RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit016x.rwl LOG FILE PROCESSED: brit016x.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_MAXIMUM 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 / -------------------------------------------------------------------- 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 0.811 0.065 0.281 3.031 0.076 0.186 2 571012 1899 1978 80 0.777 0.064 0.406 2.968 0.077 0.289 3 571021 1868 1978 111 0.850 0.085 -0.207 2.183 0.055 0.764 4 571022 1860 1978 119 0.852 0.073 -0.349 2.678 0.066 0.478 5 571031 1873 1978 106 0.855 0.079 -0.036 2.386 0.068 0.579 6 571032 1847 1978 132 0.719 0.084 0.099 2.436 0.085 0.581 7 571041 1866 1978 113 0.874 0.095 -0.862 3.254 0.058 0.791 8 571042 1864 1966 103 0.878 0.093 -0.279 2.851 0.064 0.717 9 571051 1859 1978 120 0.859 0.062 -0.244 2.587 0.066 0.404 10 571052 1899 1978 80 0.874 0.084 -0.358 3.170 0.093 0.303 11 571061 1891 1978 88 0.946 0.072 -0.395 3.450 0.057 0.555 12 571062 1883 1978 96 0.925 0.098 -1.176 4.223 0.063 0.733 13 571071 1873 1967 95 0.950 0.068 -0.815 3.018 0.065 0.333 14 571072 1876 1965 90 0.941 0.071 -0.294 2.807 0.059 0.522 15 571081 1874 1978 105 0.853 0.060 0.084 2.035 0.052 0.539 16 571082 1853 1978 126 0.843 0.082 -0.566 3.522 0.062 0.686 17 571091 1866 1978 113 0.835 0.074 -0.990 3.280 0.065 0.543 18 571092 1868 1978 111 0.825 0.068 -0.249 2.537 0.062 0.487 19 571101 1877 1976 100 0.905 0.095 -1.863 8.585 0.093 0.410 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 0.876 0.068 -0.190 2.457 0.080 0.131 21 571111 1856 1978 123 0.932 0.079 -0.953 4.509 0.072 0.468 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 0.866 0.077 -0.426 3.236 0.068 0.500 STANDARD DEVIATION 16 0.057 0.012 0.533 1.371 0.012 0.184 MEDIAN (50TH QUANTILE) 105 0.859 0.074 -0.294 2.968 0.065 0.522 INTERQUARTILE RANGE 23 0.062 0.016 0.626 0.744 0.014 0.176 MINIMUM VALUE 70 0.719 0.060 -1.863 2.035 0.052 0.131 LOWER HINGE (25TH QUANTILE) 90 0.843 0.068 -0.815 2.537 0.062 0.404 UPPER HINGE (75TH QUANTILE) 113 0.905 0.084 -0.190 3.280 0.076 0.581 MAXIMUM VALUE 132 0.950 0.098 0.406 8.585 0.093 0.791 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.240 0.228 0.016 -0.155 2.283 -0.283 0.705 MINIMUM CORRELATION: -0.283 SERIES 571012 AND 571081 80 YEARS MAXIMUM CORRELATION: 0.705 SERIES 571021 AND 571031 106 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 0.369 0.357 0.187 SDEV 0.186 0.215 0.267 SERR 0.021 0.016 0.023 EPS 0.917 0.920 0.824 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 0.845 0.075 -1.751 6.096 0.044 0.765 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.555 0.212 -0.097 22 110 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.11 0.11 1.00 1.06 1.17 1.52 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.00 0.86 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 0.759 0.704 0.641 0.598 0.524 0.460 0.427 0.378 0.298 0.256 PACF 0.759 0.301 0.101 0.070 -0.048 -0.048 0.034 -0.010 -0.110 -0.014 95% C.L. 0.174 0.255 0.309 0.347 0.377 0.398 0.414 0.427 0.437 0.443 |------------------ 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 0.717 0.375 0.278 0.103 0.162 |================== 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 0.00156959 0.75556523 2 571012 3 0.00000000 0.00000000 0.00018601 0.76959175 3 571021 3 0.00000000 0.00000000 0.00126536 0.77932024 4 571022 3 0.00000000 0.00000000 -0.00010497 0.85806292 5 571031 3 0.00000000 0.00000000 0.00145396 0.77665246 6 571032 3 0.00000000 0.00000000 -0.00083302 0.77448648 7 571041 3 0.00000000 0.00000000 0.00070906 0.83527392 8 571042 3 0.00000000 0.00000000 0.00174834 0.78733867 9 571051 3 0.00000000 0.00000000 0.00009317 0.85361344 10 571052 1 0.44326165 0.00324824 0.00000000 0.48453408 11 571061 3 0.00000000 0.00000000 0.00038842 0.92896551 12 571062 3 0.00000000 0.00000000 -0.00171039 1.00837064 13 571071 3 0.00000000 0.00000000 0.00014208 0.94349611 14 571072 3 0.00000000 0.00000000 0.00178598 0.85996002 15 571081 1 0.12285580 0.04274321 0.00000000 0.82655621 16 571082 3 0.00000000 0.00000000 0.00125075 0.76335496 17 571091 3 0.00000000 0.00000000 0.00143290 0.75301516 18 571092 3 0.00000000 0.00000000 0.00042887 0.80128664 19 571101 3 0.00000000 0.00000000 0.00079946 0.86412728 SERIES IDENT OPTION A B C D 20 571102 3 0.00000000 0.00000000 -0.00062397 0.90235227 21 571111 3 0.00000000 0.00000000 0.00106673 0.86581367 |-------------------- 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 0.069 -0.153 3.554 0.075 -0.079 2 571012 1899 1978 80 1.000 0.082 0.393 2.979 0.076 0.285 3 571021 1868 1978 111 1.000 0.089 -0.346 2.796 0.055 0.686 4 571022 1860 1978 119 1.000 0.085 -0.355 2.706 0.066 0.473 5 571031 1873 1978 106 1.000 0.077 -0.117 3.473 0.067 0.380 6 571032 1847 1978 132 1.000 0.107 -0.218 2.705 0.085 0.482 7 571041 1866 1978 113 1.000 0.106 -0.940 3.552 0.057 0.781 8 571042 1864 1966 103 1.000 0.088 -0.890 4.137 0.063 0.555 9 571051 1859 1978 120 1.000 0.072 -0.262 2.597 0.065 0.399 10 571052 1899 1978 80 1.000 0.091 -0.259 3.654 0.092 0.214 11 571061 1891 1978 88 1.000 0.075 -0.559 3.822 0.056 0.542 12 571062 1883 1978 96 1.000 0.095 -0.664 3.741 0.062 0.650 13 571071 1873 1967 95 1.000 0.071 -0.834 3.076 0.064 0.327 14 571072 1876 1965 90 1.000 0.057 -0.638 3.724 0.058 0.162 15 571081 1874 1978 105 1.000 0.061 0.177 2.525 0.052 0.407 16 571082 1853 1978 126 1.000 0.082 -0.712 4.709 0.062 0.557 17 571091 1866 1978 113 1.000 0.070 -0.391 3.025 0.064 0.234 18 571092 1868 1978 111 1.000 0.080 -0.380 2.820 0.062 0.440 19 571101 1877 1976 100 1.000 0.102 -1.900 9.323 0.092 0.366 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.076 -0.397 2.753 0.079 0.087 21 571111 1856 1978 123 1.000 0.075 -1.078 6.185 0.071 0.301 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.081 -0.501 3.707 0.068 0.393 STANDARD DEVIATION 16 0.000 0.014 0.482 1.542 0.011 0.206 MEDIAN (50TH QUANTILE) 105 1.000 0.080 -0.391 3.473 0.064 0.399 INTERQUARTILE RANGE 23 0.000 0.016 0.453 0.945 0.013 0.257 MINIMUM VALUE 70 1.000 0.057 -1.900 2.525 0.052 -0.079 LOWER HINGE (25TH QUANTILE) 90 1.000 0.072 -0.712 2.796 0.062 0.285 UPPER HINGE (75TH QUANTILE) 113 1.000 0.089 -0.259 3.741 0.075 0.542 MAXIMUM VALUE 132 1.000 0.107 0.393 9.323 0.092 0.781 |------------------------ 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 0.067 -0.140 3.214 0.075 -0.112 2 571012 1899 1978 80 1.000 0.069 0.428 2.791 0.076 0.036 3 571021 1868 1978 111 0.999 0.065 0.142 3.009 0.055 0.421 4 571022 1860 1978 119 1.000 0.076 -0.259 2.500 0.066 0.349 5 571031 1873 1978 106 1.000 0.066 -0.030 3.387 0.067 0.162 6 571032 1847 1978 132 0.999 0.087 -0.006 2.487 0.085 0.259 7 571041 1866 1978 113 0.999 0.078 -0.652 3.570 0.057 0.573 8 571042 1864 1966 103 0.999 0.077 -0.832 4.035 0.063 0.418 9 571051 1859 1978 120 1.000 0.065 -0.378 2.785 0.065 0.282 10 571052 1899 1978 80 1.000 0.088 -0.371 3.711 0.092 0.166 11 571061 1891 1978 88 1.000 0.069 -0.232 3.876 0.056 0.407 12 571062 1883 1978 96 1.000 0.080 -1.166 4.750 0.062 0.500 13 571071 1873 1967 95 1.000 0.064 -0.798 2.975 0.064 0.191 14 571072 1876 1965 90 1.000 0.053 -0.664 3.575 0.058 0.008 15 571081 1874 1978 105 1.000 0.053 -0.281 3.054 0.052 0.219 16 571082 1853 1978 126 1.000 0.075 -0.934 5.377 0.062 0.466 17 571091 1866 1978 113 1.000 0.063 -0.104 3.541 0.064 0.061 18 571092 1868 1978 111 1.000 0.073 -0.291 2.971 0.062 0.335 19 571101 1877 1976 100 1.000 0.094 -2.047 9.828 0.092 0.226 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.068 -0.384 3.002 0.079 -0.128 21 571111 1856 1978 123 1.000 0.074 -1.067 6.250 0.071 0.288 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.072 -0.479 3.842 0.068 0.244 STANDARD DEVIATION 16 0.000 0.010 0.542 1.660 0.011 0.194 MEDIAN (50TH QUANTILE) 105 1.000 0.069 -0.371 3.387 0.064 0.259 INTERQUARTILE RANGE 23 0.000 0.011 0.657 0.902 0.013 0.246 MINIMUM VALUE 70 0.999 0.053 -2.047 2.487 0.052 -0.128 LOWER HINGE (25TH QUANTILE) 90 1.000 0.065 -0.798 2.975 0.062 0.162 UPPER HINGE (75TH QUANTILE) 113 1.000 0.077 -0.140 3.876 0.075 0.407 MAXIMUM VALUE 132 1.000 0.094 0.428 9.828 0.092 0.573 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.301 0.145 0.010 -0.263 2.757 -0.070 0.610 MINIMUM CORRELATION: -0.070 SERIES 571011 AND 571071 59 YEARS MAXIMUM CORRELATION: 0.610 SERIES 571041 AND 571042 101 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 0.398 0.358 0.257 SDEV 0.149 0.185 0.162 SERR 0.017 0.013 0.014 EPS 0.925 0.921 0.875 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 0.996 0.049 -0.243 2.718 0.049 0.213 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.011 -0.005 0.060 33 99 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.58 1.00 1.06 1.64 2.40 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.09 0.00 0.86 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 0.212 0.188 0.067 0.151 0.094 0.091 0.090 0.078 -0.078 -0.065 PACF 0.212 0.150 0.002 0.118 0.040 0.029 0.050 0.022 -0.141 -0.066 95% C.L. 0.174 0.182 0.188 0.188 0.192 0.193 0.195 0.196 0.197 0.198 |------------------ 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 0.070 0.181 0.157 |======================= 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 0.239 0.172 0.083 0.128 0.091 -0.021 0.029 0.053 -0.082 -0.084 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 0.239 2 0.209 0.122 3 0.207 0.118 0.019 4 0.205 0.107 0.000 0.092 5 0.202 0.107 -0.004 0.085 0.037 6 0.205 0.114 -0.004 0.094 0.054 -0.083 7 0.207 0.113 -0.007 0.094 0.050 -0.089 0.029 8 0.206 0.117 -0.009 0.090 0.051 -0.094 0.019 0.047 9 0.212 0.120 -0.021 0.096 0.062 -0.095 0.034 0.073 -0.130 10 0.205 0.124 -0.019 0.091 0.066 -0.090 0.033 0.080 -0.118 -0.054 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) 566.45 560.72 560.73 562.68 563.55 565.37 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 566.45 568.34 570.06 569.82 571.43 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 0.239 R-SQUARED DUE TO POOLED AUTOREGRESSION: 5.69 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 106.03 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.239 0.057 0.014 0.003 0.001 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 571011 1 0.015 -0.120 2 571012 1 0.006 0.037 3 571021 1 0.222 0.421 4 571022 1 0.164 0.358 5 571031 1 0.031 0.162 6 571032 1 0.093 0.262 7 571041 1 0.353 0.577 8 571042 1 0.219 0.419 9 571051 1 0.082 0.285 10 571052 1 0.076 0.167 11 571061 1 0.185 0.425 12 571062 1 0.255 0.502 13 571071 1 0.040 0.198 14 571072 1 0.025 0.008 15 571081 1 0.056 0.219 16 571082 1 0.256 0.468 17 571091 1 0.006 0.061 18 571092 1 0.142 0.352 19 571101 1 0.057 0.227 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 571102 1 0.090 -0.130 21 571111 1 0.083 0.288 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.117 0.247 STANDARD DEVIATION 0 0.098 0.196 MEDIAN 1 0.083 0.262 INTERQUARTILE RANGE 0 0.145 0.256 MINIMUM VALUE 1 0.006 -0.130 LOWER HINGE 1 0.040 0.162 UPPER HINGE 1 0.185 0.419 MAXIMUM VALUE 1 0.353 0.577 |------------------- 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 0.066 -0.028 3.014 0.071 -0.005 2 571012 1899 1978 80 1.000 0.069 0.416 2.841 0.077 -0.003 3 571021 1868 1978 111 1.000 0.059 0.011 2.705 0.070 -0.098 4 571022 1860 1978 119 1.000 0.071 -0.100 2.931 0.078 -0.078 5 571031 1873 1978 106 1.000 0.065 0.014 3.552 0.072 -0.010 6 571032 1847 1978 132 1.000 0.084 0.104 2.443 0.096 -0.044 7 571041 1866 1978 113 1.000 0.063 -0.065 3.753 0.074 -0.097 8 571042 1864 1966 103 1.000 0.070 -0.397 3.933 0.077 -0.097 9 571051 1859 1978 120 1.000 0.062 -0.338 2.449 0.073 -0.011 10 571052 1899 1978 80 1.000 0.086 -0.372 3.822 0.099 -0.038 11 571061 1891 1978 88 1.000 0.062 -0.111 3.383 0.068 -0.019 12 571062 1883 1978 96 1.000 0.069 -1.039 4.511 0.079 -0.026 13 571071 1873 1967 95 1.000 0.062 -0.777 3.103 0.070 -0.009 14 571072 1876 1965 90 1.000 0.053 -0.664 3.580 0.058 0.001 15 571081 1874 1978 105 1.000 0.052 -0.210 2.844 0.057 0.020 16 571082 1853 1978 126 1.000 0.066 -0.617 4.363 0.079 -0.104 17 571091 1866 1978 113 1.000 0.063 -0.101 3.604 0.066 -0.003 18 571092 1868 1978 111 1.000 0.068 -0.243 2.943 0.076 -0.035 19 571101 1877 1976 100 1.000 0.091 -1.550 7.660 0.101 0.017 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.067 -0.345 2.828 0.073 0.035 21 571111 1856 1978 123 1.000 0.071 -0.681 4.695 0.079 0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.068 -0.338 3.569 0.076 -0.029 STANDARD DEVIATION 16 0.000 0.010 0.437 1.140 0.011 0.042 MEDIAN (50TH QUANTILE) 105 1.000 0.066 -0.243 3.383 0.074 -0.011 INTERQUARTILE RANGE 23 0.000 0.007 0.551 0.978 0.008 0.041 MINIMUM VALUE 70 1.000 0.052 -1.550 2.443 0.057 -0.104 LOWER HINGE (25TH QUANTILE) 90 1.000 0.062 -0.617 2.844 0.070 -0.044 UPPER HINGE (75TH QUANTILE) 113 1.000 0.070 -0.065 3.822 0.079 -0.003 MAXIMUM VALUE 132 1.000 0.091 0.416 7.660 0.101 0.035 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.307 0.137 0.009 -0.417 3.173 -0.091 0.579 MINIMUM CORRELATION: -0.091 SERIES 571011 AND 571042 58 YEARS MAXIMUM CORRELATION: 0.579 SERIES 571011 AND 571012 70 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 0.408 0.352 0.272 SDEV 0.127 0.157 0.138 SERR 0.014 0.011 0.012 EPS 0.928 0.919 0.883 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 0.997 0.046 -0.251 3.239 0.055 -0.086 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.011 0.005 0.046 43 89 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.14 0.43 1.00 1.06 1.49 17.36 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.00 0.87 0.94 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 -0.085 0.113 -0.030 0.134 0.021 0.030 0.058 0.080 -0.080 -0.066 PACF -0.085 0.107 -0.013 0.121 0.045 0.009 0.061 0.073 -0.091 -0.102 95% C.L. 0.174 0.175 0.178 0.178 0.181 0.181 0.181 0.182 0.183 0.184 |------------------ 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 0.010 0.104 -0.009 0.135 0.035 0.037 0.069 0.079 -0.080 -0.074 PACF 0.010 0.104 -0.011 0.126 0.036 0.011 0.066 0.060 -0.105 -0.095 95% C.L. 0.174 0.174 0.176 0.176 0.179 0.179 0.180 0.180 0.181 0.182 |----------------- 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 0.012 0.010 |========================= 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 0.997 0.048 -0.245 2.925 0.046 0.274 |------------ 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 0.272 0.167 0.067 0.153 0.083 0.073 0.093 0.074 -0.074 -0.091 PACF 0.272 0.100 -0.001 0.131 0.011 0.019 0.065 0.012 -0.135 -0.070 95% C.L. 0.174 0.187 0.191 0.192 0.195 0.196 0.197 0.199 0.199 0.200 |------------------- 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 0.087 0.276 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.12 MINUTES