RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM053X.rwl.conv LOG FILE PROCESSED: GERM053X.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_MAXIMUM 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 / -------------------------------------------------------------------- 16 050097 MISSING VALUES FOUND: 6 IN 1 GAPS / 1920 1925 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 050061 1882 1995 114 1.053 0.064 -0.815 3.723 0.044 0.579 2 050063 1883 1995 113 1.032 0.094 -1.249 3.616 0.042 0.814 3 050065 1882 1995 114 1.044 0.055 -1.047 3.428 0.036 0.592 4 050067 1883 1995 113 1.042 0.046 -0.700 3.150 0.035 0.469 5 050071 1881 1995 115 0.993 0.067 -0.573 3.073 0.038 0.742 6 050073 1881 1958 78 1.042 0.048 -0.534 2.586 0.039 0.408 7 050075 1881 1926 46 1.026 0.075 -0.905 2.845 0.039 0.662 8 050077 1881 1995 115 1.021 0.048 -0.532 3.384 0.036 0.504 9 050081 1883 1995 113 0.973 0.079 -1.114 4.062 0.070 0.352 10 050083 1881 1995 115 0.914 0.080 -0.656 3.056 0.082 0.325 11 050085 1881 1995 115 0.935 0.085 -1.077 4.808 0.081 0.389 12 050087 1893 1995 103 1.039 0.080 -1.706 6.653 0.067 0.188 13 050091 1882 1995 114 1.045 0.081 -1.253 4.625 0.058 0.509 14 050093 1885 1995 111 1.007 0.087 -1.462 5.898 0.069 0.446 15 050095 1896 1995 100 1.022 0.055 -1.396 5.923 0.052 0.165 16 050097 1881 1995 115 1.036 0.059 -0.785 3.150 0.045 0.432 17 050101 1884 1995 112 0.961 0.059 -2.072 12.131 0.041 0.604 18 050103 1884 1995 112 0.980 0.071 -0.890 3.625 0.040 0.733 19 050105 1887 1995 109 0.999 0.060 -0.540 3.291 0.040 0.632 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 0.993 0.046 -0.989 6.157 0.035 0.501 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 106 1.008 0.067 -1.015 4.459 0.049 0.502 STANDARD DEVIATION 17 0.039 0.015 0.417 2.177 0.016 0.174 MEDIAN (50TH QUANTILE) 112 1.021 0.066 -0.947 3.621 0.042 0.503 INTERQUARTILE RANGE 5 0.054 0.025 0.573 2.203 0.024 0.220 MINIMUM VALUE 41 0.914 0.046 -2.072 2.586 0.035 0.165 LOWER HINGE (25TH QUANTILE) 109 0.987 0.055 -1.251 3.150 0.039 0.398 UPPER HINGE (75TH QUANTILE) 114 1.040 0.080 -0.678 5.353 0.062 0.618 MAXIMUM VALUE 115 1.053 0.094 -0.532 12.131 0.082 0.814 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.447 0.188 0.014 -0.409 3.150 -0.189 0.829 MINIMUM CORRELATION: -0.189 SERIES 050075 AND 050083 46 YEARS MAXIMUM CORRELATION: 0.829 SERIES 050065 AND 050067 113 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 0.480 0.487 0.487 0.454 0.505 0.454 0.502 0.478 0.500 SDEV 0.162 0.189 0.272 0.235 0.239 0.264 0.197 0.198 0.215 SERR 0.035 0.014 0.021 0.018 0.018 0.021 0.016 0.016 0.017 EPS 0.941 0.950 0.950 0.942 0.951 0.940 0.949 0.943 0.947 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 1.012 0.048 -0.395 2.332 0.033 0.594 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.417 -0.152 0.212 55 60 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.43 0.85 1.00 1.14 1.99 14.34 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.57 0.87 0.96 1.00 |--------------------- 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 0.589 0.437 0.450 0.425 0.387 0.281 0.255 0.327 0.288 0.196 PACF 0.589 0.138 0.230 0.108 0.076 -0.083 0.016 0.144 0.009 -0.068 95% C.L. 0.187 0.243 0.269 0.294 0.314 0.331 0.339 0.345 0.356 0.364 |------------------ 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 0.427 0.475 0.018 0.255 |================== 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 -0.00033762 1.07222009 2 050063 3 0.00000000 0.00000000 -0.00112108 1.09620261 3 050065 3 0.00000000 0.00000000 0.00042863 1.01895046 4 050067 3 0.00000000 0.00000000 0.00023421 1.02903914 5 050071 3 0.00000000 0.00000000 0.00036747 0.97164303 6 050073 3 0.00000000 0.00000000 0.00056475 1.01999998 7 050075 3 0.00000000 0.00000000 0.00402240 0.92337453 8 050077 3 0.00000000 0.00000000 -0.00002628 1.02248049 9 050081 3 0.00000000 0.00000000 -0.00053921 1.00374365 10 050083 3 0.00000000 0.00000000 0.00021605 0.90173000 11 050085 3 0.00000000 0.00000000 -0.00084597 0.98410982 12 050087 3 0.00000000 0.00000000 -0.00042284 1.06062818 13 050091 3 0.00000000 0.00000000 -0.00046880 1.07178080 14 050093 3 0.00000000 0.00000000 -0.00042032 1.03029490 15 050095 3 0.00000000 0.00000000 -0.00038902 1.04134548 16 050097 3 0.00000000 0.00000000 0.00004106 1.03784561 17 050101 3 0.00000000 0.00000000 0.00015884 0.95182914 18 050103 3 0.00000000 0.00000000 0.00077980 0.93629825 19 050105 3 0.00000000 0.00000000 -0.00004680 1.00202346 SERIES IDENT OPTION A B C D 20 050107 3 0.00000000 0.00000000 0.00016892 0.98358107 |-------------------- 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 0.060 -0.834 3.715 0.044 0.551 2 050063 1883 1995 113 1.000 0.085 -0.799 2.906 0.042 0.757 3 050065 1882 1995 114 1.000 0.051 -0.687 3.047 0.036 0.576 4 050067 1883 1995 113 1.000 0.043 -0.529 2.859 0.035 0.462 5 050071 1881 1995 115 1.000 0.067 -0.471 3.236 0.038 0.732 6 050073 1881 1958 78 1.000 0.044 -0.593 2.696 0.039 0.365 7 050075 1881 1926 46 1.000 0.052 -1.379 5.886 0.042 0.359 8 050077 1881 1995 115 1.000 0.047 -0.534 3.375 0.036 0.499 9 050081 1883 1995 113 1.000 0.079 -0.954 3.631 0.069 0.325 10 050083 1881 1995 115 1.000 0.087 -0.742 3.170 0.081 0.318 11 050085 1881 1995 115 1.000 0.086 -1.019 4.441 0.080 0.312 12 050087 1893 1995 103 1.000 0.076 -1.860 7.565 0.066 0.155 13 050091 1882 1995 114 1.000 0.076 -1.201 4.386 0.057 0.484 14 050093 1885 1995 111 1.000 0.085 -1.450 5.884 0.068 0.422 15 050095 1896 1995 100 1.000 0.053 -1.322 6.167 0.051 0.126 16 050097 1881 1995 115 1.000 0.057 -0.759 3.108 0.043 0.485 17 050101 1884 1995 112 1.000 0.062 -1.900 11.296 0.041 0.601 18 050103 1884 1995 112 1.000 0.068 -0.596 3.048 0.040 0.701 19 050105 1887 1995 109 1.000 0.060 -0.546 3.286 0.039 0.626 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.046 -0.951 5.702 0.035 0.492 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.000 0.064 -0.956 4.470 0.049 0.467 STANDARD DEVIATION 16 0.000 0.015 0.432 2.125 0.015 0.174 MEDIAN (50TH QUANTILE) 113 1.000 0.061 -0.817 3.503 0.042 0.484 INTERQUARTILE RANGE 4 0.000 0.026 0.667 2.715 0.023 0.247 MINIMUM VALUE 46 1.000 0.043 -1.900 2.696 0.035 0.126 LOWER HINGE (25TH QUANTILE) 110 1.000 0.051 -1.262 3.078 0.038 0.342 UPPER HINGE (75TH QUANTILE) 114 1.000 0.078 -0.594 5.793 0.062 0.589 MAXIMUM VALUE 115 1.000 0.087 -0.471 11.296 0.081 0.757 |------------------------ 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 0.052 -1.376 5.837 0.044 0.410 2 050063 1883 1995 113 0.999 0.067 -0.619 3.705 0.042 0.634 3 050065 1882 1995 114 1.000 0.039 -0.800 3.876 0.035 0.275 4 050067 1883 1995 113 1.000 0.035 -0.823 3.929 0.035 0.215 5 050071 1881 1995 115 1.000 0.058 -0.333 3.490 0.038 0.647 6 050073 1881 1958 78 1.000 0.036 -0.609 3.034 0.039 0.120 7 050075 1881 1926 46 1.000 0.043 -0.999 4.156 0.041 0.175 8 050077 1881 1995 115 1.000 0.038 -0.864 4.268 0.036 0.275 9 050081 1883 1995 113 1.000 0.071 -0.658 4.161 0.069 0.162 10 050083 1881 1995 115 1.000 0.085 -0.720 3.215 0.081 0.264 11 050085 1881 1995 115 1.000 0.078 -0.992 4.984 0.080 0.153 12 050087 1893 1995 103 1.000 0.069 -1.943 7.441 0.066 -0.004 13 050091 1882 1995 114 1.000 0.066 -1.500 6.327 0.057 0.314 14 050093 1885 1995 111 1.000 0.077 -1.633 7.620 0.068 0.305 15 050095 1896 1995 100 1.000 0.051 -1.442 6.794 0.051 0.086 16 050097 1881 1995 115 1.000 0.044 -1.126 3.786 0.043 0.157 17 050101 1884 1995 112 1.000 0.052 -1.731 11.157 0.041 0.446 18 050103 1884 1995 112 1.000 0.049 -0.464 2.924 0.040 0.432 19 050105 1887 1995 109 1.000 0.040 -0.523 4.054 0.039 0.219 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.038 -0.490 4.965 0.035 0.262 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.000 0.054 -0.982 4.986 0.049 0.277 STANDARD DEVIATION 16 0.000 0.016 0.471 2.032 0.015 0.168 MEDIAN (50TH QUANTILE) 113 1.000 0.051 -0.843 4.159 0.041 0.263 INTERQUARTILE RANGE 4 0.000 0.029 0.796 2.336 0.023 0.203 MINIMUM VALUE 46 0.999 0.035 -1.943 2.924 0.035 -0.004 LOWER HINGE (25TH QUANTILE) 110 1.000 0.039 -1.409 3.746 0.038 0.159 UPPER HINGE (75TH QUANTILE) 114 1.000 0.068 -0.614 6.082 0.062 0.362 MAXIMUM VALUE 115 1.000 0.085 -0.333 11.157 0.081 0.647 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.380 0.142 0.010 0.268 2.837 0.037 0.777 MINIMUM CORRELATION: 0.037 SERIES 050075 AND 050107 43 YEARS MAXIMUM CORRELATION: 0.777 SERIES 050091 AND 050093 111 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 0.270 0.489 0.474 0.487 0.532 0.458 0.473 0.418 0.509 SDEV 0.155 0.191 0.255 0.207 0.226 0.239 0.200 0.244 0.205 SERR 0.034 0.014 0.020 0.016 0.017 0.019 0.016 0.020 0.017 EPS 0.865 0.950 0.947 0.948 0.956 0.941 0.943 0.928 0.949 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 1.003 0.034 -0.600 3.244 0.031 0.330 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.454 -0.191 0.230 52 63 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.59 1.12 1.01 1.13 2.26 9.73 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.07 0.81 0.88 0.95 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 0.327 0.098 0.095 0.052 0.029 -0.073 -0.137 -0.027 -0.011 -0.130 PACF 0.327 -0.010 0.074 0.000 0.008 -0.101 -0.099 0.054 -0.002 -0.124 95% C.L. 0.187 0.205 0.207 0.209 0.209 0.209 0.210 0.213 0.213 0.213 |------------------ 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 0.108 0.329 |======================= 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 0.287 0.081 0.069 0.015 0.017 -0.147 -0.149 -0.025 0.014 -0.142 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 0.287 2 0.287 -0.001 3 0.287 -0.016 0.051 4 0.289 -0.016 0.057 -0.020 5 0.289 -0.017 0.057 -0.025 0.016 6 0.292 -0.021 0.067 -0.028 0.066 -0.172 7 0.280 -0.017 0.065 -0.023 0.064 -0.153 -0.068 8 0.283 -0.010 0.062 -0.022 0.061 -0.152 -0.081 0.047 9 0.281 -0.007 0.067 -0.024 0.062 -0.154 -0.081 0.036 0.037 10 0.287 -0.001 0.054 -0.050 0.072 -0.158 -0.070 0.035 0.083 -0.166 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) 453.91 446.03 448.03 449.73 451.68 453.65 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 452.18 453.64 455.39 457.24 456.01 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 0.287 R-SQUARED DUE TO POOLED AUTOREGRESSION: 8.24 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 108.98 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.287 0.082 0.024 0.007 0.002 0.001 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 0.186 0.412 2 050063 1 0.419 0.644 3 050065 1 0.086 0.279 4 050067 1 0.056 0.219 5 050071 1 0.425 0.648 6 050073 1 0.023 0.122 7 050075 1 0.040 0.197 8 050077 1 0.077 0.277 9 050081 1 0.042 0.168 10 050083 1 0.088 0.265 11 050085 1 0.033 0.153 12 050087 1 0.001 -0.004 13 050091 1 0.099 0.314 14 050093 1 0.096 0.310 15 050095 1 0.025 0.086 16 050097 1 0.027 0.162 17 050101 1 0.263 0.456 18 050103 1 0.194 0.434 19 050105 1 0.077 0.224 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 050107 1 0.094 0.264 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.118 0.282 STANDARD DEVIATION 0 0.123 0.169 MEDIAN 1 0.081 0.265 INTERQUARTILE RANGE 0 0.106 0.198 MINIMUM VALUE 1 0.001 -0.004 LOWER HINGE 1 0.036 0.165 UPPER HINGE 1 0.142 0.363 MAXIMUM VALUE 1 0.425 0.648 |------------------- 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 0.047 -1.090 4.788 0.055 -0.054 2 050063 1883 1995 113 1.000 0.051 0.115 3.546 0.055 -0.048 3 050065 1882 1995 114 1.000 0.037 -0.815 4.010 0.040 -0.022 4 050067 1883 1995 113 1.000 0.034 -0.682 3.505 0.039 0.019 5 050071 1881 1995 115 1.000 0.044 -0.558 3.881 0.051 -0.066 6 050073 1881 1958 78 1.000 0.036 -0.570 3.050 0.041 0.009 7 050075 1881 1926 46 1.000 0.042 -1.081 4.492 0.044 0.017 8 050077 1881 1995 115 1.000 0.037 -0.743 4.044 0.041 -0.002 9 050081 1883 1995 113 1.000 0.070 -0.632 3.930 0.074 -0.013 10 050083 1881 1995 115 1.000 0.082 -0.734 3.540 0.092 -0.037 11 050085 1881 1995 115 1.000 0.077 -1.050 5.220 0.084 0.015 12 050087 1893 1995 103 1.000 0.069 -1.944 7.443 0.066 0.000 13 050091 1882 1995 114 1.000 0.063 -1.388 6.171 0.065 0.007 14 050093 1885 1995 111 1.000 0.073 -1.421 6.491 0.077 -0.008 15 050095 1896 1995 100 1.000 0.051 -1.514 7.248 0.053 0.011 16 050097 1881 1995 115 1.000 0.044 -1.080 3.744 0.046 -0.009 17 050101 1884 1995 112 1.000 0.046 -1.525 9.720 0.051 -0.108 18 050103 1884 1995 112 1.000 0.044 -0.220 3.188 0.047 0.039 19 050105 1887 1995 109 1.000 0.039 -0.402 4.169 0.042 0.039 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 050107 1884 1995 112 1.000 0.037 -0.345 4.289 0.038 0.037 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 107 1.000 0.051 -0.884 4.823 0.055 -0.009 STANDARD DEVIATION 16 0.000 0.015 0.510 1.736 0.016 0.038 MEDIAN (50TH QUANTILE) 113 1.000 0.045 -0.779 4.107 0.051 -0.001 INTERQUARTILE RANGE 4 0.000 0.028 0.674 2.051 0.024 0.045 MINIMUM VALUE 46 1.000 0.034 -1.944 3.050 0.038 -0.108 LOWER HINGE (25TH QUANTILE) 110 1.000 0.038 -1.239 3.645 0.042 -0.029 UPPER HINGE (75TH QUANTILE) 114 1.000 0.066 -0.564 5.696 0.066 0.016 MAXIMUM VALUE 115 1.000 0.082 0.115 9.720 0.092 0.039 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.378 0.142 0.010 0.471 2.778 0.056 0.776 MINIMUM CORRELATION: 0.056 SERIES 050075 AND 050107 43 YEARS MAXIMUM CORRELATION: 0.776 SERIES 050091 AND 050093 111 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 0.240 0.434 0.467 0.499 0.568 0.463 0.419 0.407 0.468 SDEV 0.181 0.194 0.226 0.190 0.187 0.213 0.221 0.238 0.223 SERR 0.039 0.014 0.017 0.015 0.014 0.017 0.018 0.019 0.018 EPS 0.845 0.939 0.946 0.951 0.961 0.942 0.930 0.925 0.941 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 1.002 0.032 -0.508 3.050 0.035 0.044 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.425 -0.189 0.226 48 67 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.39 0.77 1.00 1.19 1.96 8.69 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.73 0.87 0.94 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 0.044 -0.013 0.057 0.003 0.044 -0.071 -0.135 0.001 0.061 -0.104 PACF 0.044 -0.014 0.058 -0.003 0.046 -0.079 -0.128 0.005 0.067 -0.098 95% C.L. 0.187 0.187 0.187 0.187 0.187 0.188 0.189 0.192 0.192 0.193 |------------------ 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 0.000 -0.017 0.058 -0.002 0.047 -0.067 -0.132 0.004 0.065 -0.101 PACF 0.000 -0.017 0.058 -0.002 0.050 -0.071 -0.131 -0.004 0.072 -0.090 95% C.L. 0.187 0.187 0.187 0.187 0.187 0.188 0.188 0.192 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 0.000 0.000 |========================= 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 1.002 0.033 -0.540 3.092 0.031 0.290 |------------ 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 0.288 0.083 0.077 0.026 0.023 -0.088 -0.143 -0.030 0.017 -0.119 PACF 0.288 0.000 0.058 -0.013 0.017 -0.113 -0.099 0.044 0.035 -0.133 95% C.L. 0.187 0.201 0.203 0.204 0.204 0.204 0.205 0.209 0.209 0.209 |------------------- 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 0.084 0.290 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.25 MINUTES