RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit019n.rwl LOG FILE PROCESSED: brit019n.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 50 25 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: 375 1 Franchise Wood DENSITY_MINIMUM PISY - 375 2 Great Britain Scots pine, Scotch pine 100 5057-141 1843 1976 - 375 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 375031 MISSING VALUES FOUND: 6 IN 1 GAPS / 1916 1921 / -------------------------------------------------------------------- 11 375061 MISSING VALUES FOUND: 1 IN 1 GAPS / 1868 1868 / -------------------------------------------------------------------- 19 376101 MISSING VALUES FOUND: 1 IN 1 GAPS / 1884 1884 / -------------------------------------------------------------------- 20 376102 MISSING VALUES FOUND: 7 IN 1 GAPS / 1915 1921 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 375011 1849 1976 128 0.324 0.024 -0.483 3.406 0.051 0.565 2 375012 1843 1976 134 0.314 0.021 -0.232 3.596 0.055 0.385 3 375021 1859 1976 118 0.371 0.023 0.392 3.370 0.057 0.286 4 375022 1846 1975 130 0.364 0.023 0.408 2.960 0.054 0.308 5 375031 1852 1976 125 0.342 0.029 1.111 6.330 0.054 0.580 6 375032 1849 1976 128 0.345 0.048 1.784 6.175 0.062 0.747 7 375041 1848 1976 129 0.322 0.020 0.417 3.540 0.042 0.548 8 375042 1864 1976 113 0.313 0.018 0.099 2.789 0.041 0.569 9 375051 1844 1976 133 0.329 0.031 0.514 3.486 0.064 0.546 10 375052 1854 1976 123 0.339 0.043 -0.221 2.135 0.061 0.814 11 375061 1844 1976 133 0.352 0.025 -0.067 3.023 0.050 0.628 12 375062 1864 1976 113 0.324 0.034 0.575 2.483 0.048 0.805 13 376071 1864 1976 113 0.378 0.021 0.255 2.942 0.037 0.636 14 376072 1861 1976 116 0.387 0.025 0.359 2.836 0.036 0.712 15 376081 1862 1976 115 0.384 0.027 -0.074 2.380 0.057 0.441 16 376082 1853 1976 124 0.391 0.031 0.731 4.854 0.060 0.497 17 376091 1846 1976 131 0.341 0.025 -0.308 2.498 0.062 0.466 18 376092 1849 1976 128 0.332 0.030 -0.474 2.740 0.059 0.658 19 376101 1857 1976 120 0.356 0.041 0.466 3.014 0.055 0.787 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 376102 1848 1976 129 0.343 0.042 1.497 6.974 0.061 0.715 21 376111 1866 1976 111 0.361 0.034 0.475 3.149 0.067 0.520 22 376112 1853 1976 124 0.353 0.033 0.760 5.507 0.079 0.281 23 376121 1848 1976 129 0.346 0.023 0.111 2.785 0.059 0.364 24 376122 1854 1975 122 0.380 0.029 0.055 3.274 0.056 0.467 NUMBER OF SERIES READ IN: 24 FROM 1843 TO 1976 134 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 123 0.349 0.029 0.340 3.594 0.055 0.555 STANDARD DEVIATION 7 0.023 0.008 0.568 1.341 0.010 0.162 MEDIAN (50TH QUANTILE) 123 0.345 0.028 0.376 3.086 0.057 0.557 INTERQUARTILE RANGE 12 0.037 0.010 0.615 0.780 0.011 0.232 MINIMUM VALUE 111 0.313 0.018 -0.483 2.135 0.036 0.281 LOWER HINGE (25TH QUANTILE) 117 0.330 0.023 -0.071 2.787 0.051 0.453 UPPER HINGE (75TH QUANTILE) 129 0.367 0.033 0.544 3.568 0.061 0.685 MAXIMUM VALUE 134 0.391 0.048 1.784 6.974 0.079 0.814 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.271 0.200 0.012 -0.017 2.618 -0.280 0.747 MINIMUM CORRELATION: -0.280 SERIES 375062 AND 376122 112 YEARS MAXIMUM CORRELATION: 0.747 SERIES 375031 AND 375032 125 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 89.13 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 276. 276. 276. RBAR 0.267 0.215 0.306 SDEV 0.230 0.224 0.205 SERR 0.014 0.013 0.012 EPS 0.897 0.868 0.914 NSS 24.0 24.0 24.0 |======================== 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 1843 1976 134 0.347 0.017 -0.015 3.164 0.035 0.529 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.267 0.119 -0.008 22 112 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.62 1.15 1.00 1.02 2.16 5.05 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.00 0.87 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 124. 12. 111. 117. 129. 134. |----------- 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 0.525 0.536 0.401 0.454 0.501 0.433 0.379 0.331 0.356 0.371 PACF 0.525 0.360 0.051 0.184 0.258 0.026 -0.041 0.001 0.061 0.055 95% C.L. 0.173 0.215 0.252 0.270 0.292 0.317 0.334 0.347 0.356 0.366 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.374 0.335 0.362 |================== 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 375011 3 0.00000000 0.00000000 -0.00020163 0.33683318 2 375012 1 0.04832368 0.13081199 0.00000000 0.31130022 3 375021 3 0.00000000 0.00000000 -0.00034413 0.39123860 4 375022 3 0.00000000 0.00000000 -0.00019664 0.37641859 5 375031 1 0.08101267 0.02077290 0.00000000 0.31225589 6 375032 1 0.15374079 0.03653397 0.00000000 0.31278771 7 375041 3 0.00000000 0.00000000 -0.00020472 0.33532220 8 375042 1 0.02517015 0.07521349 0.00000000 0.31006941 9 375051 3 0.00000000 0.00000000 -0.00038380 0.35436091 10 375052 3 0.00000000 0.00000000 -0.00098457 0.39974275 11 375061 3 0.00000000 0.00000000 0.00013220 0.34286219 12 375062 1 0.10982233 0.03844406 0.00000000 0.29924181 13 376071 3 0.00000000 0.00000000 -0.00017400 0.38743994 14 376072 3 0.00000000 0.00000000 0.00001115 0.38607198 15 376081 3 0.00000000 0.00000000 -0.00030695 0.40145537 16 376082 3 0.00000000 0.00000000 -0.00033331 0.41188040 17 376091 3 0.00000000 0.00000000 -0.00006032 0.34474456 18 376092 3 0.00000000 0.00000000 -0.00029276 0.35044539 19 376101 3 0.00000000 0.00000000 -0.00061814 0.39389423 SERIES IDENT OPTION A B C D 20 376102 3 0.00000000 0.00000000 -0.00063366 0.38291419 21 376111 3 0.00000000 0.00000000 -0.00054774 0.39193448 22 376112 3 0.00000000 0.00000000 0.00001926 0.35169944 23 376121 3 0.00000000 0.00000000 0.00009923 0.33936411 24 376122 3 0.00000000 0.00000000 0.00012441 0.37210271 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 375011 1849 1976 128 1.000 0.071 -0.162 2.946 0.051 0.521 2 375012 1843 1976 134 1.000 0.062 -0.250 4.151 0.055 0.300 3 375021 1859 1976 118 1.000 0.052 -0.129 3.664 0.057 0.018 4 375022 1846 1975 130 1.000 0.060 0.157 3.094 0.054 0.218 5 375031 1852 1976 125 1.000 0.059 0.996 5.677 0.053 0.201 6 375032 1849 1976 128 1.000 0.077 0.302 6.799 0.062 0.380 7 375041 1848 1976 129 1.000 0.057 -0.144 3.492 0.041 0.450 8 375042 1864 1976 113 1.000 0.055 0.139 3.026 0.040 0.510 9 375051 1844 1976 133 1.000 0.081 0.209 3.435 0.063 0.407 10 375052 1854 1976 123 1.000 0.076 -0.346 3.408 0.061 0.463 11 375061 1844 1976 133 1.000 0.069 0.226 3.021 0.049 0.611 12 375062 1864 1976 113 1.000 0.065 -0.016 3.441 0.048 0.511 13 376071 1864 1976 113 1.000 0.053 0.471 2.730 0.037 0.604 14 376072 1861 1976 116 1.000 0.065 0.370 2.839 0.036 0.707 15 376081 1862 1976 115 1.000 0.064 -0.135 2.837 0.057 0.326 16 376082 1853 1976 124 1.000 0.072 0.528 4.128 0.059 0.434 17 376091 1846 1976 131 1.000 0.074 -0.296 2.540 0.061 0.459 18 376092 1849 1976 128 1.000 0.086 -0.225 2.360 0.059 0.609 19 376101 1857 1976 120 1.000 0.095 0.202 3.067 0.055 0.695 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 376102 1848 1976 129 1.000 0.096 1.609 9.483 0.059 0.556 21 376111 1866 1976 111 1.000 0.078 0.384 3.384 0.066 0.358 22 376112 1853 1976 124 1.000 0.092 0.783 5.658 0.079 0.278 23 376121 1848 1976 129 1.000 0.065 0.052 3.025 0.059 0.338 24 376122 1854 1975 122 1.000 0.075 0.247 3.803 0.056 0.439 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 124 1.000 0.071 0.207 3.834 0.055 0.433 STANDARD DEVIATION 7 0.000 0.013 0.451 1.607 0.010 0.164 MEDIAN (50TH QUANTILE) 124 1.000 0.070 0.180 3.396 0.056 0.445 INTERQUARTILE RANGE 12 0.000 0.017 0.516 0.982 0.010 0.206 MINIMUM VALUE 111 1.000 0.052 -0.346 2.360 0.036 0.018 LOWER HINGE (25TH QUANTILE) 117 1.000 0.061 -0.139 2.983 0.050 0.332 UPPER HINGE (75TH QUANTILE) 129 1.000 0.078 0.377 3.965 0.060 0.538 MAXIMUM VALUE 134 1.000 0.096 1.609 9.483 0.079 0.707 |------------------------ 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 375011 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 375012 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 375021 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 375022 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 375031 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 375032 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 375041 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 375042 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 375051 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 375052 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 375061 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 375062 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 376071 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 376072 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 376081 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 376082 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 376091 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 376092 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 376101 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 376102 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 376111 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 376112 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 376121 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 376122 -67 81 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 375011 1849 1976 128 1.000 0.059 0.126 2.961 0.051 0.305 2 375012 1843 1976 134 1.000 0.058 -0.293 4.436 0.055 0.202 3 375021 1859 1976 118 1.000 0.051 -0.115 3.684 0.057 0.002 4 375022 1846 1975 130 1.000 0.055 0.282 3.906 0.054 0.075 5 375031 1852 1976 125 1.000 0.056 1.143 6.165 0.053 0.136 6 375032 1849 1976 128 1.000 0.075 0.237 7.011 0.062 0.358 7 375041 1848 1976 129 1.000 0.053 -0.061 3.394 0.041 0.382 8 375042 1864 1976 113 1.000 0.053 0.302 3.398 0.041 0.482 9 375051 1844 1976 133 1.000 0.074 0.401 3.812 0.063 0.284 10 375052 1854 1976 123 1.000 0.066 -0.490 3.357 0.061 0.304 11 375061 1844 1976 133 1.000 0.060 0.291 2.865 0.049 0.506 12 375062 1864 1976 113 1.000 0.057 0.072 4.070 0.048 0.374 13 376071 1864 1976 113 1.000 0.043 0.309 3.296 0.037 0.411 14 376072 1861 1976 116 1.000 0.047 0.371 3.049 0.036 0.425 15 376081 1862 1976 115 1.000 0.061 -0.064 3.035 0.057 0.258 16 376082 1853 1976 124 1.000 0.065 0.683 4.876 0.059 0.306 17 376091 1846 1976 131 1.000 0.068 -0.341 2.642 0.061 0.360 18 376092 1849 1976 128 1.000 0.066 0.108 2.361 0.059 0.360 19 376101 1857 1976 120 0.999 0.060 -0.026 4.434 0.054 0.272 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 376102 1848 1976 129 0.999 0.071 2.002 12.954 0.059 0.253 21 376111 1866 1976 111 1.000 0.071 0.388 3.777 0.066 0.207 22 376112 1853 1976 124 1.000 0.084 1.187 7.717 0.079 0.119 23 376121 1848 1976 129 1.000 0.063 0.143 3.350 0.059 0.293 24 376122 1854 1975 122 1.000 0.065 1.368 7.753 0.056 0.190 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 124 1.000 0.062 0.334 4.513 0.055 0.286 STANDARD DEVIATION 7 0.000 0.009 0.581 2.356 0.010 0.124 MEDIAN (50TH QUANTILE) 124 1.000 0.060 0.260 3.731 0.056 0.298 INTERQUARTILE RANGE 12 0.000 0.012 0.438 1.483 0.010 0.162 MINIMUM VALUE 111 0.999 0.043 -0.490 2.361 0.036 0.002 LOWER HINGE (25TH QUANTILE) 117 1.000 0.056 -0.043 3.172 0.050 0.205 UPPER HINGE (75TH QUANTILE) 129 1.000 0.067 0.394 4.656 0.060 0.367 MAXIMUM VALUE 134 1.000 0.084 2.002 12.954 0.079 0.506 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.250 0.135 0.008 -0.328 3.138 -0.202 0.603 MINIMUM CORRELATION: -0.202 SERIES 375041 AND 376111 111 YEARS MAXIMUM CORRELATION: 0.603 SERIES 376071 AND 376072 113 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 89.13 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 276. 276. 276. RBAR 0.261 0.266 0.269 SDEV 0.176 0.175 0.159 SERR 0.011 0.011 0.010 EPS 0.894 0.897 0.899 NSS 24.0 24.0 24.0 |======================== 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 1843 1976 134 0.996 0.033 0.140 3.629 0.033 0.160 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.103 0.038 0.014 41 93 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.16 0.31 1.00 1.09 1.40 5.91 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.00 0.88 0.94 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 0.159 0.110 -0.125 0.059 0.104 0.049 -0.053 -0.054 0.064 0.101 PACF 0.159 0.087 -0.160 0.098 0.118 -0.028 -0.066 -0.008 0.088 0.056 95% C.L. 0.173 0.177 0.179 0.182 0.182 0.184 0.184 0.185 0.185 0.186 |------------------ 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 0.034 0.160 |======================= 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 0.130 0.037 -0.191 0.036 0.070 0.034 -0.076 -0.040 0.100 0.156 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 0.130 2 0.127 0.021 3 0.131 0.047 -0.202 4 0.150 0.042 -0.214 0.091 5 0.143 0.058 -0.217 0.080 0.074 6 0.146 0.061 -0.225 0.082 0.079 -0.035 7 0.143 0.066 -0.219 0.067 0.083 -0.026 -0.064 8 0.144 0.066 -0.220 0.067 0.085 -0.026 -0.065 0.007 9 0.143 0.074 -0.217 0.057 0.077 -0.001 -0.073 -0.009 0.115 10 0.131 0.075 -0.210 0.057 0.069 -0.007 -0.051 -0.017 0.101 0.101 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) 574.76 574.49 576.43 572.85 573.74 575.00 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 576.83 578.28 580.27 580.48 581.11 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 0.130 R-SQUARED DUE TO POOLED AUTOREGRESSION: 1.68 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 101.71 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.130 0.017 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 375011 1 0.098 0.309 2 375012 1 0.052 0.203 3 375021 1 0.001 0.002 4 375022 1 0.028 0.076 5 375031 1 0.020 0.138 6 375032 1 0.129 0.360 7 375041 1 0.249 0.393 8 375042 1 0.244 0.493 9 375051 1 0.089 0.285 10 375052 1 0.095 0.308 11 375061 1 0.268 0.510 12 375062 1 0.142 0.375 13 376071 1 0.187 0.412 14 376072 1 0.288 0.437 15 376081 1 0.080 0.268 16 376082 1 0.107 0.313 17 376091 1 0.131 0.360 18 376092 1 0.130 0.360 19 376101 1 0.080 0.273 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 376102 1 0.100 0.255 21 376111 1 0.050 0.214 22 376112 1 0.032 0.124 23 376121 1 0.091 0.295 24 376122 1 0.119 0.214 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.117 0.291 STANDARD DEVIATION 0 0.079 0.125 MEDIAN 1 0.099 0.301 INTERQUARTILE RANGE 0 0.070 0.154 MINIMUM VALUE 1 0.001 0.002 LOWER HINGE 1 0.066 0.214 UPPER HINGE 1 0.136 0.368 MAXIMUM VALUE 1 0.288 0.510 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 375011 1849 1976 128 1.000 0.056 0.244 2.921 0.059 0.010 2 375012 1843 1976 134 1.000 0.057 -0.275 4.934 0.062 -0.022 3 375021 1859 1976 118 1.000 0.051 -0.116 3.687 0.057 0.000 4 375022 1846 1975 130 1.000 0.055 0.254 4.151 0.056 -0.010 5 375031 1852 1976 125 1.000 0.056 1.156 5.999 0.058 -0.004 6 375032 1849 1976 128 1.000 0.070 0.824 8.638 0.072 0.003 7 375041 1848 1976 129 1.000 0.049 -0.099 3.832 0.054 -0.136 8 375042 1864 1976 113 1.000 0.046 0.315 3.462 0.050 -0.024 9 375051 1844 1976 133 1.000 0.071 0.214 4.576 0.074 -0.025 10 375052 1854 1976 123 1.000 0.063 -0.580 3.275 0.070 0.004 11 375061 1844 1976 133 1.000 0.052 -0.072 2.653 0.062 -0.051 12 375062 1864 1976 113 1.000 0.053 -0.054 4.463 0.056 -0.014 13 376071 1864 1976 113 1.000 0.039 0.306 3.248 0.045 -0.059 14 376072 1861 1976 116 1.000 0.042 0.179 3.600 0.047 -0.139 15 376081 1862 1976 115 1.000 0.058 0.043 2.981 0.064 -0.032 16 376082 1853 1976 124 1.000 0.062 0.811 4.838 0.069 -0.036 17 376091 1846 1976 131 1.000 0.064 -0.186 2.329 0.074 -0.010 18 376092 1849 1976 128 1.000 0.062 0.050 2.716 0.071 -0.012 19 376101 1857 1976 120 1.000 0.058 -0.027 4.721 0.061 -0.020 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 376102 1848 1976 129 1.000 0.069 1.699 11.676 0.068 -0.050 21 376111 1866 1976 111 1.000 0.069 0.181 3.636 0.075 -0.019 22 376112 1853 1976 124 1.000 0.084 1.231 7.830 0.083 -0.016 23 376121 1848 1976 129 1.000 0.060 0.248 3.139 0.067 -0.016 24 376122 1854 1975 122 1.000 0.064 1.326 7.659 0.064 -0.071 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 124 1.000 0.059 0.320 4.623 0.063 -0.031 STANDARD DEVIATION 7 0.000 0.010 0.565 2.254 0.009 0.038 MEDIAN (50TH QUANTILE) 124 1.000 0.058 0.198 3.759 0.063 -0.020 INTERQUARTILE RANGE 12 0.000 0.011 0.626 1.693 0.014 0.033 MINIMUM VALUE 111 1.000 0.039 -0.580 2.329 0.045 -0.139 LOWER HINGE (25TH QUANTILE) 117 1.000 0.052 -0.063 3.193 0.057 -0.043 UPPER HINGE (75TH QUANTILE) 129 1.000 0.064 0.563 4.886 0.071 -0.010 MAXIMUM VALUE 134 1.000 0.084 1.699 11.676 0.083 0.010 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.274 0.129 0.008 -0.305 2.984 -0.124 0.623 MINIMUM CORRELATION: -0.124 SERIES 375041 AND 376111 111 YEARS MAXIMUM CORRELATION: 0.623 SERIES 376091 AND 376092 128 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 89.13 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 276. 276. 276. RBAR 0.291 0.266 0.275 SDEV 0.149 0.159 0.147 SERR 0.009 0.010 0.009 EPS 0.908 0.897 0.901 NSS 24.0 24.0 24.0 |======================== 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 1843 1976 134 0.997 0.033 -0.063 4.304 0.037 -0.150 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.051 0.019 0.029 42 92 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.13 0.29 1.01 1.05 1.34 9.93 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.00 0.88 0.93 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 -0.149 0.100 -0.184 0.069 0.078 0.024 -0.059 -0.064 0.064 0.102 PACF -0.149 0.080 -0.163 0.017 0.122 0.013 -0.059 -0.052 0.060 0.103 95% C.L. 0.173 0.177 0.178 0.184 0.185 0.186 0.186 0.186 0.187 0.188 |------------------ 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 1 0.029 -0.150 |---------- 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 0.011 0.052 -0.167 0.057 0.095 0.028 -0.068 -0.066 0.073 0.119 PACF 0.011 0.052 -0.169 0.061 0.114 -0.012 -0.064 -0.034 0.080 0.095 95% C.L. 0.173 0.173 0.173 0.178 0.179 0.180 0.180 0.181 0.182 0.183 |----------------- 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 0.003 0.012 |========================= 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 1843 1976 134 0.997 0.033 0.135 3.726 0.033 0.144 |------------ 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 0.143 0.047 -0.149 0.050 0.102 0.032 -0.068 -0.063 0.080 0.128 PACF 0.143 0.027 -0.163 0.098 0.100 -0.034 -0.062 -0.014 0.095 0.081 95% C.L. 0.173 0.176 0.177 0.180 0.181 0.183 0.183 0.183 0.184 0.185 |------------------- 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 0.022 0.145 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.21 MINUTES