RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN016N.rwl LOG FILE PROCESSED: FRAN016N.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 DENSITY_MINIMUM 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 3 257090 MISSING VALUES FOUND: 10 IN 2 GAPS / 1863 1867 / 1873 1877 / -------------------------------------------------------------------- 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 0.298 0.022 0.403 4.431 0.063 0.260 2 257070 1823 1975 153 0.324 0.054 0.537 2.759 0.071 0.842 3 257090 1835 1975 141 0.288 0.027 0.461 3.659 0.074 0.462 4 257120 1881 1975 95 0.308 0.029 0.814 4.013 0.057 0.675 5 257150 1792 1975 184 0.318 0.030 0.260 2.718 0.060 0.670 6 257160 1803 1975 173 0.325 0.041 0.097 2.554 0.067 0.743 7 257220 1847 1975 129 0.284 0.027 0.178 2.278 0.053 0.743 8 257230 1826 1975 150 0.355 0.032 0.774 5.734 0.062 0.437 9 257260 1850 1975 126 0.322 0.031 0.458 3.432 0.061 0.621 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 141 0.314 0.032 0.443 3.509 0.063 0.606 STANDARD DEVIATION 26 0.022 0.009 0.245 1.101 0.007 0.184 MEDIAN (50TH QUANTILE) 131 0.318 0.030 0.458 3.432 0.062 0.670 INTERQUARTILE RANGE 24 0.026 0.005 0.277 1.295 0.007 0.280 MINIMUM VALUE 95 0.284 0.022 0.097 2.278 0.053 0.260 LOWER HINGE (25TH QUANTILE) 129 0.298 0.027 0.260 2.718 0.060 0.462 UPPER HINGE (75TH QUANTILE) 153 0.324 0.032 0.537 4.013 0.067 0.743 MAXIMUM VALUE 179 0.355 0.054 0.814 5.734 0.074 0.842 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.272 0.276 0.046 -0.277 2.560 -0.339 0.746 MINIMUM CORRELATION: -0.339 SERIES 257120 AND 257220 95 YEARS MAXIMUM CORRELATION: 0.746 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 0.026 0.315 0.228 0.495 0.327 0.122 0.450 0.499 0.399 0.479 SDEV 0.000 0.000 0.315 0.257 0.346 0.341 0.243 0.164 0.260 0.192 SERR 0.000 0.000 0.129 0.081 0.065 0.064 0.046 0.031 0.043 0.032 EPS 0.064 0.636 0.599 0.870 0.795 0.526 0.874 0.899 0.856 0.892 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 0.384 0.191 0.240 0.414 0.389 SDEV 0.349 0.381 0.264 0.227 0.210 SERR 0.058 0.064 0.044 0.038 0.035 EPS 0.849 0.680 0.740 0.864 0.852 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 0.312 0.022 0.267 2.787 0.049 0.589 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.456 0.355 -0.079 36 148 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.80 2.34 1.01 1.29 3.64 7.21 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.19 0.00 0.81 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 0.586 0.560 0.535 0.534 0.470 0.456 0.399 0.375 0.359 0.348 PACF 0.586 0.329 0.209 0.178 0.036 0.049 -0.030 -0.012 0.019 0.033 95% C.L. 0.147 0.191 0.224 0.250 0.274 0.291 0.306 0.317 0.327 0.335 |------------------ 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 0.483 0.264 0.205 0.180 0.187 |================== 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 -0.00001012 0.29864219 2 257070 3 0.00000000 0.00000000 -0.00025311 0.34354144 3 257090 3 0.00000000 0.00000000 -0.00012294 0.29767698 4 257120 3 0.00000000 0.00000000 0.00004493 0.30626428 5 257150 3 0.00000000 0.00000000 0.00002165 0.31581575 6 257160 3 0.00000000 0.00000000 -0.00036453 0.35651162 7 257220 1 0.08329668 0.01947188 0.00000000 0.25346902 8 257230 3 0.00000000 0.00000000 0.00010841 0.34688145 9 257260 3 0.00000000 0.00000000 -0.00005762 0.32532573 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 1.000 0.075 0.372 4.431 0.062 0.257 2 257070 1823 1975 153 1.000 0.163 0.712 3.021 0.070 0.834 3 257090 1835 1975 141 1.000 0.089 0.365 3.792 0.073 0.436 4 257120 1881 1975 95 1.000 0.093 0.804 3.989 0.056 0.667 5 257150 1792 1975 184 1.000 0.094 0.301 2.692 0.059 0.670 6 257160 1803 1975 173 1.000 0.114 0.474 2.845 0.067 0.685 7 257220 1847 1975 129 1.000 0.062 0.181 3.056 0.053 0.415 8 257230 1826 1975 150 1.000 0.089 0.758 5.552 0.062 0.424 9 257260 1850 1975 126 1.000 0.095 0.456 3.484 0.061 0.614 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 1.000 0.097 0.491 3.651 0.063 0.556 STANDARD DEVIATION 26 0.000 0.028 0.218 0.916 0.006 0.182 MEDIAN (50TH QUANTILE) 141 1.000 0.093 0.456 3.484 0.062 0.614 INTERQUARTILE RANGE 24 0.000 0.006 0.347 0.968 0.008 0.247 MINIMUM VALUE 95 1.000 0.062 0.181 2.692 0.053 0.257 LOWER HINGE (25TH QUANTILE) 129 1.000 0.089 0.365 3.021 0.059 0.424 UPPER HINGE (75TH QUANTILE) 153 1.000 0.095 0.712 3.989 0.067 0.670 MAXIMUM VALUE 184 1.000 0.163 0.804 5.552 0.073 0.834 |------------------------ 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 1.000 0.065 1.202 6.721 0.063 0.017 2 257070 1823 1975 153 0.999 0.110 -0.008 4.091 0.071 0.630 3 257090 1835 1975 141 1.000 0.072 0.476 4.298 0.073 0.133 4 257120 1881 1975 95 0.999 0.063 0.775 4.561 0.057 0.266 5 257150 1792 1975 184 1.000 0.065 0.404 3.302 0.059 0.335 6 257160 1803 1975 173 0.999 0.082 0.562 3.571 0.067 0.406 7 257220 1847 1975 129 1.000 0.053 0.234 2.949 0.053 0.205 8 257230 1826 1975 150 1.000 0.086 0.828 6.101 0.062 0.384 9 257260 1850 1975 126 0.999 0.080 0.364 3.459 0.061 0.453 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 0.999 0.075 0.537 4.339 0.063 0.314 STANDARD DEVIATION 26 0.000 0.017 0.358 1.288 0.006 0.183 MEDIAN (50TH QUANTILE) 141 1.000 0.072 0.476 4.091 0.062 0.335 INTERQUARTILE RANGE 24 0.000 0.018 0.411 1.102 0.008 0.201 MINIMUM VALUE 95 0.999 0.053 -0.008 2.949 0.053 0.017 LOWER HINGE (25TH QUANTILE) 129 0.999 0.065 0.364 3.459 0.059 0.205 UPPER HINGE (75TH QUANTILE) 153 1.000 0.082 0.775 4.561 0.067 0.406 MAXIMUM VALUE 184 1.000 0.110 1.202 6.721 0.073 0.630 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.322 0.143 0.024 -0.304 3.212 -0.055 0.585 MINIMUM CORRELATION: -0.055 SERIES 257070 AND 257120 95 YEARS MAXIMUM CORRELATION: 0.585 SERIES 257090 AND 257160 141 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 0.048 0.310 0.299 0.527 0.374 0.175 0.476 0.506 0.463 0.537 SDEV 0.000 0.000 0.293 0.250 0.305 0.265 0.217 0.172 0.179 0.134 SERR 0.000 0.000 0.119 0.079 0.058 0.050 0.041 0.032 0.030 0.022 EPS 0.114 0.630 0.682 0.884 0.827 0.629 0.885 0.902 0.886 0.913 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 0.401 0.178 0.283 0.381 0.443 SDEV 0.238 0.302 0.269 0.198 0.197 SERR 0.040 0.050 0.045 0.033 0.033 EPS 0.858 0.661 0.781 0.847 0.878 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 0.997 0.050 0.537 3.898 0.047 0.220 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.149 0.107 -0.052 29 155 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.37 1.01 1.01 1.18 2.19 15.60 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 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 0.219 0.149 0.150 0.139 0.102 0.113 0.059 0.062 0.070 0.072 PACF 0.219 0.106 0.104 0.082 0.037 0.057 -0.007 0.016 0.027 0.029 95% C.L. 0.147 0.154 0.157 0.161 0.163 0.164 0.166 0.167 0.167 0.168 |------------------ 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 2 0.071 0.199 0.107 |======================= 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 0.259 0.190 0.237 0.168 0.148 0.157 0.108 0.088 0.076 0.097 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 0.259 2 0.225 0.131 3 0.202 0.092 0.175 4 0.191 0.086 0.162 0.065 5 0.187 0.077 0.157 0.054 0.054 6 0.184 0.074 0.148 0.050 0.043 0.062 7 0.184 0.073 0.147 0.048 0.042 0.060 0.009 8 0.184 0.073 0.147 0.048 0.041 0.060 0.008 0.004 9 0.184 0.073 0.147 0.048 0.042 0.060 0.008 0.004 -0.002 10 0.184 0.073 0.147 0.046 0.040 0.058 0.002 0.001 -0.009 0.039 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) 597.46 586.66 585.46 581.74 582.97 584.43 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 585.73 587.71 589.71 591.71 593.43 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 0.202 0.092 0.175 R-SQUARED DUE TO POOLED AUTOREGRESSION: 11.13 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 112.53 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.202 0.133 0.220 0.092 0.062 0.060 0.034 0.023 0.018 0.0117 0.008 0.006 0.004 0.003 0.002 0.001 0.001 0.001 0.000 0.0003 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 3 0.006 0.018 -0.015 0.016 2 257070 3 0.453 0.479 0.149 0.130 3 257090 3 0.107 0.075 0.120 0.262 4 257120 3 0.092 0.242 0.042 0.122 5 257150 3 0.153 0.294 0.115 0.026 6 257160 3 0.256 0.262 0.215 0.151 7 257220 3 0.059 0.190 0.041 0.108 8 257230 3 0.175 0.339 0.148 -0.037 9 257260 3 0.289 0.302 0.172 0.194 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.177 0.245 0.110 0.108 STANDARD DEVIATION 0 0.137 0.138 0.073 0.093 MEDIAN 3 0.153 0.262 0.120 0.122 INTERQUARTILE RANGE 0 0.165 0.113 0.107 0.125 MINIMUM VALUE 3 0.006 0.018 -0.015 -0.037 LOWER HINGE 3 0.092 0.190 0.042 0.026 UPPER HINGE 3 0.256 0.302 0.149 0.151 MAXIMUM VALUE 3 0.453 0.479 0.215 0.262 |------------------- 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 0.065 1.201 6.707 0.063 0.001 2 257070 1823 1975 153 1.000 0.081 0.418 3.693 0.087 -0.007 3 257090 1835 1975 141 1.000 0.068 0.364 4.084 0.075 -0.003 4 257120 1881 1975 95 1.000 0.060 0.813 4.508 0.064 0.001 5 257150 1792 1975 184 1.000 0.060 0.409 3.165 0.068 -0.004 6 257160 1803 1975 173 1.000 0.072 0.729 4.031 0.077 -0.019 7 257220 1847 1975 129 1.000 0.051 0.231 3.060 0.058 -0.005 8 257230 1826 1975 150 1.000 0.078 1.715 10.846 0.072 0.001 9 257260 1850 1975 126 1.000 0.068 0.480 3.827 0.071 0.018 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 1.000 0.067 0.706 4.880 0.071 -0.002 STANDARD DEVIATION 26 0.000 0.009 0.479 2.480 0.009 0.010 MEDIAN (50TH QUANTILE) 141 1.000 0.068 0.480 4.031 0.071 -0.003 INTERQUARTILE RANGE 24 0.000 0.011 0.404 0.815 0.011 0.006 MINIMUM VALUE 95 1.000 0.051 0.231 3.060 0.058 -0.019 LOWER HINGE (25TH QUANTILE) 129 1.000 0.060 0.409 3.693 0.064 -0.005 UPPER HINGE (75TH QUANTILE) 153 1.000 0.072 0.813 4.508 0.075 0.001 MAXIMUM VALUE 184 1.000 0.081 1.715 10.846 0.087 0.018 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.386 0.103 0.017 0.063 3.488 0.131 0.640 MINIMUM CORRELATION: 0.131 SERIES 257030 AND 257220 129 YEARS MAXIMUM CORRELATION: 0.640 SERIES 257090 AND 257160 141 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 0.111 0.309 0.236 0.517 0.403 0.282 0.548 0.580 0.484 0.578 SDEV 0.000 0.000 0.305 0.275 0.350 0.228 0.144 0.121 0.159 0.107 SERR 0.000 0.000 0.124 0.087 0.066 0.043 0.027 0.023 0.026 0.018 EPS 0.242 0.629 0.609 0.879 0.843 0.758 0.911 0.925 0.894 0.925 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 0.418 0.154 0.342 0.428 0.478 SDEV 0.173 0.202 0.218 0.193 0.175 SERR 0.029 0.034 0.036 0.032 0.029 EPS 0.866 0.621 0.824 0.871 0.892 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 0.997 0.048 0.445 3.851 0.053 -0.055 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.246 0.167 -0.122 32 152 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.50 5.02 1.01 1.41 6.43 25.81 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 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 -0.055 -0.074 -0.014 0.051 -0.013 0.033 0.001 0.012 0.035 0.098 PACF -0.055 -0.077 -0.023 0.043 -0.010 0.039 0.006 0.016 0.040 0.102 95% C.L. 0.147 0.148 0.149 0.149 0.149 0.149 0.149 0.149 0.149 0.149 |------------------ 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 0.002 0.002 0.045 -0.010 0.038 0.010 0.025 0.037 0.091 PACF 0.000 0.002 0.002 0.045 -0.010 0.038 0.009 0.023 0.038 0.088 95% C.L. 0.147 0.147 0.147 0.147 0.148 0.148 0.148 0.148 0.148 0.148 |----------------- 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 0.002 0.000 0.002 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 1792 1975 184 0.997 0.051 0.389 3.732 0.046 0.271 |------------ 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 0.269 0.201 0.255 0.162 0.094 0.118 0.079 0.055 0.051 0.065 PACF 0.269 0.138 0.188 0.046 -0.010 0.036 0.002 0.002 0.002 0.030 95% C.L. 0.147 0.158 0.163 0.172 0.175 0.176 0.178 0.179 0.179 0.179 |------------------- 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 0.127 0.209 0.095 0.190 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.09 MINUTES