.177 95% C.L. 0.176 0.214 0.223 0.224 0.224 0.226 0.227 0.227 0.227 0.227 |------------------ 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 1 0.387 0.622 |================== 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 054101 3 0.00000000 0.00000000 -0.00145574 3.28332448 2 054103 3 0.00000000 0.00000000 0.00081733 3.50560617 3 054105 3 0.00000000 0.00000000 -0.00113549 3.29654503 4 054107 3 0.00000000 0.00000000 -0.00037466 3.23559761 5 054111 3 0.00000000 0.00000000 0.00220075 3.14114809 6 054113 3 0.00000000 0.00000000 0.00087779 3.10380292 7 054115 3 0.00000000 0.00000000 0.00342197 3.35656238 8 054117 3 0.00000000 0.00000000 0.00517213 3.08009267 9 054131 3 0.00000000 0.00000000 0.00315596 3.00736499 10 054133 3 0.00000000 0.00000000 0.00021679 3.20096779 11 054135 1 2.29677987 0.30460733 0.00000000 3.07158399 12 054137 3 0.00000000 0.00000000 -0.00254511 3.03664565 13 054141 1 0.42614189 0.01445066 0.00000000 2.79164410 14 054143 3 0.00000000 0.00000000 0.00297555 2.83526850 15 054145 3 0.00000000 0.00000000 0.00432827 2.95012808 16 054147 3 0.00000000 0.00000000 -0.00191407 3.23111153 17 054181 3 0.00000000 0.00000000 0.00519040 2.40921903 18 054183 3 0.00000000 0.00000000 0.00716533 2.77135205 19 054185 3 0.00000000 0.00000000 0.00550771 2.94967294 SERIES IDENT OPTION A B C D 20 054187 3 0.00000000 0.00000000 0.00299312 3.02552438 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 054101 1879 1995 117 1.000 0.075 0.210 3.116 0.062 0.431 2 054103 1878 1995 118 1.000 0.079 1.047 6.754 0.067 0.297 3 054105 1878 1995 118 1.000 0.072 0.304 3.690 0.064 0.313 4 054107 1878 1995 118 1.000 0.074 0.954 5.640 0.056 0.424 5 054111 1877 1995 119 1.000 0.084 0.388 4.206 0.062 0.467 6 054113 1877 1995 119 1.000 0.095 0.818 4.975 0.065 0.369 7 054115 1878 1995 118 1.000 0.072 -0.106 3.473 0.051 0.588 8 054117 1877 1995 119 1.000 0.081 0.255 5.352 0.058 0.471 9 054131 1877 1995 119 1.000 0.100 2.392 13.276 0.070 0.371 10 054133 1876 1995 120 1.000 0.095 1.157 4.695 0.073 0.434 11 054135 1876 1995 120 1.000 0.073 0.660 3.988 0.063 0.324 12 054137 1876 1995 120 1.000 0.096 1.388 7.141 0.070 0.527 13 054141 1879 1995 117 1.000 0.078 0.748 6.587 0.061 0.366 14 054143 1875 1995 121 1.000 0.060 0.490 3.278 0.059 0.225 15 054145 1873 1980 108 1.000 0.070 0.523 3.161 0.058 0.381 16 054147 1873 1995 123 1.000 0.066 0.127 3.184 0.050 0.558 17 054181 1870 1995 126 1.000 0.088 0.382 2.946 0.070 0.434 18 054183 1868 1995 128 1.000 0.092 1.662 10.999 0.065 0.423 19 054185 1867 1995 129 1.000 0.123 2.888 17.863 0.062 0.606 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 054187 1867 1995 129 1.000 0.099 3.430 22.326 0.058 0.493 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.084 0.986 6.832 0.062 0.425 STANDARD DEVIATION 4 0.000 0.015 0.949 5.316 0.006 0.099 MEDIAN (50TH QUANTILE) 119 1.000 0.080 0.704 4.835 0.062 0.427 INTERQUARTILE RANGE 4 0.000 0.022 0.929 3.572 0.008 0.115 MINIMUM VALUE 108 1.000 0.060 -0.106 2.946 0.050 0.225 LOWER HINGE (25TH QUANTILE) 118 1.000 0.072 0.343 3.375 0.058 0.367 UPPER HINGE (75TH QUANTILE) 122 1.000 0.095 1.272 6.948 0.066 0.482 MAXIMUM VALUE 129 1.000 0.123 3.430 22.326 0.073 0.606 |------------------------ 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 054101 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 054103 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 054105 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 054107 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 054111 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 054113 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 054115 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 054117 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 054131 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 054133 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 054135 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 054137 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 054141 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 054143 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 054145 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 054147 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 054181 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 054183 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 054185 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 054187 -67 86 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 054101 1879 1995 117 1.000 0.065 0.473 3.328 0.062 0.234 2 054103 1878 1995 118 1.000 0.076 1.098 6.686 0.067 0.247 3 054105 1878 1995 118 1.000 0.069 0.594 4.704 0.063 0.245 4 054107 1878 1995 118 1.000 0.071 0.765 4.946 0.056 0.398 5 054111 1877 1995 119 1.000 0.075 1.337 9.504 0.062 0.286 6 054113 1877 1995 119 1.000 0.080 1.237 7.243 0.065 0.104 7 054115 1878 1995 118 1.000 0.061 -0.134 3.470 0.051 0.413 8 054117 1877 1995 119 1.000 0.078 0.739 8.020 0.058 0.411 9 054131 1877 1995 119 1.000 0.084 1.776 8.218 0.070 0.219 10 054133 1876 1995 120 1.000 0.085 0.860 3.476 0.073 0.326 11 054135 1876 1995 120 1.000 0.066 0.535 3.370 0.063 0.211 12 054137 1876 1995 120 1.000 0.091 0.786 5.047 0.070 0.501 13 054141 1879 1995 117 1.000 0.075 0.763 7.064 0.061 0.319 14 054143 1875 1995 121 1.000 0.058 0.488 3.354 0.059 0.186 15 054145 1873 1980 108 1.000 0.062 0.424 3.264 0.058 0.232 16 054147 1873 1995 123 1.000 0.060 0.095 3.569 0.050 0.461 17 054181 1870 1995 126 1.000 0.082 0.673 4.176 0.070 0.329 18 054183 1868 1995 128 1.000 0.089 1.606 10.707 0.065 0.404 19 054185 1867 1995 129 0.999 0.107 2.703 17.780 0.062 0.553 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 054187 1867 1995 129 1.000 0.090 2.443 15.275 0.058 0.474 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.076 0.963 6.660 0.062 0.328 STANDARD DEVIATION 4 0.000 0.013 0.719 4.084 0.006 0.120 MEDIAN (50TH QUANTILE) 119 1.000 0.075 0.764 4.996 0.062 0.322 INTERQUARTILE RANGE 4 0.000 0.019 0.775 4.646 0.008 0.179 MINIMUM VALUE 108 0.999 0.058 -0.134 3.264 0.050 0.104 LOWER HINGE (25TH QUANTILE) 118 1.000 0.066 0.511 3.473 0.058 0.233 UPPER HINGE (75TH QUANTILE) 122 1.000 0.084 1.287 8.119 0.066 0.412 MAXIMUM VALUE 129 1.000 0.107 2.703 17.780 0.073 0.553 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.405 0.156 0.011 0.604 3.124 0.096 0.832 MINIMUM CORRELATION: 0.096 SERIES 054113 AND 054147 119 YEARS MAXIMUM CORRELATION: 0.832 SERIES 054185 AND 054187 129 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 91.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1877. 1890. 1900. 1910. 1920. 1930. 1940. 1950. 1960. 1970. CORR 1. 190. 190. 190. 190. 190. 190. 190. 190. 190. RBAR 0.973 0.435 0.321 0.435 0.519 0.513 0.546 0.541 0.362 0.361 SDEV 0.000 0.240 0.237 0.222 0.191 0.199 0.174 0.166 0.241 0.257 SERR 0.000 0.017 0.017 0.016 0.014 0.014 0.013 0.012 0.017 0.019 EPS 0.998 0.939 0.904 0.939 0.956 0.955 0.960 0.959 0.919 0.919 NSS 12.1 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1980. CORR 171. RBAR 0.475 SDEV 0.190 SERR 0.014 EPS 0.947 NSS 19.5 |======================== 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 1867 1995 129 1.005 0.085 3.299 20.793 0.054 0.481 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.316 0.107 -0.052 28 101 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.99 1.01 1.12 2.11 20.89 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.64 0.87 0.93 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 0.478 0.227 0.085 -0.080 -0.202 -0.158 -0.025 -0.064 0.000 0.108 PACF 0.478 -0.001 -0.030 -0.141 -0.141 0.022 0.114 -0.106 0.030 0.090 95% C.L. 0.176 0.213 0.220 0.221 0.222 0.227 0.231 0.231 0.231 0.231 |------------------ 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 0.340 0.580 |======================= 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 0.327 0.241 0.085 0.008 -0.102 -0.152 -0.068 -0.149 -0.178 -0.139 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 0.327 2 0.277 0.150 3 0.283 0.160 -0.035 4 0.281 0.168 -0.021 -0.049 5 0.275 0.166 -0.002 -0.018 -0.112 6 0.264 0.164 -0.002 -0.001 -0.085 -0.098 7 0.269 0.168 -0.002 -0.001 -0.093 -0.111 0.049 8 0.274 0.157 -0.012 -0.002 -0.094 -0.093 0.077 -0.103 9 0.261 0.166 -0.024 -0.013 -0.094 -0.095 0.096 -0.068 -0.125 10 0.257 0.164 -0.020 -0.017 -0.097 -0.095 0.095 -0.062 -0.115 -0.037 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) 605.56 593.02 592.07 593.91 595.59 595.96 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 596.72 598.41 599.04 599.01 600.83 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 0.277 0.150 R-SQUARED DUE TO POOLED AUTOREGRESSION: 12.68 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 114.53 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.277 0.227 0.105 0.063 0.033 0.019 0.010 0.006 0.003 0.0017 0.001 0.001 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 054101 2 0.063 0.242 0.020 2 054103 2 0.088 0.251 0.100 3 054105 2 0.074 0.261 0.026 4 054107 2 0.197 0.381 0.116 5 054111 2 0.136 0.286 0.126 6 054113 2 0.033 0.103 0.087 7 054115 2 0.217 0.352 0.166 8 054117 2 0.222 0.450 0.028 9 054131 2 0.063 0.241 0.018 10 054133 2 0.147 0.278 0.183 11 054135 2 0.052 0.199 0.077 12 054137 2 0.323 0.395 0.248 13 054141 2 0.167 0.264 0.201 14 054143 2 0.047 0.176 0.076 15 054145 2 0.095 0.196 0.187 16 054147 2 0.228 0.506 -0.069 17 054181 2 0.132 0.329 0.078 18 054183 2 0.290 0.332 0.288 19 054185 2 0.456 0.604 0.089 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 054187 2 0.354 0.527 0.076 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.169 0.319 0.106 STANDARD DEVIATION 0 0.116 0.128 0.086 MEDIAN 2 0.141 0.282 0.088 INTERQUARTILE RANGE 0 0.156 0.147 0.122 MINIMUM VALUE 2 0.033 0.103 -0.069 LOWER HINGE 2 0.069 0.242 0.052 UPPER HINGE 2 0.225 0.388 0.174 MAXIMUM VALUE 2 0.456 0.604 0.288 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 054101 1879 1995 117 1.000 0.063 0.209 2.994 0.071 -0.003 2 054103 1878 1995 118 1.000 0.071 0.968 6.254 0.076 -0.028 3 054105 1878 1995 118 1.000 0.066 0.559 4.604 0.073 -0.020 4 054107 1878 1995 118 1.000 0.063 0.404 4.394 0.068 -0.033 5 054111 1877 1995 119 1.000 0.070 1.270 8.447 0.071 -0.027 6 054113 1877 1995 119 1.000 0.079 1.484 8.249 0.069 0.001 7 054115 1878 1995 118 1.000 0.054 -0.113 3.565 0.059 0.013 8 054117 1877 1995 119 1.000 0.068 0.491 6.590 0.071 -0.050 9 054131 1877 1995 119 1.000 0.081 1.905 8.521 0.080 -0.021 10 054133 1876 1995 120 1.000 0.078 0.773 3.179 0.082 -0.015 11 054135 1876 1995 120 1.000 0.065 0.488 3.659 0.070 0.002 12 054137 1876 1995 120 1.000 0.073 0.554 3.526 0.085 -0.020 13 054141 1879 1995 117 1.000 0.069 1.094 9.431 0.070 -0.038 14 054143 1875 1995 121 1.000 0.057 0.503 3.330 0.064 -0.008 15 054145 1873 1980 108 1.000 0.058 0.385 3.067 0.064 0.001 16 054147 1873 1995 123 1.000 0.052 -0.021 2.630 0.061 -0.014 17 054181 1870 1995 126 1.000 0.076 0.608 4.004 0.081 -0.020 18 054183 1868 1995 128 1.000 0.073 1.250 8.437 0.074 -0.032 19 054185 1867 1995 129 1.000 0.074 1.408 8.331 0.077 -0.117 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 054187 1867 1995 129 1.000 0.070 1.631 9.490 0.073 -0.081 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.068 0.793 5.635 0.072 -0.025 STANDARD DEVIATION 4 0.000 0.008 0.558 2.519 0.007 0.030 MEDIAN (50TH QUANTILE) 119 1.000 0.069 0.584 4.499 0.071 -0.020 INTERQUARTILE RANGE 4 0.000 0.011 0.814 4.956 0.009 0.027 MINIMUM VALUE 108 1.000 0.052 -0.113 2.630 0.059 -0.117 LOWER HINGE (25TH QUANTILE) 118 1.000 0.063 0.446 3.428 0.068 -0.032 UPPER HINGE (75TH QUANTILE) 122 1.000 0.074 1.260 8.384 0.077 -0.005 MAXIMUM VALUE 129 1.000 0.081 1.905 9.490 0.085 0.013 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.401 0.134 0.010 0.660 3.141 0.100 0.772 MINIMUM CORRELATION: 0.100 SERIES 054107 AND 054133 118 YEARS MAXIMUM CORRELATION: 0.772 SERIES 054185 AND 054187 129 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 91.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1877. 1890. 1900. 1910. 1920. 1930. 1940. 1950. 1960. 1970. CORR 1. 190. 190. 190. 190. 190. 190. 190. 190. 190. RBAR 0.952 0.445 0.327 0.401 0.443 0.499 0.536 0.502 0.351 0.325 SDEV 0.000 0.207 0.235 0.222 0.206 0.187 0.172 0.163 0.235 0.247 SERR 0.000 0.015 0.017 0.016 0.015 0.014 0.012 0.012 0.017 0.018 EPS 0.996 0.941 0.907 0.931 0.941 0.952 0.959 0.953 0.915 0.906 NSS 12.1 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 20.0 YEAR 1980. CORR 171. RBAR 0.405 SDEV 0.192 SERR 0.015 EPS 0.930 NSS 19.5 |======================== 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 1867 1995 129 0.998 0.058 1.596 10.908 0.059 -0.006 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.179 0.067 -0.020 38 91 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.61 1.00 1.05 1.65 31.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.58 0.87 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 -0.006 -0.005 0.035 -0.018 -0.189 -0.143 0.074 -0.098 -0.069 0.127 PACF -0.006 -0.005 0.035 -0.018 -0.189 -0.152 0.072 -0.086 -0.076 0.085 95% C.L. 0.176 0.176 0.176 0.176 0.176 0.183 0.186 0.187 0.188 0.189 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.001 0.001 0.034 -0.020 -0.190 -0.144 0.071 -0.098 -0.068 0.126 PACF 0.001 0.001 0.034 -0.020 -0.190 -0.151 0.073 -0.086 -0.075 0.085 95% C.L. 0.176 0.176 0.176 0.176 0.176 0.183 0.186 0.187 0.188 0.189 |----------------- 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 0.002 0.001 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 1867 1995 129 0.999 0.063 1.608 11.310 0.051 0.318 |------------ 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 0.315 0.207 0.075 -0.049 -0.199 -0.188 -0.042 -0.115 -0.057 0.076 PACF 0.315 0.119 -0.023 -0.100 -0.188 -0.074 0.112 -0.085 -0.034 0.091 95% C.L. 0.176 0.193 0.200 0.200 0.201 0.207 0.212 0.212 0.214 0.215 |------------------- 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 0.154 0.319 0.134 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.28 MINUTES