RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN016P.rwl LOG FILE PROCESSED: FRAN016P.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: 257 1 Col dAllos LATEWOOD_PERCENT PCAB - 257 2 France Norway spruce 1900 4416-634 1792 1975 - 257 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 257150 MISSING VALUES FOUND: 5 IN 1 GAPS / 1933 1937 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 2.763 0.732 1.452 6.922 0.177 0.411 2 257070 1823 1975 153 3.217 1.494 1.069 3.980 0.184 0.793 3 257090 1835 1975 141 2.111 0.434 0.800 5.297 0.189 0.239 4 257120 1881 1975 95 2.930 1.037 2.231 10.667 0.225 0.455 5 257150 1792 1975 184 2.940 0.751 0.756 4.025 0.181 0.531 6 257160 1803 1975 173 2.819 0.893 0.466 2.787 0.196 0.630 7 257220 1847 1975 129 2.839 0.633 0.576 3.013 0.168 0.555 8 257230 1826 1975 150 3.706 0.920 0.739 3.370 0.195 0.445 9 257260 1850 1975 126 3.376 0.985 0.842 3.558 0.216 0.526 NUMBER OF SERIES READ IN: 9 FROM 1792 TO 1975 184 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 2.967 0.875 0.992 4.847 0.192 0.509 STANDARD DEVIATION 25 0.446 0.299 0.546 2.531 0.018 0.153 MEDIAN (50TH QUANTILE) 141 2.930 0.893 0.800 3.980 0.189 0.526 INTERQUARTILE RANGE 24 0.397 0.254 0.330 1.927 0.015 0.110 MINIMUM VALUE 95 2.111 0.434 0.466 2.787 0.168 0.239 LOWER HINGE (25TH QUANTILE) 129 2.819 0.732 0.739 3.370 0.181 0.445 UPPER HINGE (75TH QUANTILE) 153 3.217 0.985 1.069 5.297 0.196 0.555 MAXIMUM VALUE 179 3.706 1.494 2.231 10.667 0.225 0.793 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.297 0.224 0.037 -0.352 2.573 -0.187 0.730 MINIMUM CORRELATION: -0.187 SERIES 257070 AND 257120 95 YEARS MAXIMUM CORRELATION: 0.730 SERIES 257070 AND 257160 153 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 68.75 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. CORR 1. 1. 6. 10. 28. 28. 28. 28. 36. 36. RBAR 0.397 0.525 0.536 0.378 0.299 0.195 0.342 0.336 0.441 0.467 SDEV 0.000 0.000 0.109 0.179 0.263 0.302 0.215 0.270 0.202 0.157 SERR 0.000 0.000 0.045 0.057 0.050 0.057 0.041 0.051 0.034 0.026 EPS 0.627 0.808 0.854 0.805 0.773 0.660 0.815 0.819 0.876 0.887 NSS 2.5 3.8 5.1 6.8 8.0 8.0 8.4 8.9 9.0 9.0 YEAR 1920. 1930. 1940. 1950. 1960. CORR 36. 36. 36. 36. 36. RBAR 0.209 0.205 0.209 0.315 0.237 SDEV 0.317 0.247 0.203 0.192 0.188 SERR 0.053 0.041 0.034 0.032 0.031 EPS 0.704 0.699 0.704 0.805 0.737 NSS 9.0 9.0 9.0 9.0 9.0 |======================== 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 1792 1975 184 2.892 0.562 0.352 3.019 0.140 0.534 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.545 0.389 -0.398 31 153 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.71 1.88 1.00 1.22 3.09 15.38 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.18 0.00 0.82 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 141. 24. 95. 129. 153. 184. |----------- 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 0.531 0.465 0.404 0.455 0.370 0.227 0.291 0.310 0.349 0.233 PACF 0.531 0.254 0.126 0.222 0.022 -0.152 0.120 0.097 0.126 -0.046 95% C.L. 0.147 0.184 0.208 0.225 0.244 0.256 0.260 0.267 0.275 0.284 |------------------ 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 4 0.393 0.317 0.156 0.065 0.244 |================== 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 257030 3 0.00000000 0.00000000 -0.00964445 3.39030027 2 257070 3 0.00000000 0.00000000 -0.00930692 3.93336511 3 257090 3 0.00000000 0.00000000 -0.00426221 2.41346812 4 257120 3 0.00000000 0.00000000 0.00229759 2.81950498 5 257150 3 0.00000000 0.00000000 -0.00065590 2.99896836 6 257160 3 0.00000000 0.00000000 -0.00943411 3.64007401 7 257220 1 1.60446668 0.03667541 0.00000000 2.50906491 8 257230 3 0.00000000 0.00000000 -0.00900410 4.38594294 9 257260 3 0.00000000 0.00000000 -0.00381162 3.61775231 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 0.999 0.217 1.063 5.060 0.176 0.234 2 257070 1823 1975 153 0.996 0.451 1.409 5.077 0.182 0.778 3 257090 1835 1975 141 1.000 0.188 0.912 5.186 0.188 0.126 4 257120 1881 1975 95 1.000 0.352 2.242 10.824 0.223 0.447 5 257150 1792 1975 184 1.000 0.253 0.821 4.190 0.178 0.524 6 257160 1803 1975 173 0.997 0.267 0.908 3.524 0.195 0.530 7 257220 1847 1975 129 1.000 0.178 0.444 2.751 0.166 0.289 8 257230 1826 1975 150 1.000 0.227 1.080 4.975 0.193 0.306 9 257260 1850 1975 126 1.000 0.288 0.866 3.636 0.214 0.515 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 0.999 0.269 1.083 5.025 0.191 0.416 STANDARD DEVIATION 26 0.002 0.087 0.504 2.338 0.018 0.197 MEDIAN (50TH QUANTILE) 141 1.000 0.253 0.912 4.975 0.188 0.447 INTERQUARTILE RANGE 24 0.001 0.071 0.214 1.441 0.017 0.235 MINIMUM VALUE 95 0.996 0.178 0.444 2.751 0.166 0.126 LOWER HINGE (25TH QUANTILE) 129 0.999 0.217 0.866 3.636 0.178 0.289 UPPER HINGE (75TH QUANTILE) 153 1.000 0.288 1.080 5.077 0.195 0.524 MAXIMUM VALUE 184 1.000 0.451 2.242 10.824 0.223 0.778 |------------------------ 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 257030 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 257070 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 257090 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 257120 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 257150 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 257160 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 257220 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 257230 -67 100 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 257260 -67 84 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 257030 1847 1975 129 0.999 0.205 1.275 6.769 0.176 0.137 2 257070 1823 1975 153 0.990 0.283 0.956 4.544 0.182 0.568 3 257090 1835 1975 141 0.999 0.176 0.913 5.490 0.188 0.005 4 257120 1881 1975 95 0.994 0.263 1.859 8.820 0.223 0.187 5 257150 1792 1975 184 0.997 0.186 0.727 3.547 0.178 0.235 6 257160 1803 1975 173 0.997 0.208 0.693 3.455 0.195 0.248 7 257220 1847 1975 129 0.999 0.162 0.464 2.752 0.166 0.178 8 257230 1826 1975 150 1.000 0.224 1.017 4.797 0.193 0.292 9 257260 1850 1975 126 0.994 0.219 0.347 2.967 0.213 0.236 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 0.997 0.214 0.917 4.794 0.190 0.232 STANDARD DEVIATION 26 0.003 0.039 0.453 1.985 0.018 0.151 MEDIAN (50TH QUANTILE) 141 0.997 0.208 0.913 4.544 0.188 0.235 INTERQUARTILE RANGE 24 0.005 0.038 0.324 2.034 0.016 0.070 MINIMUM VALUE 95 0.990 0.162 0.347 2.752 0.166 0.005 LOWER HINGE (25TH QUANTILE) 129 0.994 0.186 0.693 3.455 0.178 0.178 UPPER HINGE (75TH QUANTILE) 153 0.999 0.224 1.017 5.490 0.195 0.248 MAXIMUM VALUE 184 1.000 0.283 1.859 8.820 0.223 0.568 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.247 0.145 0.024 0.231 2.747 -0.009 0.542 MINIMUM CORRELATION: -0.009 SERIES 257070 AND 257120 95 YEARS MAXIMUM CORRELATION: 0.542 SERIES 257070 AND 257160 153 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 68.75 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. CORR 1. 1. 6. 10. 28. 28. 28. 28. 36. 36. RBAR 0.410 0.535 0.559 0.392 0.332 0.231 0.345 0.345 0.465 0.447 SDEV 0.000 0.000 0.078 0.219 0.234 0.281 0.223 0.272 0.178 0.174 SERR 0.000 0.000 0.032 0.069 0.044 0.053 0.042 0.051 0.030 0.029 EPS 0.639 0.814 0.865 0.814 0.799 0.706 0.816 0.825 0.887 0.879 NSS 2.5 3.8 5.1 6.8 8.0 8.0 8.4 8.9 9.0 9.0 YEAR 1920. 1930. 1940. 1950. 1960. CORR 36. 36. 36. 36. 36. RBAR 0.207 0.170 0.201 0.222 0.297 SDEV 0.277 0.216 0.210 0.197 0.177 SERR 0.046 0.036 0.035 0.033 0.030 EPS 0.701 0.648 0.693 0.719 0.792 NSS 9.0 9.0 9.0 9.0 9.0 |======================== 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 1792 1975 184 0.987 0.133 0.645 3.615 0.129 0.197 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.273 0.175 -0.021 28 156 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.92 1.94 1.01 1.08 3.02 7.72 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.17 0.00 0.83 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 0.196 0.112 0.045 0.130 0.015 -0.082 0.016 0.090 0.140 0.000 PACF 0.196 0.077 0.010 0.117 -0.035 -0.106 0.051 0.087 0.116 -0.040 95% C.L. 0.147 0.153 0.155 0.155 0.157 0.157 0.158 0.158 0.159 0.162 |------------------ 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 0.046 0.200 |======================= 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 0.118 0.100 0.025 0.133 0.006 -0.066 0.047 0.124 0.163 -0.001 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 0.118 2 0.108 0.088 3 0.108 0.087 0.004 4 0.107 0.076 -0.009 0.124 5 0.110 0.076 -0.007 0.126 -0.025 6 0.108 0.087 -0.008 0.133 -0.015 -0.090 7 0.114 0.088 -0.017 0.134 -0.021 -0.097 0.067 8 0.106 0.100 -0.015 0.118 -0.019 -0.107 0.054 0.114 9 0.090 0.092 0.000 0.121 -0.035 -0.105 0.040 0.100 0.139 10 0.095 0.096 0.002 0.117 -0.037 -0.101 0.040 0.103 0.142 -0.035 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) 942.84 942.24 942.83 944.83 943.99 945.88 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 946.38 947.57 947.14 945.56 947.33 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 0.118 R-SQUARED DUE TO POOLED AUTOREGRESSION: 1.40 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 101.42 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.118 0.014 0.002 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 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 257030 1 0.024 0.140 2 257070 1 0.380 0.584 3 257090 1 0.017 0.005 4 257120 1 0.037 0.188 5 257150 1 0.060 0.238 6 257160 1 0.089 0.251 7 257220 1 0.048 0.180 8 257230 1 0.086 0.292 9 257260 1 0.203 0.241 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.105 0.236 STANDARD DEVIATION 0 0.117 0.155 MEDIAN 1 0.060 0.238 INTERQUARTILE RANGE 0 0.052 0.071 MINIMUM VALUE 1 0.017 0.005 LOWER HINGE 1 0.037 0.180 UPPER HINGE 1 0.089 0.251 MAXIMUM VALUE 1 0.380 0.584 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 1.000 0.203 1.159 6.506 0.190 0.008 2 257070 1823 1975 153 1.000 0.228 1.059 4.890 0.248 -0.143 3 257090 1835 1975 141 1.000 0.176 0.915 5.493 0.188 -0.001 4 257120 1881 1975 95 1.000 0.258 2.091 9.578 0.243 -0.006 5 257150 1792 1975 184 1.000 0.181 0.667 3.443 0.199 -0.015 6 257160 1803 1975 173 1.000 0.201 0.617 3.289 0.221 -0.041 7 257220 1847 1975 129 1.000 0.160 0.400 2.759 0.184 -0.021 8 257230 1826 1975 150 1.000 0.214 1.104 5.502 0.218 0.005 9 257260 1850 1975 126 1.000 0.213 0.355 3.065 0.243 -0.088 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 1.000 0.204 0.930 4.947 0.215 -0.033 STANDARD DEVIATION 26 0.000 0.030 0.528 2.174 0.025 0.051 MEDIAN (50TH QUANTILE) 141 1.000 0.203 0.915 4.890 0.218 -0.015 INTERQUARTILE RANGE 24 0.000 0.033 0.487 2.213 0.052 0.040 MINIMUM VALUE 95 1.000 0.160 0.355 2.759 0.184 -0.143 LOWER HINGE (25TH QUANTILE) 129 1.000 0.181 0.617 3.289 0.190 -0.041 UPPER HINGE (75TH QUANTILE) 153 1.000 0.214 1.104 5.502 0.243 -0.001 MAXIMUM VALUE 184 1.000 0.258 2.091 9.578 0.248 0.008 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.280 0.127 0.021 0.440 2.638 0.075 0.552 MINIMUM CORRELATION: 0.075 SERIES 257120 AND 257230 95 YEARS MAXIMUM CORRELATION: 0.552 SERIES 257150 AND 257260 126 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 68.75 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. CORR 1. 1. 6. 10. 28. 28. 28. 28. 36. 36. RBAR 0.310 0.511 0.461 0.394 0.339 0.227 0.361 0.373 0.480 0.507 SDEV 0.000 0.000 0.155 0.222 0.246 0.318 0.227 0.237 0.164 0.152 SERR 0.000 0.000 0.063 0.070 0.047 0.060 0.043 0.045 0.027 0.025 EPS 0.534 0.799 0.812 0.816 0.804 0.701 0.827 0.842 0.893 0.903 NSS 2.5 3.8 5.1 6.8 8.0 8.0 8.4 8.9 9.0 9.0 YEAR 1920. 1930. 1940. 1950. 1960. CORR 36. 36. 36. 36. 36. RBAR 0.235 0.173 0.239 0.233 0.308 SDEV 0.217 0.192 0.192 0.186 0.157 SERR 0.036 0.032 0.032 0.031 0.026 EPS 0.734 0.653 0.739 0.732 0.800 NSS 9.0 9.0 9.0 9.0 9.0 |======================== 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 1792 1975 184 0.989 0.130 0.704 3.816 0.145 -0.078 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.270 0.163 -0.020 35 149 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.37 1.30 1.01 1.16 2.46 16.38 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.17 0.00 0.83 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 -0.078 0.055 -0.050 0.132 -0.002 -0.129 0.010 0.043 0.160 -0.013 PACF -0.078 0.050 -0.042 0.124 0.021 -0.145 0.002 0.045 0.159 0.043 95% C.L. 0.147 0.148 0.149 0.149 0.152 0.152 0.154 0.154 0.154 0.158 |------------------ 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 0.003 0.045 -0.036 0.129 -0.002 -0.130 0.003 0.059 0.165 -0.002 PACF 0.003 0.045 -0.036 0.128 0.000 -0.145 0.016 0.058 0.159 0.028 95% C.L. 0.147 0.147 0.148 0.148 0.150 0.150 0.153 0.153 0.153 0.157 |----------------- 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 0.002 0.003 |========================= 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 1792 1975 184 0.989 0.130 0.743 3.821 0.130 0.123 |------------ 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 0.123 0.055 -0.014 0.124 -0.001 -0.126 -0.003 0.079 0.171 0.012 PACF 0.123 0.041 -0.026 0.128 -0.030 -0.139 0.039 0.077 0.152 0.000 95% C.L. 0.147 0.150 0.150 0.150 0.152 0.152 0.155 0.155 0.155 0.159 |------------------- 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 0.017 0.125 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.09 MINUTES