RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM053N.rwl.conv LOG FILE PROCESSED: GERM053N.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: 050 1 Mźnstertal (D), EU-Pr. DENSITY_MINIMUM PCAB - 050 2 Germany Norway spruce 490 4751-747 1881 1995 - 050 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 050075 MISSING VALUES FOUND: 5 IN 1 GAPS / 1890 1894 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 0.288 0.026 -0.137 3.257 0.076 0.471 2 050063 1883 1995 113 0.289 0.035 -0.458 2.775 0.069 0.762 3 050065 1882 1995 114 0.281 0.032 0.199 3.578 0.066 0.697 4 050067 1883 1995 113 0.272 0.022 0.301 3.223 0.078 0.228 5 050071 1881 1995 115 0.284 0.031 0.517 3.606 0.077 0.520 6 050073 1881 1958 78 0.302 0.036 0.221 3.060 0.093 0.438 7 050075 1881 1926 46 0.333 0.043 2.970 11.458 0.080 0.526 8 050077 1881 1995 115 0.290 0.034 1.074 4.997 0.077 0.484 9 050081 1883 1995 113 0.262 0.036 4.152 29.590 0.075 0.430 10 050083 1881 1995 115 0.239 0.036 1.386 9.823 0.101 0.494 11 050085 1881 1995 115 0.249 0.030 2.351 14.246 0.083 0.376 12 050087 1893 1995 103 0.267 0.029 0.132 2.528 0.062 0.705 13 050091 1882 1995 114 0.288 0.033 -0.288 3.491 0.073 0.630 14 050093 1885 1995 111 0.271 0.035 0.723 4.142 0.072 0.689 15 050095 1896 1995 100 0.269 0.031 -0.042 2.700 0.064 0.757 16 050097 1881 1995 115 0.287 0.048 0.239 2.552 0.061 0.856 17 050101 1884 1995 112 0.299 0.033 1.181 5.472 0.085 0.382 18 050103 1884 1995 112 0.293 0.038 1.336 6.757 0.090 0.380 19 050105 1887 1995 109 0.299 0.046 0.804 4.022 0.074 0.682 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 0.269 0.035 0.533 3.438 0.080 0.544 NUMBER OF SERIES READ IN: 20 FROM 1881 TO 1995 115 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 0.282 0.034 0.860 6.236 0.077 0.552 STANDARD DEVIATION 17 0.021 0.006 1.155 6.368 0.010 0.163 MEDIAN (50TH QUANTILE) 113 0.286 0.034 0.525 3.592 0.077 0.523 INTERQUARTILE RANGE 4 0.023 0.005 1.093 2.973 0.011 0.259 MINIMUM VALUE 41 0.239 0.022 -0.458 2.528 0.061 0.228 LOWER HINGE (25TH QUANTILE) 110 0.269 0.031 0.166 3.141 0.070 0.434 UPPER HINGE (75TH QUANTILE) 114 0.292 0.036 1.259 6.115 0.082 0.693 MAXIMUM VALUE 115 0.333 0.048 4.152 29.590 0.101 0.856 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.516 0.223 0.016 -1.128 4.714 -0.305 0.869 MINIMUM CORRELATION: -0.305 SERIES 050063 AND 050075 44 YEARS MAXIMUM CORRELATION: 0.869 SERIES 050095 AND 050097 100 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.613 0.340 0.398 0.562 0.639 0.581 0.514 0.415 0.473 SDEV 0.269 0.261 0.235 0.230 0.134 0.167 0.226 0.238 0.180 SERR 0.059 0.019 0.018 0.018 0.010 0.013 0.018 0.019 0.015 EPS 0.965 0.912 0.929 0.961 0.971 0.963 0.951 0.927 0.942 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== 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 1881 1995 115 0.280 0.029 0.718 4.719 0.058 0.652 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.620 0.146 -0.014 41 74 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.32 0.89 1.00 1.09 1.98 7.22 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.07 0.71 0.87 0.94 0.99 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 113. 4. 46. 110. 114. 115. |----------- 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 0.646 0.562 0.502 0.495 0.453 0.415 0.400 0.350 0.374 0.367 PACF 0.646 0.247 0.126 0.150 0.053 0.027 0.053 -0.027 0.098 0.053 95% C.L. 0.187 0.253 0.293 0.321 0.347 0.367 0.383 0.397 0.408 0.419 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.535 0.488 0.298 |================== 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 050061 3 0.00000000 0.00000000 -0.00044385 0.31332868 2 050063 3 0.00000000 0.00000000 -0.00036529 0.31002527 3 050065 3 0.00000000 0.00000000 -0.00062676 0.31717902 4 050067 1 0.02977349 0.11426564 0.00000000 0.27003577 5 050071 1 0.11207744 0.00589935 0.00000000 0.20330255 6 050073 1 0.08169193 0.02580257 0.00000000 0.26772282 7 050075 3 0.00000000 0.00000000 -0.00132764 0.37036476 8 050077 1 0.30066177 0.00214144 0.00000000 0.02371156 9 050081 3 0.00000000 0.00000000 -0.00039923 0.28443742 10 050083 3 0.00000000 0.00000000 -0.00025369 0.25323570 11 050085 3 0.00000000 0.00000000 -0.00022599 0.26180321 12 050087 3 0.00000000 0.00000000 -0.00055342 0.29567105 13 050091 3 0.00000000 0.00000000 -0.00057800 0.32156807 14 050093 3 0.00000000 0.00000000 -0.00067576 0.30919412 15 050095 1 0.23910598 0.00416410 0.00000000 0.07384627 16 050097 3 0.00000000 0.00000000 -0.00117249 0.35496110 17 050101 3 0.00000000 0.00000000 -0.00012540 0.30583495 18 050103 3 0.00000000 0.00000000 -0.00046230 0.31951255 19 050105 3 0.00000000 0.00000000 -0.00080651 0.34298167 SERIES IDENT OPTION A B C D 20 050107 3 0.00000000 0.00000000 -0.00069349 0.30802125 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.000 0.077 -0.024 2.836 0.076 0.265 2 050063 1883 1995 113 1.000 0.114 -0.556 2.966 0.068 0.715 3 050065 1882 1995 114 1.000 0.085 0.551 3.807 0.066 0.507 4 050067 1883 1995 113 1.000 0.077 0.337 3.451 0.077 0.202 5 050071 1881 1995 115 1.000 0.093 0.352 3.443 0.076 0.378 6 050073 1881 1958 78 1.000 0.101 0.529 3.383 0.091 0.276 7 050075 1881 1926 46 1.000 0.130 2.501 8.877 0.101 0.278 8 050077 1881 1995 115 1.000 0.097 1.661 7.146 0.076 0.306 9 050081 1883 1995 113 1.000 0.124 3.423 23.535 0.075 0.394 10 050083 1881 1995 115 1.000 0.142 0.871 7.898 0.100 0.480 11 050085 1881 1995 115 1.000 0.115 1.951 10.967 0.083 0.362 12 050087 1893 1995 103 1.000 0.091 0.595 3.509 0.062 0.603 13 050091 1882 1995 114 1.000 0.096 -0.004 3.906 0.073 0.448 14 050093 1885 1995 111 1.000 0.097 0.421 4.950 0.072 0.458 15 050095 1896 1995 100 1.000 0.080 1.043 5.985 0.064 0.439 16 050097 1881 1995 115 1.000 0.099 0.493 3.030 0.061 0.656 17 050101 1884 1995 112 1.000 0.110 1.138 4.889 0.084 0.383 18 050103 1884 1995 112 1.000 0.116 1.478 7.830 0.090 0.289 19 050105 1887 1995 109 1.000 0.124 1.120 6.428 0.074 0.525 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.100 1.043 3.988 0.080 0.278 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.000 0.103 0.946 6.141 0.077 0.412 STANDARD DEVIATION 16 0.000 0.018 0.924 4.691 0.011 0.139 MEDIAN (50TH QUANTILE) 113 1.000 0.100 0.733 4.438 0.076 0.389 INTERQUARTILE RANGE 4 0.000 0.024 0.922 4.041 0.014 0.210 MINIMUM VALUE 46 1.000 0.077 -0.556 2.836 0.061 0.202 LOWER HINGE (25TH QUANTILE) 110 1.000 0.092 0.386 3.447 0.070 0.283 UPPER HINGE (75TH QUANTILE) 114 1.000 0.116 1.308 7.488 0.084 0.493 MAXIMUM VALUE 115 1.000 0.142 3.423 23.535 0.101 0.715 |------------------------ 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 050061 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 050063 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 050065 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 050067 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 050071 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 050073 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 050075 -67 30 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 050077 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 050081 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 050083 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 050085 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 050087 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 050091 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 050093 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 050095 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 050097 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 050101 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 050103 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 050105 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 050107 -67 75 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 050061 1882 1995 114 1.000 0.075 0.060 2.774 0.076 0.215 2 050063 1883 1995 113 0.999 0.082 -0.272 3.661 0.068 0.444 3 050065 1882 1995 114 1.000 0.076 0.671 3.948 0.066 0.358 4 050067 1883 1995 113 1.000 0.073 0.321 3.468 0.077 0.107 5 050071 1881 1995 115 1.000 0.090 0.369 3.522 0.076 0.338 6 050073 1881 1958 78 1.000 0.095 0.543 3.563 0.091 0.205 7 050075 1881 1926 46 0.999 0.115 1.999 7.127 0.101 0.134 8 050077 1881 1995 115 1.000 0.089 1.801 7.577 0.076 0.182 9 050081 1883 1995 113 0.999 0.110 2.380 16.027 0.075 0.363 10 050083 1881 1995 115 0.999 0.124 0.070 5.486 0.100 0.390 11 050085 1881 1995 115 1.000 0.104 1.257 7.132 0.083 0.302 12 050087 1893 1995 103 0.999 0.078 0.481 3.395 0.062 0.462 13 050091 1882 1995 114 1.000 0.086 0.118 3.571 0.073 0.326 14 050093 1885 1995 111 1.000 0.089 0.456 5.287 0.072 0.353 15 050095 1896 1995 100 1.000 0.070 0.947 5.841 0.064 0.287 16 050097 1881 1995 115 0.999 0.082 0.511 3.427 0.061 0.478 17 050101 1884 1995 112 1.000 0.108 1.066 4.623 0.084 0.374 18 050103 1884 1995 112 1.000 0.106 1.738 7.733 0.090 0.133 19 050105 1887 1995 109 0.999 0.094 1.552 7.602 0.074 0.231 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.095 1.082 4.102 0.080 0.201 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 0.999 0.092 0.857 5.493 0.078 0.294 STANDARD DEVIATION 16 0.000 0.015 0.732 2.993 0.012 0.113 MEDIAN (50TH QUANTILE) 113 1.000 0.089 0.607 4.363 0.076 0.314 INTERQUARTILE RANGE 4 0.000 0.025 1.059 3.587 0.014 0.166 MINIMUM VALUE 46 0.999 0.070 -0.272 2.774 0.061 0.107 LOWER HINGE (25TH QUANTILE) 110 0.999 0.080 0.345 3.543 0.070 0.203 UPPER HINGE (75TH QUANTILE) 114 1.000 0.105 1.404 7.130 0.084 0.369 MAXIMUM VALUE 115 1.000 0.124 2.380 16.027 0.101 0.478 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.476 0.145 0.010 -1.532 7.774 -0.238 0.763 MINIMUM CORRELATION: -0.238 SERIES 050075 AND 050095 31 YEARS MAXIMUM CORRELATION: 0.763 SERIES 050071 AND 050073 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.642 0.359 0.398 0.584 0.663 0.530 0.405 0.373 0.451 SDEV 0.201 0.249 0.238 0.207 0.127 0.186 0.223 0.230 0.196 SERR 0.044 0.018 0.018 0.016 0.010 0.015 0.018 0.019 0.016 EPS 0.969 0.918 0.929 0.964 0.974 0.955 0.926 0.915 0.937 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== 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 1881 1995 115 0.999 0.069 1.073 5.254 0.058 0.303 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.520 0.152 -0.091 35 80 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.35 1.25 1.00 1.10 2.34 9.67 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.70 0.87 0.92 0.98 |----------- 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 0.300 0.190 0.054 0.075 0.013 -0.049 -0.070 -0.113 -0.040 -0.066 PACF 0.300 0.110 -0.032 0.053 -0.023 -0.070 -0.041 -0.079 0.028 -0.033 95% C.L. 0.187 0.203 0.209 0.209 0.210 0.210 0.211 0.211 0.213 0.214 |------------------ 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 0.114 0.316 |======================= 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 0.256 0.170 0.000 0.051 0.016 -0.063 -0.071 -0.054 0.022 0.004 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 0.256 2 0.227 0.112 3 0.235 0.129 -0.073 4 0.239 0.122 -0.086 0.052 5 0.239 0.122 -0.086 0.051 0.005 6 0.239 0.127 -0.094 0.062 0.026 -0.090 7 0.236 0.128 -0.092 0.059 0.031 -0.081 -0.038 8 0.236 0.127 -0.091 0.059 0.031 -0.080 -0.036 -0.008 9 0.236 0.129 -0.088 0.058 0.028 -0.076 -0.042 -0.019 0.048 10 0.236 0.129 -0.088 0.058 0.028 -0.076 -0.042 -0.019 0.048 -0.002 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) 589.59 583.80 584.34 585.72 587.41 589.40 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 590.46 592.29 594.29 596.03 598.03 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 0.256 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.55 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 107.01 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.256 0.066 0.017 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 050061 1 0.071 0.220 2 050063 1 0.275 0.448 3 050065 1 0.215 0.374 4 050067 1 0.122 0.108 5 050071 1 0.148 0.341 6 050073 1 0.062 0.212 7 050075 1 0.094 0.135 8 050077 1 0.046 0.188 9 050081 1 0.194 0.440 10 050083 1 0.178 0.414 11 050085 1 0.114 0.337 12 050087 1 0.229 0.469 13 050091 1 0.116 0.327 14 050093 1 0.137 0.355 15 050095 1 0.093 0.293 16 050097 1 0.257 0.495 17 050101 1 0.155 0.394 18 050103 1 0.022 0.141 19 050105 1 0.054 0.231 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 050107 1 0.043 0.204 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.131 0.306 STANDARD DEVIATION 0 0.074 0.120 MEDIAN 1 0.119 0.332 INTERQUARTILE RANGE 0 0.120 0.196 MINIMUM VALUE 1 0.022 0.108 LOWER HINGE 1 0.066 0.208 UPPER HINGE 1 0.186 0.404 MAXIMUM VALUE 1 0.275 0.495 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.000 0.073 0.126 2.622 0.087 -0.037 2 050063 1883 1995 113 1.000 0.074 0.184 3.687 0.090 -0.135 3 050065 1882 1995 114 1.000 0.070 0.586 3.888 0.082 -0.123 4 050067 1883 1995 113 1.000 0.072 0.359 3.458 0.084 -0.036 5 050071 1881 1995 115 1.000 0.084 0.473 4.081 0.091 -0.067 6 050073 1881 1958 78 1.000 0.093 0.499 3.544 0.102 -0.023 7 050075 1881 1926 46 1.000 0.114 2.045 7.605 0.110 -0.038 8 050077 1881 1995 115 1.000 0.087 1.794 7.863 0.085 -0.023 9 050081 1883 1995 113 1.000 0.095 1.872 12.899 0.092 -0.094 10 050083 1881 1995 115 1.000 0.111 -0.122 5.986 0.123 -0.058 11 050085 1881 1995 115 1.000 0.097 1.020 6.606 0.098 -0.036 12 050087 1893 1995 103 1.000 0.069 0.211 3.132 0.080 -0.055 13 050091 1882 1995 114 1.000 0.081 0.103 4.036 0.089 -0.031 14 050093 1885 1995 111 1.000 0.083 0.352 5.046 0.086 -0.038 15 050095 1896 1995 100 1.000 0.066 0.819 5.229 0.076 -0.031 16 050097 1881 1995 115 1.000 0.070 0.829 3.780 0.076 -0.075 17 050101 1884 1995 112 1.000 0.099 0.926 4.912 0.098 -0.027 18 050103 1884 1995 112 1.000 0.105 1.689 7.616 0.097 -0.001 19 050105 1887 1995 109 1.000 0.091 1.687 9.150 0.085 -0.007 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.093 1.056 4.572 0.089 -0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.000 0.086 0.825 5.486 0.091 -0.047 STANDARD DEVIATION 16 0.000 0.014 0.670 2.517 0.011 0.036 MEDIAN (50TH QUANTILE) 113 1.000 0.086 0.703 4.742 0.089 -0.037 INTERQUARTILE RANGE 4 0.000 0.023 1.090 3.372 0.014 0.037 MINIMUM VALUE 46 1.000 0.066 -0.122 2.622 0.076 -0.135 LOWER HINGE (25TH QUANTILE) 110 1.000 0.073 0.281 3.734 0.084 -0.062 UPPER HINGE (75TH QUANTILE) 114 1.000 0.096 1.371 7.105 0.098 -0.025 MAXIMUM VALUE 115 1.000 0.114 2.045 12.899 0.123 -0.001 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.489 0.120 0.009 -0.985 6.706 -0.123 0.766 MINIMUM CORRELATION: -0.123 SERIES 050075 AND 050095 31 YEARS MAXIMUM CORRELATION: 0.766 SERIES 050073 AND 050077 78 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 86.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1891. 1910. 1920. 1930. 1940. 1950. 1960. 1970. 1980. CORR 21. 190. 171. 171. 171. 153. 153. 153. 153. RBAR 0.695 0.404 0.374 0.610 0.666 0.515 0.428 0.414 0.463 SDEV 0.157 0.228 0.228 0.199 0.121 0.173 0.179 0.192 0.177 SERR 0.034 0.017 0.017 0.015 0.009 0.014 0.014 0.016 0.014 EPS 0.975 0.931 0.922 0.968 0.974 0.953 0.932 0.927 0.939 NSS 17.2 20.0 19.9 19.4 19.0 19.0 18.5 18.0 18.0 |======================== 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 1881 1995 115 0.999 0.063 1.047 5.532 0.066 -0.031 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.453 0.139 -0.082 36 79 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 1.10 1.02 1.11 2.21 8.46 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.70 0.85 0.91 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 -0.031 0.104 -0.043 0.057 0.025 -0.036 -0.037 -0.100 0.007 -0.010 PACF -0.031 0.103 -0.037 0.045 0.036 -0.048 -0.042 -0.096 0.003 0.010 95% C.L. 0.187 0.187 0.189 0.189 0.190 0.190 0.190 0.190 0.192 0.192 |------------------ 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 0.005 0.102 -0.038 0.057 0.025 -0.037 -0.042 -0.101 0.003 -0.013 PACF 0.005 0.102 -0.039 0.048 0.033 -0.050 -0.043 -0.094 0.007 0.006 95% C.L. 0.187 0.187 0.188 0.189 0.189 0.189 0.190 0.190 0.192 0.192 |----------------- 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 0.011 0.005 |========================= 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 1881 1995 115 0.999 0.066 1.048 5.124 0.057 0.287 |------------ 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 0.284 0.160 0.022 0.060 0.025 -0.044 -0.073 -0.116 -0.039 -0.051 PACF 0.284 0.086 -0.049 0.058 0.001 -0.071 -0.049 -0.080 0.024 -0.023 95% C.L. 0.187 0.201 0.205 0.205 0.206 0.206 0.207 0.207 0.210 0.210 |------------------- 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 0.097 0.297 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.20 MINUTES