RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit016n.rwl LOG FILE PROCESSED: brit016n.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: 571 1 Shieldaig DENSITY_MINIMUM PISY - 571 2 Great Britain Scots pine, Scotch pine 12 5730-537 1847 1978 - 571 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 571031 MISSING VALUES FOUND: 1 IN 1 GAPS / 1924 1924 / -------------------------------------------------------------------- 7 571041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1959 1959 / -------------------------------------------------------------------- 13 571071 MISSING VALUES FOUND: 5 IN 1 GAPS / 1902 1906 / -------------------------------------------------------------------- 18 571092 MISSING VALUES FOUND: 1 IN 1 GAPS / 1889 1889 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 0.334 0.022 -0.220 2.771 0.061 0.293 2 571012 1899 1978 80 0.328 0.027 0.837 5.806 0.074 0.164 3 571021 1868 1978 111 0.345 0.032 -0.183 2.900 0.071 0.550 4 571022 1860 1978 119 0.356 0.036 0.303 2.444 0.067 0.604 5 571031 1873 1978 106 0.349 0.022 0.086 2.263 0.061 0.277 6 571032 1847 1978 132 0.325 0.029 0.397 2.907 0.055 0.689 7 571041 1866 1978 113 0.362 0.024 0.746 3.499 0.056 0.445 8 571042 1864 1966 103 0.373 0.039 0.599 2.928 0.051 0.789 9 571051 1859 1978 120 0.316 0.022 0.580 2.809 0.048 0.571 10 571052 1899 1978 80 0.330 0.025 0.484 2.992 0.065 0.394 11 571061 1891 1978 88 0.373 0.028 0.286 2.600 0.071 0.354 12 571062 1883 1978 96 0.368 0.029 0.261 3.325 0.064 0.489 13 571071 1873 1967 95 0.365 0.030 0.006 4.373 0.065 0.513 14 571072 1876 1965 90 0.376 0.042 0.496 2.690 0.067 0.726 15 571081 1874 1978 105 0.354 0.030 -0.026 2.985 0.053 0.707 16 571082 1853 1978 126 0.368 0.023 -0.510 2.812 0.042 0.614 17 571091 1866 1978 113 0.326 0.021 0.516 3.169 0.052 0.434 18 571092 1868 1978 111 0.323 0.020 -0.213 3.725 0.053 0.382 19 571101 1877 1976 100 0.328 0.024 -0.421 5.339 0.069 0.252 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 0.340 0.030 -0.131 3.146 0.072 0.419 21 571111 1856 1978 123 0.348 0.041 0.174 2.995 0.081 0.581 NUMBER OF SERIES READ IN: 21 FROM 1847 TO 1978 132 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.347 0.028 0.194 3.261 0.062 0.488 STANDARD DEVIATION 16 0.019 0.007 0.383 0.894 0.010 0.170 MEDIAN (50TH QUANTILE) 105 0.348 0.028 0.261 2.985 0.064 0.489 INTERQUARTILE RANGE 23 0.037 0.007 0.628 0.516 0.016 0.222 MINIMUM VALUE 70 0.316 0.020 -0.510 2.263 0.042 0.164 LOWER HINGE (25TH QUANTILE) 90 0.328 0.023 -0.131 2.809 0.053 0.382 UPPER HINGE (75TH QUANTILE) 113 0.365 0.030 0.496 3.325 0.069 0.604 MAXIMUM VALUE 132 0.376 0.042 0.837 5.806 0.081 0.789 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.160 0.215 0.015 -0.222 2.774 -0.453 0.666 MINIMUM CORRELATION: -0.453 SERIES 571032 AND 571072 90 YEARS MAXIMUM CORRELATION: 0.666 SERIES 571042 AND 571072 90 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.140 0.139 0.234 SDEV 0.237 0.227 0.175 SERR 0.027 0.016 0.015 EPS 0.753 0.771 0.861 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.342 0.016 -0.409 2.690 0.036 0.529 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.596 0.412 -0.111 25 107 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.16 0.35 1.01 1.08 1.42 3.08 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.85 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 105. 23. 70. 90. 113. 132. |----------- 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 0.534 0.493 0.435 0.443 0.498 0.407 0.359 0.360 0.373 PACF 0.525 0.357 0.198 0.073 0.111 0.212 0.002 -0.074 0.012 0.100 95% C.L. 0.174 0.217 0.254 0.281 0.301 0.320 0.343 0.357 0.368 0.378 |------------------ 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 0.422 0.248 0.315 0.211 |================== 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 571011 3 0.00000000 0.00000000 0.00052209 0.31575155 2 571012 3 0.00000000 0.00000000 0.00037307 0.31301582 3 571021 3 0.00000000 0.00000000 0.00061004 0.31124324 4 571022 3 0.00000000 0.00000000 0.00046802 0.32754877 5 571031 3 0.00000000 0.00000000 0.00014459 0.34082088 6 571032 3 0.00000000 0.00000000 -0.00026519 0.34286261 7 571041 3 0.00000000 0.00000000 0.00022511 0.34948286 8 571042 3 0.00000000 0.00000000 0.00102128 0.31941748 9 571051 3 0.00000000 0.00000000 -0.00012411 0.32317507 10 571052 3 0.00000000 0.00000000 -0.00028211 0.34155062 11 571061 3 0.00000000 0.00000000 0.00026091 0.36145768 12 571062 3 0.00000000 0.00000000 0.00028140 0.35416448 13 571071 3 0.00000000 0.00000000 0.00059136 0.33647799 14 571072 3 0.00000000 0.00000000 0.00121414 0.32075655 15 571081 1 0.07340939 0.03321443 0.00000000 0.33374149 16 571082 3 0.00000000 0.00000000 0.00024684 0.35234159 17 571091 3 0.00000000 0.00000000 0.00008608 0.32093394 18 571092 3 0.00000000 0.00000000 0.00001147 0.32229692 19 571101 3 0.00000000 0.00000000 0.00012091 0.32159394 SERIES IDENT OPTION A B C D 20 571102 3 0.00000000 0.00000000 -0.00052060 0.36236376 21 571111 3 0.00000000 0.00000000 0.00086095 0.29483274 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 1.000 0.058 -0.198 2.813 0.060 0.089 2 571012 1899 1978 80 1.000 0.077 1.401 8.442 0.073 0.070 3 571021 1868 1978 111 1.000 0.076 0.003 3.608 0.071 0.289 4 571022 1860 1978 119 1.000 0.089 0.328 2.732 0.067 0.506 5 571031 1873 1978 106 1.000 0.062 0.062 2.399 0.060 0.232 6 571032 1847 1978 132 1.000 0.083 0.413 2.982 0.054 0.641 7 571041 1866 1978 113 1.000 0.063 0.592 3.784 0.056 0.375 8 571042 1864 1966 103 1.000 0.066 0.104 3.272 0.051 0.482 9 571051 1859 1978 120 1.000 0.067 0.492 2.884 0.047 0.552 10 571052 1899 1978 80 1.000 0.072 0.261 2.947 0.064 0.337 11 571061 1891 1978 88 1.000 0.073 0.325 2.547 0.071 0.306 12 571062 1883 1978 96 1.000 0.076 0.302 3.179 0.063 0.445 13 571071 1873 1967 95 1.000 0.068 -0.168 4.288 0.063 0.291 14 571072 1876 1965 90 1.000 0.075 0.115 3.422 0.066 0.395 15 571081 1874 1978 105 1.000 0.068 0.117 3.767 0.052 0.539 16 571082 1853 1978 126 1.000 0.058 -0.390 2.480 0.042 0.559 17 571091 1866 1978 113 1.000 0.063 0.580 3.370 0.052 0.418 18 571092 1868 1978 111 1.000 0.061 -0.197 3.689 0.053 0.391 19 571101 1877 1976 100 1.000 0.073 -0.266 5.412 0.069 0.237 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.079 0.133 2.860 0.071 0.310 21 571111 1856 1978 123 1.000 0.079 0.893 7.537 0.080 0.077 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.071 0.233 3.734 0.061 0.359 STANDARD DEVIATION 16 0.000 0.008 0.417 1.578 0.010 0.162 MEDIAN (50TH QUANTILE) 105 1.000 0.072 0.133 3.272 0.063 0.375 INTERQUARTILE RANGE 23 0.000 0.013 0.411 0.907 0.016 0.193 MINIMUM VALUE 70 1.000 0.058 -0.390 2.399 0.042 0.070 LOWER HINGE (25TH QUANTILE) 90 1.000 0.063 0.003 2.860 0.053 0.289 UPPER HINGE (75TH QUANTILE) 113 1.000 0.076 0.413 3.767 0.069 0.482 MAXIMUM VALUE 132 1.000 0.089 1.401 8.442 0.080 0.641 |------------------------ 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 571011 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 571012 -67 53 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 571021 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 571022 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 571031 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 571032 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 571041 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 571042 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 571051 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 571052 -67 53 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 571061 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 571062 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 571071 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 571072 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 571081 -67 70 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 571082 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 571091 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 571092 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 571101 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 571102 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 571111 -67 82 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 571011 1909 1978 70 1.000 0.056 -0.382 3.034 0.060 0.010 2 571012 1899 1978 80 1.000 0.071 1.291 7.972 0.073 -0.045 3 571021 1868 1978 111 1.000 0.070 0.077 3.901 0.071 0.155 4 571022 1860 1978 119 1.000 0.071 -0.194 3.183 0.067 0.250 5 571031 1873 1978 106 1.000 0.057 0.121 2.573 0.060 0.093 6 571032 1847 1978 132 1.000 0.065 0.255 2.977 0.054 0.432 7 571041 1866 1978 113 1.000 0.062 0.482 3.730 0.056 0.346 8 571042 1864 1966 103 1.000 0.060 -0.016 3.926 0.051 0.371 9 571051 1859 1978 120 1.000 0.061 0.580 2.988 0.048 0.448 10 571052 1899 1978 80 1.000 0.069 0.270 3.224 0.065 0.273 11 571061 1891 1978 88 1.000 0.071 0.298 2.469 0.071 0.272 12 571062 1883 1978 96 1.000 0.072 0.377 3.039 0.063 0.376 13 571071 1873 1967 95 1.000 0.064 0.100 4.895 0.063 0.182 14 571072 1876 1965 90 1.000 0.059 -0.099 2.781 0.066 0.062 15 571081 1874 1978 105 1.000 0.060 0.196 3.512 0.052 0.407 16 571082 1853 1978 126 1.000 0.049 -0.239 2.465 0.042 0.392 17 571091 1866 1978 113 1.000 0.054 0.172 2.912 0.052 0.220 18 571092 1868 1978 111 1.000 0.057 0.003 3.432 0.053 0.288 19 571101 1877 1976 100 1.000 0.068 -0.586 5.525 0.069 0.115 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.075 0.371 2.796 0.071 0.252 21 571111 1856 1978 123 1.000 0.075 0.562 6.455 0.080 -0.027 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.064 0.173 3.704 0.061 0.232 STANDARD DEVIATION 16 0.000 0.007 0.395 1.411 0.010 0.153 MEDIAN (50TH QUANTILE) 105 1.000 0.064 0.172 3.183 0.063 0.252 INTERQUARTILE RANGE 23 0.000 0.012 0.387 0.989 0.016 0.256 MINIMUM VALUE 70 1.000 0.049 -0.586 2.465 0.042 -0.045 LOWER HINGE (25TH QUANTILE) 90 1.000 0.059 -0.016 2.912 0.053 0.115 UPPER HINGE (75TH QUANTILE) 113 1.000 0.071 0.371 3.901 0.069 0.371 MAXIMUM VALUE 132 1.000 0.075 1.291 7.972 0.080 0.448 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.201 0.132 0.009 0.135 3.248 -0.095 0.663 MINIMUM CORRELATION: -0.095 SERIES 571051 AND 571062 96 YEARS MAXIMUM CORRELATION: 0.663 SERIES 571042 AND 571081 93 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.181 0.189 0.249 SDEV 0.186 0.173 0.148 SERR 0.021 0.013 0.013 EPS 0.806 0.829 0.870 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.998 0.033 -0.094 2.837 0.037 0.056 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.054 0.030 0.022 32 100 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.11 0.34 1.00 1.04 1.39 2.50 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.10 0.00 0.85 0.95 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.056 0.066 0.048 -0.119 -0.106 0.048 -0.115 -0.179 -0.064 -0.041 PACF 0.056 0.064 0.041 -0.129 -0.101 0.075 -0.097 -0.192 -0.068 0.008 95% C.L. 0.174 0.175 0.175 0.176 0.178 0.180 0.181 0.183 0.188 0.189 |------------------ 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 0 0.000 |======================= 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 0.004 0.055 0.047 -0.097 -0.103 0.065 -0.148 -0.152 -0.048 0.004 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 0.004 2 0.003 0.055 3 0.001 0.054 0.047 4 0.006 0.060 0.047 -0.101 5 -0.005 0.065 0.054 -0.100 -0.109 6 0.003 0.073 0.050 -0.105 -0.109 0.076 7 0.013 0.059 0.036 -0.099 -0.099 0.077 -0.129 8 -0.009 0.071 0.019 -0.115 -0.093 0.087 -0.127 -0.167 9 -0.019 0.064 0.025 -0.121 -0.100 0.088 -0.123 -0.167 -0.062 10 -0.017 0.070 0.030 -0.125 -0.096 0.093 -0.124 -0.170 -0.062 0.041 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) 488.79 490.79 492.40 494.10 494.75 495.18 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 496.40 496.18 494.46 495.95 497.73 SELECTED AUTOREGRESSION ORDER: 0 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 571011 0 0.000 2 571012 0 0.002 3 571021 0 0.025 4 571022 0 0.063 5 571031 0 0.009 6 571032 0 0.186 7 571041 0 0.120 8 571042 0 0.139 9 571051 0 0.201 10 571052 0 0.075 11 571061 0 0.075 12 571062 0 0.143 13 571071 0 0.033 14 571072 0 0.004 15 571081 0 0.167 16 571082 0 0.155 17 571091 0 0.049 18 571092 0 0.083 19 571101 0 0.014 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 571102 0 0.065 21 571111 0 0.001 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.077 STANDARD DEVIATION 0 0.067 MEDIAN 0 0.065 INTERQUARTILE RANGE 0 0.125 MINIMUM VALUE 0 0.000 LOWER HINGE 0 0.014 UPPER HINGE 0 0.139 MAXIMUM VALUE 0 0.201 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 1.000 0.056 -0.382 3.034 0.060 0.010 2 571012 1899 1978 80 1.000 0.071 1.291 7.972 0.073 -0.045 3 571021 1868 1978 111 1.000 0.070 0.077 3.901 0.071 0.155 4 571022 1860 1978 119 1.000 0.071 -0.194 3.183 0.067 0.250 5 571031 1873 1978 106 1.000 0.057 0.121 2.573 0.060 0.093 6 571032 1847 1978 132 1.000 0.065 0.255 2.977 0.054 0.432 7 571041 1866 1978 113 1.000 0.062 0.482 3.730 0.056 0.346 8 571042 1864 1966 103 1.000 0.060 -0.016 3.926 0.051 0.371 9 571051 1859 1978 120 1.000 0.061 0.580 2.988 0.047 0.448 10 571052 1899 1978 80 1.000 0.069 0.270 3.224 0.064 0.273 11 571061 1891 1978 88 1.000 0.071 0.298 2.469 0.071 0.272 12 571062 1883 1978 96 1.000 0.072 0.377 3.039 0.063 0.376 13 571071 1873 1967 95 1.000 0.064 0.100 4.895 0.063 0.182 14 571072 1876 1965 90 1.000 0.059 -0.099 2.781 0.066 0.062 15 571081 1874 1978 105 1.000 0.060 0.196 3.512 0.052 0.407 16 571082 1853 1978 126 1.000 0.049 -0.239 2.465 0.042 0.392 17 571091 1866 1978 113 1.000 0.054 0.172 2.912 0.052 0.220 18 571092 1868 1978 111 1.000 0.057 0.003 3.432 0.053 0.288 19 571101 1877 1976 100 1.000 0.068 -0.585 5.525 0.069 0.115 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.075 0.371 2.796 0.071 0.252 21 571111 1856 1978 123 1.000 0.075 0.562 6.455 0.080 -0.027 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.064 0.173 3.704 0.061 0.232 STANDARD DEVIATION 16 0.000 0.007 0.395 1.411 0.010 0.153 MEDIAN (50TH QUANTILE) 105 1.000 0.064 0.172 3.183 0.063 0.252 INTERQUARTILE RANGE 23 0.000 0.012 0.387 0.989 0.016 0.256 MINIMUM VALUE 70 1.000 0.049 -0.585 2.465 0.042 -0.045 LOWER HINGE (25TH QUANTILE) 90 1.000 0.059 -0.016 2.912 0.053 0.115 UPPER HINGE (75TH QUANTILE) 113 1.000 0.071 0.371 3.901 0.069 0.371 MAXIMUM VALUE 132 1.000 0.075 1.291 7.972 0.080 0.448 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.201 0.132 0.009 0.135 3.248 -0.095 0.663 MINIMUM CORRELATION: -0.095 SERIES 571051 AND 571062 96 YEARS MAXIMUM CORRELATION: 0.663 SERIES 571042 AND 571081 93 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.181 0.189 0.249 SDEV 0.186 0.173 0.148 SERR 0.021 0.013 0.013 EPS 0.806 0.829 0.870 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.999 0.033 -0.094 2.838 0.037 0.056 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.054 0.030 0.023 32 100 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.11 0.34 1.00 1.04 1.38 2.51 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.10 0.00 0.85 0.95 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 0.056 0.067 0.048 -0.119 -0.106 0.048 -0.115 -0.179 -0.064 -0.041 PACF 0.056 0.064 0.041 -0.129 -0.101 0.075 -0.098 -0.192 -0.068 0.007 95% C.L. 0.174 0.175 0.175 0.176 0.178 0.180 0.181 0.183 0.188 0.189 |------------------ 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 |========================= 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 1847 1978 132 0.999 0.033 -0.094 2.838 0.037 0.056 |------------ 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 0.056 0.067 0.048 -0.119 -0.106 0.048 -0.115 -0.179 -0.064 -0.041 PACF 0.056 0.064 0.041 -0.129 -0.101 0.075 -0.098 -0.192 -0.068 0.007 95% C.L. 0.174 0.175 0.175 0.176 0.178 0.180 0.181 0.183 0.188 0.189 |------------------- 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 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.28 MINUTES