RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit022n.rwl LOG FILE PROCESSED: brit022n.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: 384 1 Mar Lodge (PCAB) DENSITY_MINIMUM PCAB - 384 2 Great Britain Norway spruce 400 5659-330 1849 1976 - 384 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 11 385091 MISSING VALUES FOUND: 5 IN 1 GAPS / 1939 1943 / -------------------------------------------------------------------- 15 386111 MISSING VALUES FOUND: 12 IN 2 GAPS / 1863 1869 / 1904 1908 / -------------------------------------------------------------------- 16 386112 MISSING VALUES FOUND: 5 IN 1 GAPS / 1931 1935 / -------------------------------------------------------------------- 22 386142 MISSING VALUES FOUND: 5 IN 1 GAPS / 1940 1944 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 384031 1911 1976 66 0.289 0.026 1.029 3.954 0.062 0.559 2 384032 1924 1976 53 0.290 0.028 0.544 3.432 0.050 0.752 3 384041 1885 1976 92 0.293 0.029 -0.074 3.709 0.057 0.669 4 384042 1863 1976 114 0.295 0.032 1.092 6.186 0.069 0.600 5 384061 1871 1976 106 0.300 0.020 -0.246 2.813 0.058 0.412 6 384062 1886 1976 91 0.253 0.017 0.307 3.188 0.057 0.430 7 385071 1871 1976 106 0.308 0.034 0.383 2.999 0.072 0.637 8 385072 1861 1976 116 0.308 0.032 0.773 4.423 0.075 0.564 9 385081 1861 1976 116 0.314 0.036 -0.090 2.373 0.064 0.736 10 385082 1869 1976 108 0.327 0.031 0.014 2.809 0.066 0.557 11 385091 1863 1976 114 0.293 0.028 -0.107 2.582 0.059 0.698 12 385092 1849 1976 128 0.311 0.037 -0.182 2.150 0.064 0.773 13 385101 1886 1976 91 0.289 0.025 0.659 3.636 0.072 0.427 14 385102 1873 1976 104 0.270 0.023 0.932 4.253 0.065 0.431 15 386111 1859 1976 118 0.301 0.034 0.535 3.482 0.069 0.665 16 386112 1881 1976 96 0.324 0.044 0.065 3.215 0.064 0.759 17 386121 1887 1976 90 0.271 0.041 0.403 2.578 0.061 0.797 18 386122 1898 1976 79 0.320 0.031 -0.204 3.784 0.062 0.680 19 386131 1867 1973 107 0.328 0.048 0.811 3.289 0.076 0.753 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 0.304 0.022 -0.048 3.178 0.066 0.334 21 386141 1873 1976 104 0.277 0.022 0.058 3.856 0.066 0.512 22 386142 1876 1976 101 0.285 0.040 0.349 2.927 0.075 0.761 NUMBER OF SERIES READ IN: 22 FROM 1849 TO 1976 128 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 100 0.298 0.031 0.318 3.401 0.065 0.614 STANDARD DEVIATION 17 0.019 0.008 0.429 0.860 0.007 0.140 MEDIAN (50TH QUANTILE) 105 0.297 0.031 0.328 3.252 0.064 0.651 INTERQUARTILE RANGE 18 0.022 0.011 0.733 0.971 0.008 0.240 MINIMUM VALUE 53 0.253 0.017 -0.246 2.150 0.050 0.334 LOWER HINGE (25TH QUANTILE) 91 0.289 0.025 -0.074 2.813 0.061 0.512 UPPER HINGE (75TH QUANTILE) 109 0.311 0.036 0.659 3.784 0.069 0.752 MAXIMUM VALUE 128 0.328 0.048 1.092 6.186 0.076 0.797 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.394 0.263 0.017 -0.404 2.450 -0.339 0.876 MINIMUM CORRELATION: -0.339 SERIES 385092 AND 385102 104 YEARS MAXIMUM CORRELATION: 0.876 SERIES 386112 AND 386142 96 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 71.00 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 210. RBAR 0.318 0.424 0.317 SDEV 0.257 0.277 0.195 SERR 0.029 0.020 0.013 EPS 0.898 0.940 0.911 NSS 18.8 21.3 22.0 |======================== 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 1849 1976 128 0.295 0.021 0.118 2.960 0.054 0.486 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.324 0.153 -0.016 19 109 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.73 1.01 1.10 1.83 3.82 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.00 0.86 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 105. 23. 53. 91. 114. 128. |----------- 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 0.482 0.588 0.472 0.498 0.522 0.492 0.476 0.477 0.387 0.468 PACF 0.482 0.464 0.160 0.147 0.214 0.116 0.048 0.080 -0.082 0.080 95% C.L. 0.177 0.214 0.260 0.285 0.311 0.337 0.359 0.378 0.397 0.408 |------------------ 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 5 0.472 0.125 0.332 0.048 0.115 0.231 |================== 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 384031 3 0.00000000 0.00000000 -0.00010249 0.29237297 2 384032 3 0.00000000 0.00000000 0.00084744 0.26674166 3 384041 3 0.00000000 0.00000000 0.00076807 0.25743669 4 384042 1 0.08603558 0.11754736 0.00000000 0.28851104 5 384061 3 0.00000000 0.00000000 -0.00004056 0.30207548 6 384062 3 0.00000000 0.00000000 0.00033923 0.23780219 7 385071 3 0.00000000 0.00000000 0.00069214 0.27070621 8 385072 3 0.00000000 0.00000000 0.00055003 0.27540931 9 385081 3 0.00000000 0.00000000 0.00085573 0.26356071 10 385082 3 0.00000000 0.00000000 0.00060548 0.29413119 11 385091 3 0.00000000 0.00000000 0.00052509 0.26306939 12 385092 3 0.00000000 0.00000000 0.00074981 0.26273128 13 385101 3 0.00000000 0.00000000 -0.00011865 0.29468864 14 385102 1 0.05757921 0.07144218 0.00000000 0.26223993 15 386111 3 0.00000000 0.00000000 0.00061341 0.26086363 16 386112 3 0.00000000 0.00000000 0.00126078 0.26349169 17 386121 3 0.00000000 0.00000000 0.00131885 0.21110362 18 386122 3 0.00000000 0.00000000 0.00045886 0.30139241 19 386131 3 0.00000000 0.00000000 0.00125061 0.26069123 SERIES IDENT OPTION A B C D 20 386132 3 0.00000000 0.00000000 -0.00009057 0.30949175 21 386141 3 0.00000000 0.00000000 0.00031073 0.26051345 22 386142 3 0.00000000 0.00000000 0.00111282 0.23012772 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 384031 1911 1976 66 1.000 0.091 1.005 4.016 0.061 0.544 2 384032 1924 1976 53 1.000 0.085 0.774 3.249 0.050 0.711 3 384041 1885 1976 92 1.000 0.070 0.034 3.122 0.057 0.432 4 384042 1863 1976 114 1.000 0.096 0.880 5.190 0.068 0.538 5 384061 1871 1976 106 1.000 0.068 -0.265 2.821 0.057 0.407 6 384062 1886 1976 91 1.000 0.057 0.189 2.926 0.057 0.205 7 385071 1871 1976 106 1.000 0.084 0.715 3.355 0.072 0.390 8 385072 1861 1976 116 1.000 0.085 0.594 4.357 0.075 0.335 9 385081 1861 1976 116 1.000 0.070 0.280 3.766 0.064 0.271 10 385082 1869 1976 108 1.000 0.074 0.364 2.925 0.066 0.345 11 385091 1863 1976 114 1.000 0.075 0.824 3.751 0.057 0.487 12 385092 1849 1976 128 1.000 0.083 0.570 2.847 0.063 0.500 13 385101 1886 1976 91 1.000 0.086 0.574 3.658 0.071 0.419 14 385102 1873 1976 104 1.000 0.070 0.549 3.522 0.064 0.194 15 386111 1859 1976 118 1.000 0.087 0.786 4.187 0.067 0.491 16 386112 1881 1976 96 1.000 0.079 0.851 6.894 0.062 0.365 17 386121 1887 1976 90 1.000 0.076 0.349 2.630 0.061 0.411 18 386122 1898 1976 79 1.000 0.091 0.177 3.369 0.061 0.615 19 386131 1867 1973 107 1.000 0.083 0.368 3.211 0.076 0.313 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 1.000 0.072 -0.010 3.233 0.065 0.320 21 386141 1873 1976 104 1.000 0.074 0.103 4.001 0.065 0.419 22 386142 1876 1976 101 1.000 0.081 1.448 8.414 0.072 0.337 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 101 1.000 0.079 0.507 3.884 0.064 0.411 STANDARD DEVIATION 17 0.000 0.009 0.395 1.378 0.007 0.126 MEDIAN (50TH QUANTILE) 105 1.000 0.080 0.559 3.445 0.064 0.409 INTERQUARTILE RANGE 23 0.000 0.013 0.597 0.894 0.008 0.157 MINIMUM VALUE 53 1.000 0.057 -0.265 2.630 0.050 0.194 LOWER HINGE (25TH QUANTILE) 91 1.000 0.072 0.189 3.122 0.061 0.335 UPPER HINGE (75TH QUANTILE) 114 1.000 0.085 0.786 4.016 0.068 0.491 MAXIMUM VALUE 128 1.000 0.096 1.448 8.414 0.076 0.711 |------------------------ 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 384031 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 384032 -67 35 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 384041 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 384042 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 384061 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 384062 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 385071 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 385072 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 385081 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 385082 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 385091 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 385092 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 385101 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 385102 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 386111 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 386112 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 386121 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 386122 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 386131 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 386132 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 386141 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 386142 -67 67 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 384031 1911 1976 66 1.000 0.076 1.017 4.331 0.061 0.397 2 384032 1924 1976 53 1.000 0.061 0.750 3.041 0.050 0.446 3 384041 1885 1976 92 1.000 0.062 0.128 3.256 0.056 0.252 4 384042 1863 1976 114 0.999 0.082 1.269 8.224 0.069 0.363 5 384061 1871 1976 106 1.000 0.062 -0.418 3.206 0.057 0.264 6 384062 1886 1976 91 1.000 0.055 0.229 2.798 0.057 0.151 7 385071 1871 1976 106 1.000 0.065 0.520 3.686 0.072 -0.002 8 385072 1861 1976 116 1.000 0.073 0.680 5.060 0.075 0.092 9 385081 1861 1976 116 1.000 0.064 0.176 4.091 0.064 0.112 10 385082 1869 1976 108 1.000 0.066 0.377 3.041 0.066 0.187 11 385091 1863 1976 114 1.000 0.061 0.578 3.122 0.057 0.217 12 385092 1849 1976 128 0.999 0.066 0.519 2.899 0.063 0.243 13 385101 1886 1976 91 1.000 0.083 0.491 3.345 0.071 0.369 14 385102 1873 1976 104 1.000 0.067 0.546 3.510 0.064 0.135 15 386111 1859 1976 118 0.999 0.072 0.941 4.481 0.067 0.235 16 386112 1881 1976 96 1.000 0.076 0.842 5.982 0.062 0.314 17 386121 1887 1976 90 1.000 0.066 0.611 4.428 0.061 0.183 18 386122 1898 1976 79 1.000 0.067 0.147 3.825 0.061 0.247 19 386131 1867 1973 107 1.000 0.078 0.346 2.927 0.076 0.218 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 1.000 0.069 0.054 3.489 0.065 0.248 21 386141 1873 1976 104 1.000 0.069 0.029 4.090 0.065 0.318 22 386142 1876 1976 101 1.000 0.073 1.371 8.030 0.071 0.197 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 101 1.000 0.069 0.509 4.130 0.064 0.236 STANDARD DEVIATION 17 0.000 0.007 0.425 1.511 0.007 0.106 MEDIAN (50TH QUANTILE) 105 1.000 0.067 0.519 3.598 0.064 0.239 INTERQUARTILE RANGE 23 0.000 0.009 0.574 1.306 0.008 0.132 MINIMUM VALUE 53 0.999 0.055 -0.418 2.798 0.050 -0.002 LOWER HINGE (25TH QUANTILE) 91 1.000 0.064 0.176 3.122 0.061 0.183 UPPER HINGE (75TH QUANTILE) 114 1.000 0.073 0.750 4.428 0.069 0.314 MAXIMUM VALUE 128 1.000 0.083 1.371 8.224 0.076 0.446 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.363 0.125 0.008 -0.027 2.902 0.009 0.681 MINIMUM CORRELATION: 0.009 SERIES 385092 AND 386122 79 YEARS MAXIMUM CORRELATION: 0.681 SERIES 385101 AND 386142 91 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 71.00 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 210. RBAR 0.306 0.314 0.383 SDEV 0.154 0.185 0.147 SERR 0.017 0.013 0.010 EPS 0.893 0.907 0.932 NSS 18.8 21.3 22.0 |======================== 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 1849 1976 128 1.002 0.050 0.596 4.172 0.054 0.023 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.056 -0.020 0.070 31 97 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.53 1.00 1.07 1.60 5.48 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.00 0.87 0.92 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 0.023 0.180 -0.102 -0.008 -0.029 0.076 -0.065 0.011 -0.136 -0.009 PACF 0.023 0.180 -0.113 -0.036 0.012 0.077 -0.075 -0.016 -0.101 -0.008 95% C.L. 0.177 0.177 0.182 0.184 0.184 0.184 0.185 0.186 0.186 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 2 0.048 0.019 0.185 |======================= 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 0.052 0.134 -0.185 0.026 -0.098 0.099 -0.084 0.027 -0.153 -0.070 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 0.052 2 0.045 0.132 3 0.072 0.141 -0.202 4 0.078 0.137 -0.205 0.032 5 0.080 0.126 -0.197 0.036 -0.052 6 0.084 0.123 -0.184 0.028 -0.058 0.070 7 0.089 0.119 -0.182 0.015 -0.049 0.076 -0.071 8 0.088 0.120 -0.182 0.015 -0.051 0.077 -0.070 -0.012 9 0.086 0.113 -0.174 0.009 -0.049 0.057 -0.057 -0.002 -0.108 10 0.076 0.112 -0.179 0.015 -0.054 0.058 -0.073 0.008 -0.100 -0.094 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) 565.82 567.48 567.23 563.88 565.75 567.40 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 568.78 570.14 572.12 572.60 573.46 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 0.072 0.141 -0.202 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.02 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 106.40 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.072 0.146 -0.182 -0.007 -0.056 0.032 -0.004 0.015 -0.006 0.0026 -0.004 0.001 -0.001 0.001 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 384031 3 0.179 0.387 0.105 -0.128 2 384032 3 0.259 0.455 0.151 -0.210 3 384041 3 0.099 0.276 -0.035 -0.152 4 384042 3 0.278 0.315 0.297 -0.159 5 384061 3 0.087 0.265 0.031 -0.137 6 384062 3 0.137 0.147 0.322 -0.137 7 385071 3 0.107 -0.011 0.324 0.030 8 385072 3 0.050 0.097 0.153 -0.118 9 385081 3 0.028 0.101 0.103 -0.001 10 385082 3 0.096 0.170 0.162 -0.039 11 385091 3 0.141 0.159 0.310 -0.021 12 385092 3 0.185 0.120 0.315 0.135 13 385101 3 0.175 0.354 0.163 -0.125 14 385102 3 0.021 0.132 0.015 0.043 15 386111 3 0.081 0.223 0.093 -0.024 16 386112 3 0.128 0.323 0.038 -0.165 17 386121 3 0.094 0.150 0.222 0.017 18 386122 3 0.141 0.289 -0.205 -0.135 19 386131 3 0.066 0.221 0.024 -0.133 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 386132 3 0.178 0.261 0.143 -0.341 21 386141 3 0.139 0.317 0.094 -0.193 22 386142 3 0.053 0.186 0.108 -0.073 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.124 0.224 0.133 -0.094 STANDARD DEVIATION 0 0.067 0.111 0.132 0.104 MEDIAN 3 0.117 0.222 0.126 -0.126 INTERQUARTILE RANGE 0 0.093 0.168 0.184 0.131 MINIMUM VALUE 3 0.021 -0.011 -0.205 -0.341 LOWER HINGE 3 0.081 0.147 0.038 -0.152 UPPER HINGE 3 0.175 0.315 0.222 -0.021 MAXIMUM VALUE 3 0.278 0.455 0.324 0.135 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 384031 1911 1976 66 1.000 0.068 1.119 5.475 0.075 0.001 2 384032 1924 1976 53 1.000 0.052 0.739 3.241 0.058 0.030 3 384041 1885 1976 92 1.000 0.058 0.265 3.519 0.064 0.022 4 384042 1863 1976 114 1.000 0.073 1.331 9.732 0.076 0.044 5 384061 1871 1976 106 1.000 0.059 -0.318 3.070 0.066 0.001 6 384062 1886 1976 91 1.000 0.051 0.153 3.734 0.056 -0.009 7 385071 1871 1976 106 1.000 0.062 0.344 4.382 0.066 -0.001 8 385072 1861 1976 116 1.000 0.071 0.700 5.103 0.076 0.008 9 385081 1861 1976 116 1.000 0.063 0.243 4.211 0.068 0.000 10 385082 1869 1976 108 1.000 0.064 0.303 3.004 0.071 -0.001 11 385091 1863 1976 114 1.000 0.057 0.396 2.993 0.061 -0.001 12 385092 1849 1976 128 1.000 0.059 0.222 2.757 0.066 0.001 13 385101 1886 1976 91 1.000 0.074 0.299 3.359 0.084 -0.018 14 385102 1873 1976 104 1.000 0.067 0.634 3.831 0.069 0.001 15 386111 1859 1976 118 1.000 0.070 0.930 4.584 0.075 0.002 16 386112 1881 1976 96 1.000 0.071 1.026 6.223 0.070 -0.010 17 386121 1887 1976 90 1.000 0.063 0.468 4.550 0.065 0.006 18 386122 1898 1976 79 1.000 0.061 0.227 3.391 0.068 -0.010 19 386131 1867 1973 107 1.000 0.076 0.472 3.046 0.083 0.001 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 1.000 0.062 -0.178 3.406 0.070 0.008 21 386141 1873 1976 104 1.000 0.064 -0.007 3.141 0.072 0.004 22 386142 1876 1976 101 1.000 0.071 1.313 7.292 0.078 -0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 101 1.000 0.064 0.485 4.275 0.070 0.004 STANDARD DEVIATION 17 0.000 0.007 0.447 1.681 0.007 0.013 MEDIAN (50TH QUANTILE) 105 1.000 0.063 0.370 3.626 0.069 0.001 INTERQUARTILE RANGE 23 0.000 0.011 0.512 1.443 0.010 0.007 MINIMUM VALUE 53 1.000 0.051 -0.318 2.757 0.056 -0.018 LOWER HINGE (25TH QUANTILE) 91 1.000 0.059 0.227 3.141 0.066 -0.001 UPPER HINGE (75TH QUANTILE) 114 1.000 0.071 0.739 4.584 0.075 0.006 MAXIMUM VALUE 128 1.000 0.076 1.331 9.732 0.084 0.044 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.385 0.106 0.007 -0.040 2.868 0.082 0.645 MINIMUM CORRELATION: 0.082 SERIES 384031 AND 385102 66 YEARS MAXIMUM CORRELATION: 0.645 SERIES 385101 AND 386142 91 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 71.00 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 210. RBAR 0.326 0.351 0.406 SDEV 0.131 0.141 0.120 SERR 0.015 0.010 0.008 EPS 0.901 0.920 0.938 NSS 18.8 21.3 22.0 |======================== 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 1849 1976 128 1.000 0.046 0.407 3.826 0.056 -0.191 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.065 -0.023 0.068 33 95 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.73 1.01 1.05 1.79 5.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.09 0.00 0.86 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 -0.190 0.050 -0.071 -0.009 -0.035 0.055 -0.070 0.039 -0.119 0.011 PACF -0.190 0.014 -0.061 -0.035 -0.042 0.039 -0.057 0.009 -0.109 -0.040 95% C.L. 0.177 0.183 0.183 0.184 0.184 0.185 0.185 0.186 0.186 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 0.038 -0.195 |---------- 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 -0.002 -0.003 -0.004 -0.046 -0.027 0.027 -0.058 0.004 -0.109 -0.024 PACF -0.002 -0.003 -0.004 -0.046 -0.028 0.027 -0.059 0.001 -0.113 -0.024 95% C.L. 0.177 0.177 0.177 0.177 0.177 0.177 0.177 0.178 0.178 0.180 |----------------- 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 -0.002 -0.003 -0.004 |========================= 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 1849 1976 128 1.000 0.047 0.482 4.178 0.050 0.054 |------------ 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 0.054 0.130 -0.197 -0.034 -0.083 0.069 -0.067 0.016 -0.137 -0.004 PACF 0.054 0.127 -0.214 -0.028 -0.025 0.046 -0.078 -0.014 -0.106 -0.014 95% C.L. 0.177 0.177 0.180 0.187 0.187 0.188 0.189 0.190 0.190 0.193 |------------------- 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 0.068 0.077 0.141 -0.220 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.13 MINUTES