RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN015N.rwl LOG FILE PROCESSED: FRAN015N.rwl_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: 256 1 Col dAllos DENSITY_MINIMUM ABAL - 256 2 France silver fir, European fir 1900 4416-634 1771 1975 - 256 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 256020 MISSING VALUES FOUND: 6 IN 1 GAPS / 1953 1958 / -------------------------------------------------------------------- 4 256080 MISSING VALUES FOUND: 5 IN 1 GAPS / 1834 1838 / -------------------------------------------------------------------- 7 256190 MISSING VALUES FOUND: 10 IN 2 GAPS / 1949 1953 / 1962 1966 / -------------------------------------------------------------------- 8 256200 MISSING VALUES FOUND: 6 IN 1 GAPS / 1908 1913 / -------------------------------------------------------------------- 9 256240 MISSING VALUES FOUND: 5 IN 1 GAPS / 1969 1973 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 0.274 0.021 0.767 4.699 0.058 0.472 2 256020 1772 1975 204 0.276 0.019 0.729 4.476 0.053 0.427 3 256040 1845 1975 131 0.290 0.026 0.754 3.189 0.059 0.601 4 256080 1828 1975 148 0.279 0.022 0.340 2.591 0.056 0.598 5 256130 1819 1975 157 0.300 0.050 1.108 5.220 0.057 0.862 6 256170 1889 1975 87 0.301 0.032 0.275 2.314 0.055 0.786 7 256190 1771 1975 205 0.288 0.022 -0.317 3.218 0.047 0.629 8 256200 1799 1975 177 0.250 0.019 0.183 2.463 0.050 0.661 9 256240 1831 1975 145 0.286 0.039 1.283 4.102 0.068 0.773 10 256250 1846 1975 130 0.245 0.015 -0.141 2.408 0.048 0.504 11 256270 1827 1975 149 0.237 0.026 0.735 4.528 0.057 0.719 NUMBER OF SERIES READ IN: 11 FROM 1771 TO 1975 205 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 150 0.275 0.026 0.520 3.564 0.055 0.639 STANDARD DEVIATION 31 0.022 0.010 0.498 1.068 0.006 0.138 MEDIAN (50TH QUANTILE) 149 0.279 0.022 0.729 3.218 0.056 0.629 INTERQUARTILE RANGE 28 0.027 0.009 0.532 1.975 0.006 0.195 MINIMUM VALUE 87 0.237 0.015 -0.317 2.314 0.047 0.427 LOWER HINGE (25TH QUANTILE) 135 0.262 0.020 0.229 2.527 0.051 0.551 UPPER HINGE (75TH QUANTILE) 164 0.289 0.029 0.761 4.502 0.058 0.746 MAXIMUM VALUE 198 0.301 0.050 1.283 5.220 0.068 0.862 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.477 0.162 0.022 -0.838 4.915 -0.090 0.823 MINIMUM CORRELATION: -0.090 SERIES 256010 AND 256170 87 YEARS MAXIMUM CORRELATION: 0.823 SERIES 256170 AND 256200 87 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.43 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. CORR 1. 3. 3. 6. 21. 28. 45. 45. 45. 45. RBAR 0.095 0.160 0.121 0.504 0.672 0.548 0.482 0.291 0.405 0.473 SDEV 0.000 0.129 0.348 0.198 0.109 0.203 0.228 0.249 0.198 0.221 SERR 0.000 0.074 0.201 0.081 0.024 0.038 0.034 0.037 0.029 0.033 EPS 0.211 0.367 0.364 0.869 0.945 0.920 0.903 0.804 0.872 0.905 NSS 2.5 3.0 4.2 6.6 8.4 9.4 10.0 10.0 10.1 10.6 YEAR 1900. 1910. 1920. 1930. 1940. 1950. 1960. CORR 55. 55. 55. 55. 55. 55. 55. RBAR 0.424 0.399 0.275 0.453 0.608 0.466 0.222 SDEV 0.219 0.199 0.320 0.226 0.151 0.201 0.249 SERR 0.030 0.027 0.043 0.031 0.020 0.027 0.034 EPS 0.890 0.880 0.807 0.901 0.945 0.906 0.759 NSS 11.0 11.0 11.0 11.0 11.0 11.0 11.0 |======================== 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 1771 1975 205 0.275 0.017 -0.050 2.439 0.044 0.585 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.220 0.156 -0.017 54 151 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.58 2.02 1.00 1.18 3.19 69.94 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.13 0.00 0.87 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 149. 29. 87. 138. 167. 205. |----------- 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 0.583 0.548 0.525 0.429 0.433 0.394 0.403 0.354 0.347 0.371 PACF 0.583 0.316 0.207 0.010 0.092 0.038 0.099 -0.010 0.035 0.086 95% C.L. 0.140 0.181 0.211 0.235 0.250 0.264 0.275 0.287 0.295 0.303 |------------------ 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 0.442 0.316 0.242 0.225 |================== 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 256010 3 0.00000000 0.00000000 -0.00012002 0.28362057 2 256020 3 0.00000000 0.00000000 -0.00011006 0.28635594 3 256040 1 0.08558295 0.00791559 0.00000000 0.23739882 4 256080 3 0.00000000 0.00000000 -0.00007814 0.28455177 5 256130 1 0.17331503 0.01274765 0.00000000 0.22590461 6 256170 1 0.09890053 0.01566883 0.00000000 0.24758390 7 256190 3 0.00000000 0.00000000 -0.00010294 0.29656029 8 256200 3 0.00000000 0.00000000 -0.00007868 0.25778344 9 256240 3 0.00000000 0.00000000 -0.00029909 0.30604568 10 256250 3 0.00000000 0.00000000 -0.00021164 0.25901610 11 256270 3 0.00000000 0.00000000 -0.00035407 0.26400506 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 1.000 0.073 0.716 4.606 0.058 0.437 2 256020 1772 1975 204 1.000 0.067 0.583 3.792 0.054 0.387 3 256040 1845 1975 131 1.000 0.068 0.748 3.423 0.059 0.367 4 256080 1828 1975 148 1.000 0.076 0.314 2.683 0.055 0.594 5 256130 1819 1975 157 1.000 0.087 0.715 4.214 0.058 0.528 6 256170 1889 1975 87 1.000 0.080 0.311 2.876 0.055 0.601 7 256190 1771 1975 205 1.000 0.079 0.121 2.726 0.046 0.680 8 256200 1799 1975 177 1.000 0.077 0.301 2.495 0.048 0.676 9 256240 1831 1975 145 1.000 0.128 1.195 4.305 0.067 0.744 10 256250 1846 1975 130 1.000 0.053 -0.182 3.193 0.048 0.311 11 256270 1827 1975 149 1.000 0.089 1.904 11.567 0.057 0.577 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.080 0.611 4.171 0.055 0.536 STANDARD DEVIATION 33 0.000 0.019 0.565 2.556 0.006 0.143 MEDIAN (50TH QUANTILE) 149 1.000 0.077 0.583 3.423 0.055 0.577 INTERQUARTILE RANGE 29 0.000 0.013 0.426 1.458 0.007 0.226 MINIMUM VALUE 87 1.000 0.053 -0.182 2.495 0.046 0.311 LOWER HINGE (25TH QUANTILE) 138 1.000 0.071 0.306 2.801 0.051 0.412 UPPER HINGE (75TH QUANTILE) 167 1.000 0.083 0.732 4.259 0.058 0.639 MAXIMUM VALUE 205 1.000 0.128 1.904 11.567 0.067 0.744 |------------------------ 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 256010 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 256020 -67 136 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 256040 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 256080 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 256130 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 256170 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 256190 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 256200 -67 118 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 256240 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 256250 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 256270 -67 99 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 256010 1823 1975 153 1.000 0.069 0.703 4.774 0.058 0.370 2 256020 1772 1975 204 1.000 0.061 0.688 4.700 0.054 0.265 3 256040 1845 1975 131 1.000 0.064 0.684 3.370 0.059 0.280 4 256080 1828 1975 148 1.000 0.062 0.345 2.749 0.055 0.377 5 256130 1819 1975 157 1.000 0.076 0.952 5.305 0.058 0.373 6 256170 1889 1975 87 0.999 0.055 0.415 4.235 0.055 0.222 7 256190 1771 1975 205 1.000 0.054 0.508 3.432 0.047 0.321 8 256200 1799 1975 177 1.000 0.053 0.057 2.841 0.049 0.334 9 256240 1831 1975 145 0.999 0.110 1.148 5.104 0.067 0.661 10 256250 1846 1975 130 1.000 0.047 -0.079 3.265 0.048 0.122 11 256270 1827 1975 149 1.000 0.085 1.709 10.609 0.057 0.535 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.067 0.648 4.580 0.055 0.351 STANDARD DEVIATION 33 0.000 0.018 0.502 2.196 0.006 0.146 MEDIAN (50TH QUANTILE) 149 1.000 0.062 0.684 4.235 0.055 0.334 INTERQUARTILE RANGE 29 0.000 0.018 0.448 1.621 0.007 0.103 MINIMUM VALUE 87 0.999 0.047 -0.079 2.749 0.047 0.122 LOWER HINGE (25TH QUANTILE) 138 1.000 0.055 0.380 3.318 0.051 0.273 UPPER HINGE (75TH QUANTILE) 167 1.000 0.073 0.828 4.939 0.058 0.375 MAXIMUM VALUE 205 1.000 0.110 1.709 10.609 0.067 0.661 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.376 0.114 0.015 -0.257 3.067 0.091 0.602 MINIMUM CORRELATION: 0.091 SERIES 256200 AND 256240 145 YEARS MAXIMUM CORRELATION: 0.602 SERIES 256080 AND 256130 148 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.43 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. CORR 1. 3. 3. 6. 21. 28. 45. 45. 45. 45. RBAR 0.093 0.220 0.154 0.522 0.686 0.603 0.468 0.316 0.406 0.458 SDEV 0.000 0.126 0.352 0.165 0.133 0.160 0.242 0.235 0.199 0.227 SERR 0.000 0.073 0.203 0.068 0.029 0.030 0.036 0.035 0.030 0.034 EPS 0.207 0.462 0.431 0.877 0.948 0.935 0.898 0.822 0.873 0.899 NSS 2.5 3.0 4.2 6.6 8.4 9.4 10.0 10.0 10.1 10.6 YEAR 1900. 1910. 1920. 1930. 1940. 1950. 1960. CORR 55. 55. 55. 55. 55. 55. 55. RBAR 0.431 0.385 0.344 0.384 0.515 0.415 0.269 SDEV 0.227 0.205 0.263 0.228 0.177 0.180 0.200 SERR 0.031 0.028 0.036 0.031 0.024 0.024 0.027 EPS 0.893 0.873 0.852 0.873 0.921 0.886 0.802 NSS 11.0 11.0 11.0 11.0 11.0 11.0 11.0 |======================== 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 1771 1975 205 0.998 0.043 0.109 2.826 0.041 0.259 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.283 0.166 -0.119 39 166 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.21 1.04 1.00 1.08 2.12 10.55 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 1.00 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 0.258 0.253 0.237 0.086 0.088 -0.003 0.089 0.058 0.018 0.090 PACF 0.258 0.200 0.148 -0.042 0.003 -0.069 0.094 0.033 -0.014 0.049 95% C.L. 0.140 0.149 0.157 0.164 0.165 0.165 0.165 0.166 0.167 0.167 |------------------ 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 3 0.127 0.179 0.169 0.148 |======================= 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 0.285 0.299 0.291 0.094 0.112 -0.010 0.084 0.062 0.045 0.107 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 0.285 2 0.217 0.237 3 0.174 0.197 0.183 4 0.189 0.213 0.197 -0.081 5 0.188 0.214 0.198 -0.080 -0.005 6 0.188 0.206 0.218 -0.058 0.015 -0.101 7 0.198 0.204 0.224 -0.080 -0.006 -0.120 0.101 8 0.193 0.210 0.224 -0.076 -0.017 -0.130 0.092 0.047 9 0.192 0.207 0.228 -0.076 -0.015 -0.137 0.086 0.041 0.030 10 0.191 0.206 0.225 -0.070 -0.014 -0.134 0.076 0.033 0.022 0.042 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) 717.19 701.82 691.97 686.97 687.63 689.63 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 689.51 689.40 690.94 692.75 694.39 SELECTED AUTOREGRESSION ORDER: 3 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 0.174 0.197 0.183 R-SQUARED DUE TO POOLED AUTOREGRESSION: 16.19 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 119.32 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.174 0.227 0.257 0.121 0.114 0.091 0.060 0.049 0.037 0.0272 0.021 0.016 0.012 0.009 0.007 0.005 0.004 0.003 0.002 0.0017 0.001 0.001 0.001 0.001 0.000 0.000 0.000 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 256010 3 0.202 0.260 0.165 0.156 2 256020 3 0.117 0.204 0.139 0.134 3 256040 3 0.176 0.156 0.262 0.148 4 256080 3 0.225 0.253 0.175 0.181 5 256130 3 0.190 0.294 0.186 0.054 6 256170 3 0.115 0.146 0.170 0.167 7 256190 3 0.151 0.257 0.221 -0.009 8 256200 3 0.151 0.285 0.054 0.168 9 256240 3 0.510 0.439 0.346 -0.009 10 256250 3 0.155 0.094 0.173 0.042 11 256270 3 0.325 0.452 0.082 0.106 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.211 0.258 0.179 0.103 STANDARD DEVIATION 0 0.115 0.112 0.080 0.072 MEDIAN 3 0.176 0.257 0.173 0.134 INTERQUARTILE RANGE 0 0.063 0.109 0.051 0.113 MINIMUM VALUE 3 0.115 0.094 0.054 -0.009 LOWER HINGE 3 0.151 0.180 0.152 0.048 UPPER HINGE 3 0.214 0.289 0.203 0.161 MAXIMUM VALUE 3 0.510 0.452 0.346 0.181 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 1.000 0.062 0.663 4.843 0.067 -0.017 2 256020 1772 1975 204 1.000 0.057 0.540 4.258 0.060 -0.003 3 256040 1845 1975 131 1.000 0.058 0.676 3.858 0.064 0.005 4 256080 1828 1975 148 1.000 0.054 0.270 2.572 0.063 0.015 5 256130 1819 1975 157 1.000 0.069 0.974 5.663 0.068 -0.001 6 256170 1889 1975 87 1.000 0.052 0.223 3.874 0.058 0.005 7 256190 1771 1975 205 1.000 0.050 0.344 3.355 0.055 0.002 8 256200 1799 1975 177 1.000 0.049 0.197 3.092 0.056 -0.010 9 256240 1831 1975 145 1.000 0.078 1.601 9.631 0.082 -0.003 10 256250 1846 1975 130 1.000 0.046 -0.117 3.492 0.051 0.013 11 256270 1827 1975 149 1.000 0.071 1.990 12.708 0.072 0.018 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.059 0.669 5.213 0.063 0.002 STANDARD DEVIATION 33 0.000 0.010 0.635 3.138 0.009 0.010 MEDIAN (50TH QUANTILE) 149 1.000 0.057 0.540 3.874 0.063 0.002 INTERQUARTILE RANGE 29 0.000 0.014 0.579 1.830 0.010 0.012 MINIMUM VALUE 87 1.000 0.046 -0.117 2.572 0.051 -0.017 LOWER HINGE (25TH QUANTILE) 138 1.000 0.051 0.246 3.424 0.057 -0.003 UPPER HINGE (75TH QUANTILE) 167 1.000 0.065 0.825 5.253 0.067 0.009 MAXIMUM VALUE 205 1.000 0.078 1.990 12.708 0.082 0.018 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.411 0.083 0.011 0.333 3.489 0.199 0.614 MINIMUM CORRELATION: 0.199 SERIES 256170 AND 256250 87 YEARS MAXIMUM CORRELATION: 0.614 SERIES 256080 AND 256130 148 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.43 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. CORR 1. 3. 3. 6. 21. 28. 45. 45. 45. 45. RBAR 0.109 0.293 0.302 0.598 0.694 0.647 0.496 0.360 0.449 0.532 SDEV 0.000 0.087 0.232 0.190 0.117 0.123 0.168 0.206 0.162 0.156 SERR 0.000 0.050 0.134 0.078 0.025 0.023 0.025 0.031 0.024 0.023 EPS 0.237 0.558 0.643 0.907 0.950 0.945 0.908 0.849 0.891 0.923 NSS 2.5 3.0 4.2 6.6 8.4 9.4 10.0 10.0 10.1 10.6 YEAR 1900. 1910. 1920. 1930. 1940. 1950. 1960. CORR 55. 55. 55. 55. 55. 55. 55. RBAR 0.427 0.388 0.369 0.375 0.454 0.441 0.293 SDEV 0.154 0.176 0.183 0.170 0.201 0.182 0.185 SERR 0.021 0.024 0.025 0.023 0.027 0.025 0.025 EPS 0.891 0.875 0.866 0.868 0.901 0.897 0.820 NSS 11.0 11.0 11.0 11.0 11.0 11.0 11.0 |======================== 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 1771 1975 205 0.999 0.040 0.150 2.983 0.047 -0.097 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.246 0.142 -0.102 42 163 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.32 1.99 1.01 1.09 3.08 38.28 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 1.00 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 -0.096 -0.001 0.075 -0.081 0.007 -0.098 0.023 0.032 -0.001 0.094 PACF -0.096 -0.011 0.074 -0.068 -0.007 -0.105 0.015 0.030 0.020 0.081 95% C.L. 0.140 0.141 0.141 0.142 0.143 0.143 0.144 0.144 0.144 0.144 |------------------ 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 0.004 -0.001 0.002 -0.070 -0.014 -0.104 0.016 0.038 0.018 0.088 PACF 0.004 -0.001 0.002 -0.070 -0.013 -0.105 0.017 0.033 0.017 0.074 95% C.L. 0.140 0.140 0.140 0.140 0.140 0.140 0.142 0.142 0.142 0.142 |----------------- 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 3 0.005 0.004 -0.001 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 1771 1975 205 0.999 0.043 0.074 3.008 0.041 0.254 |------------ 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 0.253 0.264 0.250 0.072 0.100 0.002 0.067 0.069 0.038 0.089 PACF 0.253 0.214 0.160 -0.067 0.011 -0.065 0.068 0.051 0.014 0.039 95% C.L. 0.140 0.148 0.157 0.165 0.165 0.167 0.167 0.167 0.168 0.168 |------------------- 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 3 0.136 0.165 0.183 0.161 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.17 MINUTES