RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit022e.rwl LOG FILE PROCESSED: brit022e.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) WIDTH_EARLY 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 --- NO GAPS IN DATA FOUND --- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 384031 1911 1976 66 1.207 0.415 0.429 3.334 0.276 0.472 2 384032 1924 1976 53 0.838 0.312 0.273 3.345 0.264 0.595 3 384041 1885 1976 92 1.720 0.858 0.985 3.276 0.203 0.823 4 384042 1863 1976 114 1.293 0.581 0.450 2.250 0.227 0.752 5 384061 1871 1976 106 1.559 0.638 1.035 4.088 0.238 0.740 6 384062 1886 1976 91 2.222 0.758 -0.125 2.420 0.180 0.783 7 385071 1871 1976 106 1.234 0.834 1.630 5.150 0.229 0.835 8 385072 1861 1976 116 1.189 0.405 0.704 3.602 0.250 0.561 9 385081 1861 1976 116 1.340 0.840 0.652 2.140 0.212 0.905 10 385082 1869 1976 108 1.098 0.792 1.081 3.084 0.239 0.916 11 385091 1863 1976 114 1.809 1.286 1.982 6.252 0.211 0.896 12 385092 1849 1976 128 1.539 1.151 0.823 2.181 0.233 0.916 13 385101 1886 1976 91 1.135 0.463 0.834 3.132 0.231 0.747 14 385102 1873 1976 104 1.502 0.558 1.136 5.040 0.229 0.587 15 386111 1859 1976 118 1.309 0.703 0.661 2.379 0.174 0.894 16 386112 1881 1976 96 1.091 0.722 1.050 3.124 0.270 0.842 17 386121 1887 1976 90 1.425 0.876 0.964 3.225 0.229 0.890 18 386122 1898 1976 79 1.393 0.417 0.370 2.938 0.229 0.541 19 386131 1867 1973 107 0.925 0.674 0.894 2.738 0.297 0.888 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 1.519 0.582 0.446 2.567 0.236 0.702 21 386141 1873 1976 104 1.438 0.871 1.132 3.702 0.230 0.849 22 386142 1876 1976 101 1.310 0.781 1.203 4.759 0.235 0.812 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 101 1.368 0.705 0.846 3.397 0.233 0.770 STANDARD DEVIATION 17 0.303 0.239 0.460 1.078 0.028 0.137 MEDIAN (50TH QUANTILE) 105 1.325 0.712 0.864 3.179 0.231 0.818 INTERQUARTILE RANGE 23 0.330 0.282 0.631 1.135 0.012 0.187 MINIMUM VALUE 53 0.838 0.312 -0.125 2.140 0.174 0.472 LOWER HINGE (25TH QUANTILE) 91 1.189 0.558 0.450 2.567 0.227 0.702 UPPER HINGE (75TH QUANTILE) 114 1.519 0.840 1.081 3.702 0.239 0.890 MAXIMUM VALUE 128 2.222 1.286 1.982 6.252 0.297 0.916 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.570 0.246 0.016 -0.753 2.966 -0.119 0.923 MINIMUM CORRELATION: -0.119 SERIES 384031 AND 386142 66 YEARS MAXIMUM CORRELATION: 0.923 SERIES 385081 AND 385082 108 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 0.424 0.500 0.354 SDEV 0.361 0.275 0.206 SERR 0.041 0.020 0.014 EPS 0.933 0.955 0.923 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 1.561 0.729 0.591 2.522 0.170 0.852 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.418 0.150 0.288 47 81 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.43 0.63 1.01 1.10 1.72 5.43 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.00 0.85 0.95 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 0.846 0.825 0.820 0.806 0.776 0.764 0.730 0.714 0.703 0.689 PACF 0.846 0.385 0.271 0.156 0.019 0.042 -0.064 -0.006 0.032 0.037 95% C.L. 0.177 0.276 0.344 0.401 0.448 0.489 0.525 0.555 0.583 0.609 |------------------ 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 0.854 0.231 0.234 0.207 0.137 0.163 |================== 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 0.00388936 1.07667601 2 384032 1 0.60063303 0.03296994 0.00000000 0.55930722 3 384041 1 2.71572804 0.03111917 0.00000000 0.83986980 4 384042 3 0.00000000 0.00000000 -0.01071246 1.90859807 5 384061 3 0.00000000 0.00000000 -0.00960763 2.07315898 6 384062 3 0.00000000 0.00000000 -0.02374439 3.31443954 7 385071 1 3.01770806 0.03910394 0.00000000 0.53166461 8 385072 1 1.03974903 0.03041777 0.00000000 0.90762872 9 385081 3 0.00000000 0.00000000 -0.02227344 2.64325476 10 385082 1 2.88137817 0.02963394 0.00000000 0.24731176 11 385091 1 5.60505342 0.06507321 0.00000000 1.07848763 12 385092 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 385101 3 0.00000000 0.00000000 -0.01240357 1.70528936 14 385102 3 0.00000000 0.00000000 -0.01114403 2.08717704 15 386111 3 0.00000000 0.00000000 -0.01740723 2.34513688 16 386112 1 2.57729554 0.02693243 0.00000000 0.18158974 17 386121 1 3.26083350 0.03322794 0.00000000 0.40688148 18 386122 1 0.86407268 0.02579067 0.00000000 1.02911139 19 386131 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 386132 3 0.00000000 0.00000000 -0.01228980 2.26876855 21 386141 1 3.08626461 0.03392952 0.00000000 0.60355544 22 386142 1 2.87056422 0.02056948 0.00000000 0.11410473 |-------------------- 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 0.329 0.105 2.992 0.272 0.431 2 384032 1924 1976 53 1.000 0.341 0.008 2.780 0.259 0.480 3 384041 1885 1976 92 1.000 0.330 1.268 5.598 0.201 0.658 4 384042 1863 1976 114 1.002 0.374 0.832 4.352 0.226 0.693 5 384061 1871 1976 106 0.996 0.349 0.955 3.843 0.235 0.641 6 384062 1886 1976 91 0.995 0.213 0.699 4.081 0.177 0.456 7 385071 1871 1976 106 1.002 0.274 0.178 2.825 0.226 0.474 8 385072 1861 1976 116 1.000 0.266 0.308 3.028 0.248 0.341 9 385081 1861 1976 116 1.165 0.678 2.717 11.762 0.216 0.714 10 385082 1869 1976 108 1.002 0.327 0.904 4.438 0.238 0.601 11 385091 1863 1976 114 1.002 0.274 0.218 2.510 0.208 0.606 12 385092 1849 1976 128 0.986 0.289 0.021 2.538 0.229 0.506 13 385101 1886 1976 91 1.005 0.271 -0.131 2.746 0.228 0.510 14 385102 1873 1976 104 0.999 0.267 0.140 3.179 0.226 0.404 15 386111 1859 1976 118 1.040 0.370 1.051 3.814 0.170 0.773 16 386112 1881 1976 96 1.007 0.339 1.571 8.209 0.264 0.453 17 386121 1887 1976 90 1.001 0.306 0.347 4.331 0.225 0.559 18 386122 1898 1976 79 1.000 0.263 0.277 3.176 0.226 0.387 19 386131 1867 1973 107 1.002 0.297 0.091 3.239 0.293 0.231 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 1.004 0.280 0.505 3.333 0.233 0.447 21 386141 1873 1976 104 0.998 0.316 0.950 4.992 0.226 0.580 22 386142 1876 1976 101 0.993 0.264 0.050 2.648 0.232 0.448 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 101 1.009 0.319 0.594 4.110 0.230 0.518 STANDARD DEVIATION 17 0.036 0.090 0.666 2.146 0.028 0.131 MEDIAN (50TH QUANTILE) 105 1.001 0.301 0.328 3.286 0.227 0.493 INTERQUARTILE RANGE 23 0.003 0.068 0.845 1.527 0.013 0.159 MINIMUM VALUE 53 0.986 0.213 -0.131 2.510 0.170 0.231 LOWER HINGE (25TH QUANTILE) 91 0.999 0.271 0.105 2.825 0.225 0.447 UPPER HINGE (75TH QUANTILE) 114 1.002 0.339 0.950 4.352 0.238 0.606 MAXIMUM VALUE 128 1.165 0.678 2.717 11.762 0.293 0.773 |------------------------ 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 0.996 0.315 0.055 3.001 0.271 0.406 2 384032 1924 1976 53 0.994 0.324 0.136 3.149 0.256 0.427 3 384041 1885 1976 92 0.990 0.275 1.200 5.094 0.200 0.541 4 384042 1863 1976 114 0.985 0.312 0.820 4.760 0.225 0.592 5 384061 1871 1976 106 0.991 0.275 0.609 3.177 0.235 0.434 6 384062 1886 1976 91 0.998 0.187 0.493 3.427 0.176 0.297 7 385071 1871 1976 106 0.997 0.250 -0.044 2.981 0.225 0.390 8 385072 1861 1976 116 0.999 0.260 0.269 3.032 0.248 0.316 9 385081 1861 1976 116 0.991 0.241 0.290 3.977 0.214 0.397 10 385082 1869 1976 108 0.998 0.316 0.768 3.955 0.238 0.582 11 385091 1863 1976 114 0.995 0.238 0.173 2.566 0.208 0.482 12 385092 1849 1976 128 0.992 0.252 -0.106 2.878 0.229 0.369 13 385101 1886 1976 91 0.997 0.252 -0.053 2.947 0.228 0.439 14 385102 1873 1976 104 0.999 0.262 0.140 3.185 0.226 0.378 15 386111 1859 1976 118 0.991 0.232 0.223 3.278 0.170 0.536 16 386112 1881 1976 96 0.997 0.317 1.650 9.047 0.264 0.424 17 386121 1887 1976 90 0.998 0.290 0.022 4.079 0.225 0.516 18 386122 1898 1976 79 0.997 0.246 0.227 3.355 0.225 0.299 19 386131 1867 1973 107 1.000 0.293 0.046 3.264 0.293 0.223 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 0.999 0.263 0.371 3.389 0.234 0.383 21 386141 1873 1976 104 0.996 0.291 0.703 4.338 0.225 0.504 22 386142 1876 1976 101 0.997 0.241 0.002 2.825 0.233 0.324 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 101 0.995 0.270 0.363 3.714 0.229 0.421 STANDARD DEVIATION 17 0.004 0.035 0.442 1.356 0.028 0.098 MEDIAN (50TH QUANTILE) 105 0.997 0.263 0.225 3.271 0.227 0.415 INTERQUARTILE RANGE 23 0.006 0.047 0.563 0.976 0.013 0.136 MINIMUM VALUE 53 0.985 0.187 -0.106 2.566 0.170 0.223 LOWER HINGE (25TH QUANTILE) 91 0.992 0.246 0.046 3.001 0.225 0.369 UPPER HINGE (75TH QUANTILE) 114 0.998 0.293 0.609 3.977 0.238 0.504 MAXIMUM VALUE 128 1.000 0.324 1.650 9.047 0.293 0.592 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.325 0.148 0.010 0.053 3.277 -0.079 0.842 MINIMUM CORRELATION: -0.079 SERIES 384061 AND 385091 106 YEARS MAXIMUM CORRELATION: 0.842 SERIES 384041 AND 384042 92 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 0.196 0.302 0.387 SDEV 0.199 0.184 0.178 SERR 0.023 0.013 0.012 EPS 0.821 0.902 0.933 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 0.983 0.155 -0.257 4.327 0.166 0.158 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.362 0.174 0.027 29 99 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.38 1.01 1.05 1.43 4.18 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.00 0.85 0.93 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 0.157 0.207 -0.029 -0.127 -0.047 -0.192 -0.099 -0.002 -0.028 -0.035 PACF 0.157 0.187 -0.090 -0.161 0.016 -0.139 -0.070 0.078 -0.026 -0.108 95% C.L. 0.177 0.181 0.188 0.188 0.191 0.192 0.197 0.199 0.199 0.199 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.071 0.131 0.194 |======================= 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 0.204 0.249 -0.049 -0.169 -0.077 -0.218 -0.116 -0.006 -0.054 -0.019 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 0.204 2 0.160 0.216 3 0.192 0.240 -0.146 4 0.161 0.290 -0.105 -0.212 5 0.169 0.294 -0.117 -0.218 0.039 6 0.174 0.265 -0.132 -0.179 0.062 -0.134 7 0.162 0.271 -0.149 -0.191 0.086 -0.118 -0.092 8 0.171 0.282 -0.157 -0.173 0.101 -0.144 -0.108 0.096 9 0.177 0.276 -0.166 -0.167 0.090 -0.153 -0.090 0.107 -0.061 10 0.169 0.289 -0.177 -0.186 0.101 -0.174 -0.111 0.141 -0.039 -0.124 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) 905.95 902.50 898.37 897.62 893.73 895.53 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 895.22 896.13 896.93 898.45 898.48 SELECTED AUTOREGRESSION ORDER: 4 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 0.161 0.290 -0.105 -0.212 R-SQUARED DUE TO POOLED AUTOREGRESSION: 14.62 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 117.12 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 4) PROCESS OUT TO ORDER 50: 1.0000 0.161 0.316 -0.008 -0.138 -0.092 -0.121 -0.030 -0.001 0.023 0.0323 0.018 0.010 -0.001 -0.006 -0.006 -0.005 -0.002 0.000 0.001 0.0015 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 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 4 0.209 0.398 0.115 -0.087 -0.102 2 384032 4 0.282 0.469 -0.102 -0.161 -0.118 3 384041 4 0.375 0.479 0.266 -0.134 -0.181 4 384042 4 0.445 0.432 0.390 0.015 -0.194 5 384061 4 0.237 0.352 0.100 0.047 0.110 6 384062 4 0.124 0.337 -0.123 0.099 -0.167 7 385071 4 0.218 0.341 0.270 -0.143 -0.003 8 385072 4 0.142 0.281 0.198 -0.081 -0.001 9 385081 4 0.220 0.353 0.194 -0.037 -0.186 10 385082 4 0.395 0.531 0.170 0.012 -0.212 11 385091 4 0.311 0.386 0.345 -0.131 -0.057 12 385092 4 0.246 0.278 0.378 -0.085 -0.060 13 385101 4 0.232 0.403 0.128 -0.112 0.136 14 385102 4 0.201 0.327 0.212 -0.092 0.031 15 386111 4 0.351 0.479 0.247 -0.141 -0.136 16 386112 4 0.222 0.365 0.224 -0.080 -0.096 17 386121 4 0.353 0.463 0.306 -0.194 -0.011 18 386122 4 0.121 0.276 0.125 -0.008 -0.041 19 386131 4 0.078 0.226 0.069 -0.138 0.028 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 386132 4 0.198 0.337 0.222 -0.096 -0.097 21 386141 4 0.266 0.452 0.110 -0.015 0.015 22 386142 4 0.211 0.284 0.295 -0.159 -0.027 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 4 0.247 0.375 0.188 -0.078 -0.062 STANDARD DEVIATION 0 0.094 0.081 0.133 0.076 0.097 MEDIAN 4 0.227 0.359 0.205 -0.090 -0.058 INTERQUARTILE RANGE 0 0.110 0.125 0.154 0.123 0.135 MINIMUM VALUE 4 0.078 0.226 -0.123 -0.194 -0.212 LOWER HINGE 4 0.201 0.327 0.115 -0.138 -0.136 UPPER HINGE 4 0.311 0.452 0.270 -0.015 -0.001 MAXIMUM VALUE 4 0.445 0.531 0.390 0.099 0.136 |------------------- 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 0.280 0.654 3.199 0.294 0.010 2 384032 1924 1976 53 1.000 0.274 0.691 4.011 0.273 0.009 3 384041 1885 1976 92 1.000 0.217 0.842 5.620 0.228 0.007 4 384042 1863 1976 114 1.000 0.232 0.221 4.656 0.250 0.000 5 384061 1871 1976 106 1.000 0.242 0.138 3.146 0.267 -0.012 6 384062 1886 1976 91 1.000 0.175 0.476 3.412 0.193 0.008 7 385071 1871 1976 106 1.000 0.221 -0.064 3.280 0.254 0.006 8 385072 1861 1976 116 1.000 0.241 0.299 3.156 0.271 0.005 9 385081 1861 1976 116 1.000 0.213 0.044 4.099 0.238 0.012 10 385082 1869 1976 108 1.000 0.246 0.176 3.422 0.283 0.026 11 385091 1863 1976 114 1.000 0.198 0.011 2.759 0.242 0.002 12 385092 1849 1976 128 1.000 0.219 -0.129 3.339 0.248 0.010 13 385101 1886 1976 91 1.000 0.221 -0.068 3.470 0.260 0.008 14 385102 1873 1976 104 1.000 0.234 0.168 3.194 0.257 -0.005 15 386111 1859 1976 118 1.000 0.186 0.628 4.343 0.193 0.006 16 386112 1881 1976 96 1.000 0.280 1.216 5.995 0.303 0.001 17 386121 1887 1976 90 1.000 0.233 -0.051 4.655 0.255 0.017 18 386122 1898 1976 79 1.000 0.232 -0.047 3.154 0.252 -0.001 19 386131 1867 1973 107 1.000 0.282 -0.134 3.763 0.319 0.008 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 386132 1856 1976 121 1.000 0.236 0.154 3.213 0.260 0.003 21 386141 1873 1976 104 1.000 0.249 1.051 5.499 0.268 -0.003 22 386142 1876 1976 101 1.000 0.217 0.167 2.966 0.246 -0.005 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 101 1.000 0.233 0.293 3.834 0.257 0.005 STANDARD DEVIATION 17 0.000 0.029 0.393 0.923 0.030 0.008 MEDIAN (50TH QUANTILE) 105 1.000 0.233 0.168 3.417 0.256 0.006 INTERQUARTILE RANGE 23 0.000 0.029 0.675 1.149 0.025 0.009 MINIMUM VALUE 53 1.000 0.175 -0.134 2.759 0.193 -0.012 LOWER HINGE (25TH QUANTILE) 91 1.000 0.217 -0.047 3.194 0.246 0.000 UPPER HINGE (75TH QUANTILE) 114 1.000 0.246 0.628 4.343 0.271 0.009 MAXIMUM VALUE 128 1.000 0.282 1.216 5.995 0.319 0.026 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.397 0.117 0.008 0.240 3.390 0.107 0.795 MINIMUM CORRELATION: 0.107 SERIES 384061 AND 384062 91 YEARS MAXIMUM CORRELATION: 0.795 SERIES 384041 AND 384042 92 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 0.323 0.404 0.447 SDEV 0.134 0.140 0.124 SERR 0.015 0.010 0.009 EPS 0.900 0.935 0.947 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 0.994 0.150 -0.375 3.795 0.191 -0.223 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.310 0.130 0.030 36 92 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.54 1.00 1.14 1.68 4.92 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.00 0.85 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 -0.221 0.023 -0.014 -0.104 0.118 -0.149 -0.056 0.055 -0.010 0.020 PACF -0.221 -0.027 -0.016 -0.116 0.074 -0.116 -0.125 0.009 0.013 -0.021 95% C.L. 0.177 0.185 0.185 0.185 0.187 0.189 0.193 0.194 0.194 0.194 |------------------ 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 0.052 -0.226 |---------- 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 -0.019 -0.018 0.007 0.039 -0.161 -0.105 0.021 0.003 -0.039 PACF 0.002 -0.019 -0.018 0.007 0.039 -0.161 -0.105 0.017 -0.007 -0.045 95% C.L. 0.177 0.177 0.177 0.177 0.177 0.177 0.182 0.184 0.184 0.184 |----------------- 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 4 0.003 0.002 -0.019 -0.020 0.006 |========================= 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 0.995 0.158 -0.220 4.423 0.163 0.205 |------------ 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 0.203 0.241 -0.044 -0.187 -0.104 -0.233 -0.099 -0.009 -0.015 0.005 PACF 0.203 0.209 -0.136 -0.230 0.009 -0.133 -0.053 0.071 -0.036 -0.099 95% C.L. 0.177 0.184 0.194 0.194 0.199 0.201 0.209 0.211 0.211 0.211 |------------------- 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 4 0.159 0.161 0.295 -0.094 -0.244 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.53 MINUTES