RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit049w.rwl LOG FILE PROCESSED: brit049w.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: 392 1 Mallaig, Loch Morar WIDTH_RING PISY - 392 2 Great Britain Scots pine, Scotch pine 20 5658-545 1903 1976 - 392 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 392011 1921 1976 56 2.925 1.139 0.407 3.080 0.240 0.766 2 392012 1917 1968 52 3.211 1.085 -0.110 3.157 0.197 0.743 3 392021 1904 1976 73 3.381 1.340 0.981 4.075 0.189 0.830 4 392022 1906 1976 71 3.749 1.055 0.255 3.190 0.194 0.640 5 392031 1930 1976 47 2.961 0.924 0.294 3.111 0.239 0.646 6 392032 1921 1976 56 3.191 1.050 -0.306 3.005 0.237 0.588 7 392041 1950 1976 27 3.430 1.037 0.390 3.351 0.228 0.610 8 392042 1937 1976 40 2.868 1.574 1.617 4.513 0.251 0.800 9 392051 1933 1976 44 3.872 1.476 0.873 3.493 0.182 0.858 10 392052 1928 1976 49 3.671 1.465 0.086 2.371 0.211 0.803 11 392061 1938 1976 39 3.195 0.837 0.178 3.495 0.202 0.547 12 392062 1920 1976 57 3.464 0.994 -0.617 2.636 0.225 0.539 13 393071 1922 1976 55 4.606 1.748 0.298 2.420 0.254 0.650 14 393072 1921 1976 56 4.146 1.096 0.465 3.311 0.162 0.673 15 393081 1914 1976 63 2.350 1.473 0.898 3.150 0.251 0.870 16 393082 1904 1976 73 2.582 1.316 0.680 2.831 0.247 0.826 17 393091 1916 1976 61 4.397 1.610 -0.823 2.813 0.169 0.846 18 393092 1921 1976 56 4.371 1.605 -0.485 3.069 0.180 0.777 19 393101 1903 1976 74 2.436 1.460 1.760 6.027 0.233 0.813 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 2.741 1.435 0.859 2.792 0.245 0.841 21 394111 1931 1976 46 4.381 1.348 -0.209 2.484 0.146 0.859 22 394112 1934 1976 43 4.158 1.483 0.367 2.806 0.187 0.849 23 394121 1913 1976 64 2.130 1.720 2.341 8.462 0.290 0.422 24 394122 1916 1976 61 3.437 2.402 0.773 2.328 0.310 0.711 25 394131 1934 1976 43 5.105 1.150 0.255 2.849 0.210 0.357 26 394132 1932 1976 45 4.085 1.111 0.689 6.280 0.232 0.470 NUMBER OF SERIES READ IN: 26 FROM 1903 TO 1976 74 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 3.494 1.344 0.458 3.504 0.220 0.705 STANDARD DEVIATION 12 0.765 0.334 0.721 1.402 0.039 0.148 MEDIAN (50TH QUANTILE) 56 3.433 1.344 0.379 3.095 0.227 0.754 INTERQUARTILE RANGE 18 1.221 0.399 0.773 0.687 0.056 0.221 MINIMUM VALUE 26 2.130 0.837 -0.823 2.328 0.146 0.357 LOWER HINGE (25TH QUANTILE) 45 2.925 1.085 0.086 2.806 0.189 0.610 UPPER HINGE (75TH QUANTILE) 63 4.146 1.483 0.859 3.493 0.245 0.830 MAXIMUM VALUE 74 5.105 2.402 2.341 8.462 0.310 0.870 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 324 0.307 0.291 0.016 -0.445 2.593 -0.496 0.903 MINIMUM CORRELATION: -0.496 SERIES 392041 AND 393092 27 YEARS MAXIMUM CORRELATION: 0.903 SERIES 393101 AND 393102 71 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 99.69 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 63.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| |======================== 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 1903 1976 74 3.656 0.985 1.159 7.291 0.131 0.637 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.012 0.006 1.395 10 64 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.29 1.01 1.20 1.49 2.31 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.10 0.00 0.87 0.97 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 56. 18. 27. 45. 63. 74. |----------- 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 0.628 0.556 0.431 0.356 0.310 0.380 0.367 0.376 0.287 0.302 PACF 0.628 0.267 0.012 0.011 0.044 0.225 0.072 0.039 -0.106 0.082 95% C.L. 0.232 0.311 0.361 0.388 0.405 0.417 0.436 0.452 0.469 0.478 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.554 0.584 0.202 |================== 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 392011 3 0.00000000 0.00000000 -0.00221326 2.98807788 2 392012 3 0.00000000 0.00000000 -0.02467003 3.86490941 3 392021 1 3.61948347 0.02425900 0.00000000 1.70586479 4 392022 3 0.00000000 0.00000000 -0.01374581 4.24414492 5 392031 3 0.00000000 0.00000000 -0.02775324 3.62692881 6 392032 3 0.00000000 0.00000000 0.02776384 2.39962339 7 392041 3 0.00000000 0.00000000 0.08316850 2.26564097 8 392042 1 6.27880144 0.14652455 0.00000000 1.87562811 9 392051 3 0.00000000 0.00000000 -0.06931501 5.43140602 10 392052 3 0.00000000 0.00000000 -0.05726735 5.10290813 11 392061 1 1.30887258 0.06331373 0.00000000 2.72461748 12 392062 3 0.00000000 0.00000000 -0.02624060 4.22483730 13 393071 3 0.00000000 0.00000000 -0.07124892 6.60078812 14 393072 1 2.93651104 0.07161105 0.00000000 3.45289230 15 393081 3 0.00000000 0.00000000 -0.06903658 4.55932951 16 393082 3 0.00000000 0.00000000 -0.04359558 4.19481754 17 393091 3 0.00000000 0.00000000 -0.05180962 6.00331163 18 393092 3 0.00000000 0.00000000 -0.06538004 6.23404551 19 393101 1 6.03723240 0.08736663 0.00000000 1.54359603 SERIES IDENT OPTION A B C D 20 393102 1 4.97979736 0.04138278 0.00000000 1.16918600 21 394111 3 0.00000000 0.00000000 -0.06556522 5.92208719 22 394112 3 0.00000000 0.00000000 -0.08264119 5.97601318 23 394121 1 5.96419716 0.09719830 0.00000000 1.21889722 24 394122 1 7.88786936 0.05680506 0.00000000 1.29344249 25 394131 3 0.00000000 0.00000000 0.00275748 5.04421949 26 394132 3 0.00000000 0.00000000 0.01247299 3.79823232 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 392011 1921 1976 56 1.000 0.387 0.362 3.078 0.235 0.749 2 392012 1917 1968 52 0.998 0.298 -0.592 3.757 0.193 0.659 3 392021 1904 1976 73 1.001 0.290 -0.192 3.563 0.188 0.678 4 392022 1906 1976 71 1.000 0.263 -0.055 3.266 0.192 0.581 5 392031 1930 1976 47 0.999 0.286 0.205 2.694 0.233 0.509 6 392032 1921 1976 56 0.998 0.318 0.159 3.396 0.232 0.583 7 392041 1950 1976 27 0.996 0.220 0.040 3.433 0.215 0.297 8 392042 1937 1976 40 1.000 0.270 0.441 4.089 0.242 0.425 9 392051 1933 1976 44 1.001 0.295 0.395 2.731 0.180 0.729 10 392052 1928 1976 49 0.997 0.341 -0.078 1.927 0.208 0.688 11 392061 1938 1976 39 1.000 0.242 -0.142 2.819 0.198 0.501 12 392062 1920 1976 57 0.999 0.275 0.029 3.067 0.221 0.495 13 393071 1922 1976 55 0.997 0.291 0.547 2.864 0.250 0.370 14 393072 1921 1976 56 1.000 0.208 0.151 3.355 0.160 0.542 15 393081 1914 1976 63 1.118 0.738 4.773 27.066 0.248 0.483 16 393082 1904 1976 73 1.001 0.363 0.384 2.675 0.245 0.664 17 393091 1916 1976 61 0.993 0.342 -0.106 2.710 0.167 0.777 18 393092 1921 1976 56 0.990 0.308 -0.042 2.691 0.176 0.677 19 393101 1903 1976 74 1.000 0.292 0.539 2.980 0.228 0.475 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 1.000 0.276 0.185 3.113 0.242 0.416 21 394111 1931 1976 46 0.994 0.231 -0.019 2.212 0.143 0.709 22 394112 1934 1976 43 0.997 0.247 -0.074 2.780 0.185 0.583 23 394121 1913 1976 64 1.001 0.426 0.639 2.979 0.284 0.551 24 394122 1916 1976 61 1.009 0.501 1.703 8.423 0.301 0.581 25 394131 1934 1976 43 1.000 0.225 0.262 2.885 0.205 0.346 26 394132 1932 1976 45 1.000 0.268 0.454 5.287 0.227 0.458 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 1.003 0.315 0.383 4.225 0.215 0.559 STANDARD DEVIATION 12 0.024 0.108 0.986 4.816 0.037 0.130 MEDIAN (50TH QUANTILE) 56 1.000 0.291 0.172 3.023 0.218 0.566 INTERQUARTILE RANGE 18 0.004 0.077 0.496 0.702 0.055 0.202 MINIMUM VALUE 26 0.990 0.208 -0.592 1.927 0.143 0.297 LOWER HINGE (25TH QUANTILE) 45 0.997 0.263 -0.055 2.731 0.188 0.475 UPPER HINGE (75TH QUANTILE) 63 1.000 0.341 0.441 3.433 0.242 0.677 MAXIMUM VALUE 74 1.118 0.738 4.773 27.066 0.301 0.777 |------------------------ 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 392011 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 392012 -67 34 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 392021 -67 48 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 392022 -67 47 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 392031 -67 31 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 392032 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 392041 -67 18 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 392042 -67 26 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 392051 -67 29 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 392052 -67 32 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 392061 -67 26 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 392062 -67 38 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 393071 -67 36 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 393072 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 393081 -67 42 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 393082 -67 48 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 393091 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 393092 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 393101 -67 49 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 393102 -67 47 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 394111 -67 30 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 394112 -67 28 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 394121 -67 42 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 394122 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 25 394131 -67 28 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 26 394132 -67 30 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 392011 1921 1976 56 0.985 0.280 0.112 2.894 0.231 0.548 2 392012 1917 1968 52 0.986 0.217 -0.888 4.377 0.185 0.435 3 392021 1904 1976 73 0.994 0.252 -0.509 3.553 0.187 0.523 4 392022 1906 1976 71 0.997 0.239 -0.180 2.894 0.190 0.520 5 392031 1930 1976 47 0.995 0.249 -0.176 2.564 0.231 0.365 6 392032 1921 1976 56 0.986 0.223 0.070 3.579 0.225 0.250 7 392041 1950 1976 27 0.998 0.176 -0.121 3.158 0.213 -0.003 8 392042 1937 1976 40 0.995 0.234 0.218 3.817 0.241 0.241 9 392051 1933 1976 44 0.993 0.255 0.054 2.660 0.177 0.674 10 392052 1928 1976 49 0.991 0.302 -0.070 2.189 0.204 0.638 11 392061 1938 1976 39 0.998 0.231 -0.218 2.839 0.196 0.457 12 392062 1920 1976 57 0.997 0.245 -0.333 3.352 0.223 0.392 13 393071 1922 1976 55 0.995 0.248 0.359 3.686 0.250 0.153 14 393072 1921 1976 56 0.998 0.185 -0.004 3.704 0.162 0.432 15 393081 1914 1976 63 0.993 0.346 0.970 4.965 0.246 0.509 16 393082 1904 1976 73 0.994 0.325 0.123 2.426 0.242 0.616 17 393091 1916 1976 61 0.997 0.302 0.590 4.732 0.169 0.629 18 393092 1921 1976 56 0.993 0.231 0.591 3.670 0.177 0.468 19 393101 1903 1976 74 0.997 0.263 0.655 3.739 0.228 0.297 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 0.995 0.245 -0.241 3.075 0.242 0.329 21 394111 1931 1976 46 0.997 0.160 0.275 3.658 0.140 0.408 22 394112 1934 1976 43 0.995 0.211 -0.118 3.105 0.183 0.413 23 394121 1913 1976 64 0.990 0.295 -0.029 4.134 0.282 0.174 24 394122 1916 1976 61 0.986 0.324 -0.349 3.550 0.303 0.311 25 394131 1934 1976 43 0.999 0.212 0.135 2.717 0.202 0.316 26 394132 1932 1976 45 0.998 0.232 -0.244 4.106 0.227 0.306 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 0.994 0.249 0.026 3.429 0.214 0.400 STANDARD DEVIATION 12 0.004 0.046 0.395 0.695 0.037 0.163 MEDIAN (50TH QUANTILE) 56 0.995 0.245 -0.016 3.551 0.218 0.410 INTERQUARTILE RANGE 18 0.004 0.057 0.436 0.845 0.056 0.214 MINIMUM VALUE 26 0.985 0.160 -0.888 2.189 0.140 -0.003 LOWER HINGE (25TH QUANTILE) 45 0.993 0.223 -0.218 2.894 0.185 0.306 UPPER HINGE (75TH QUANTILE) 63 0.997 0.280 0.218 3.739 0.241 0.520 MAXIMUM VALUE 74 0.999 0.346 0.970 4.965 0.303 0.674 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 324 0.258 0.215 0.012 -0.119 2.712 -0.350 0.806 MINIMUM CORRELATION: -0.350 SERIES 392042 AND 393091 40 YEARS MAXIMUM CORRELATION: 0.806 SERIES 392051 AND 393082 44 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 99.69 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 63.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| |======================== 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 1903 1976 74 0.994 0.131 -0.351 3.478 0.114 0.444 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.029 -0.016 0.221 20 54 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 0.60 1.04 1.22 1.82 5.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.11 0.00 0.87 0.98 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 0.438 -0.048 -0.047 -0.058 -0.260 -0.373 -0.114 0.052 -0.047 -0.180 PACF 0.438 -0.297 0.150 -0.157 -0.232 -0.197 0.123 -0.079 -0.098 -0.234 95% C.L. 0.232 0.273 0.274 0.274 0.275 0.288 0.313 0.315 0.316 0.316 |------------------ 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 0.283 0.574 -0.295 |======================= 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 0.447 -0.078 -0.049 0.010 -0.223 -0.451 -0.202 0.059 -0.003 -0.135 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 0.447 2 0.603 -0.348 3 0.679 -0.479 0.218 4 0.709 -0.545 0.311 -0.137 5 0.673 -0.464 0.170 0.047 -0.260 6 0.602 -0.451 0.216 -0.080 -0.076 -0.274 7 0.640 -0.440 0.227 -0.110 -0.013 -0.358 0.139 8 0.652 -0.472 0.226 -0.119 0.007 -0.396 0.196 -0.088 9 0.648 -0.462 0.207 -0.119 0.001 -0.386 0.173 -0.057 -0.048 10 0.640 -0.472 0.235 -0.181 0.001 -0.405 0.206 -0.131 0.056 -0.161 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) 477.25 462.73 455.20 453.58 454.18 450.99 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 447.23 447.78 449.20 451.03 451.10 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 0.679 -0.479 0.218 R-SQUARED DUE TO POOLED AUTOREGRESSION: 33.03 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 149.31 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.679 -0.019 -0.119 0.076 0.105 0.009 -0.028 0.000 0.015 0.0042 -0.004 -0.002 0.002 0.001 -0.001 0.000 0.000 0.000 0.000 -.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 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 392011 3 0.425 0.803 -0.477 0.222 2 392012 3 0.279 0.605 -0.244 0.039 3 392021 3 0.305 0.586 -0.102 -0.038 4 392022 3 0.357 0.663 -0.247 0.039 5 392031 3 0.171 0.423 -0.149 0.048 6 392032 3 0.127 0.325 -0.188 0.157 7 392041 3 0.226 -0.102 -0.345 -0.282 8 392042 3 0.136 0.271 -0.203 -0.118 9 392051 3 0.557 0.912 -0.303 -0.065 10 392052 3 0.485 0.756 -0.083 -0.090 11 392061 3 0.290 0.513 -0.100 -0.216 12 392062 3 0.188 0.410 -0.005 -0.096 13 393071 3 0.044 0.174 -0.110 0.042 14 393072 3 0.198 0.480 -0.104 0.009 15 393081 3 0.415 0.700 -0.191 -0.162 16 393082 3 0.435 0.700 -0.034 -0.149 17 393091 3 0.545 0.892 -0.360 -0.087 18 393092 3 0.297 0.556 -0.179 -0.142 19 393101 3 0.116 0.313 -0.041 -0.074 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 393102 3 0.170 0.380 -0.167 0.215 21 394111 3 0.280 0.603 -0.416 0.193 22 394112 3 0.283 0.592 -0.352 0.078 23 394121 3 0.066 0.192 -0.081 0.061 24 394122 3 0.142 0.336 -0.074 -0.082 25 394131 3 0.393 0.612 -0.613 0.260 26 394132 3 0.312 0.303 -0.249 -0.314 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.279 0.500 -0.208 -0.021 STANDARD DEVIATION 0 0.142 0.238 0.149 0.152 MEDIAN 3 0.282 0.534 -0.184 -0.052 INTERQUARTILE RANGE 0 0.223 0.338 0.204 0.179 MINIMUM VALUE 3 0.044 -0.102 -0.613 -0.314 LOWER HINGE 3 0.170 0.325 -0.303 -0.118 UPPER HINGE 3 0.393 0.663 -0.100 0.061 MAXIMUM VALUE 3 0.557 0.912 -0.005 0.260 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 392011 1921 1976 56 1.000 0.213 0.715 4.125 0.234 0.030 2 392012 1917 1968 52 1.000 0.179 -0.411 3.566 0.206 -0.053 3 392021 1904 1976 73 1.000 0.212 -0.820 6.467 0.245 -0.004 4 392022 1906 1976 71 1.000 0.195 -0.007 4.033 0.207 -0.006 5 392031 1930 1976 47 1.000 0.229 -0.138 3.011 0.264 -0.007 6 392032 1921 1976 56 1.000 0.209 -0.037 3.256 0.244 -0.031 7 392041 1950 1976 27 1.000 0.158 0.436 2.767 0.185 -0.044 8 392042 1937 1976 40 1.000 0.219 0.382 3.645 0.250 -0.013 9 392051 1933 1976 44 1.000 0.172 -0.058 4.593 0.195 0.001 10 392052 1928 1976 49 1.000 0.221 0.024 2.803 0.252 0.009 11 392061 1938 1976 39 1.000 0.195 -0.226 3.387 0.233 -0.022 12 392062 1920 1976 57 1.000 0.223 -0.646 3.857 0.253 -0.019 13 393071 1922 1976 55 1.000 0.244 0.302 3.792 0.269 -0.005 14 393072 1921 1976 56 1.000 0.165 -0.310 3.221 0.192 0.002 15 393081 1914 1976 63 1.000 0.266 0.516 4.337 0.285 0.070 16 393082 1904 1976 73 1.000 0.246 -0.210 3.109 0.284 -0.011 17 393091 1916 1976 61 1.000 0.206 -0.045 7.162 0.219 0.008 18 393092 1921 1976 56 1.000 0.194 0.082 4.234 0.219 0.013 19 393101 1903 1976 74 1.000 0.250 0.645 4.079 0.261 -0.010 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 1.000 0.225 -0.235 3.363 0.268 -0.025 21 394111 1931 1976 46 1.000 0.135 0.265 3.275 0.157 -0.010 22 394112 1934 1976 43 1.000 0.180 0.061 2.424 0.207 0.035 23 394121 1913 1976 64 1.000 0.288 -0.069 4.657 0.305 -0.006 24 394122 1916 1976 61 1.001 0.300 -0.120 4.763 0.308 0.005 25 394131 1934 1976 43 1.000 0.167 -0.297 2.585 0.178 0.075 26 394132 1932 1976 45 1.000 0.193 -0.552 5.539 0.196 -0.036 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 1.000 0.211 -0.029 3.925 0.235 -0.002 STANDARD DEVIATION 12 0.000 0.039 0.381 1.130 0.040 0.030 MEDIAN (50TH QUANTILE) 56 1.000 0.211 -0.051 3.718 0.239 -0.006 INTERQUARTILE RANGE 18 0.000 0.050 0.501 1.116 0.058 0.027 MINIMUM VALUE 26 1.000 0.135 -0.820 2.424 0.157 -0.053 LOWER HINGE (25TH QUANTILE) 45 1.000 0.180 -0.235 3.221 0.206 -0.019 UPPER HINGE (75TH QUANTILE) 63 1.000 0.229 0.265 4.337 0.264 0.008 MAXIMUM VALUE 74 1.001 0.300 0.715 7.162 0.308 0.075 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 324 0.231 0.174 0.010 -0.037 2.805 -0.270 0.747 MINIMUM CORRELATION: -0.270 SERIES 392012 AND 392042 32 YEARS MAXIMUM CORRELATION: 0.747 SERIES 392021 AND 392022 71 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 99.69 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 63.91 |--------------------------- RUNNING RBAR STATISTICS --------------------------| |======================== 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 1903 1976 74 0.997 0.106 -0.375 3.568 0.119 0.077 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.027 0.015 0.158 30 44 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.65 1.00 1.09 1.74 40.37 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.87 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 0.076 -0.155 -0.016 0.040 -0.073 -0.355 -0.038 0.146 -0.048 -0.150 PACF 0.076 -0.162 0.011 0.016 -0.081 -0.346 -0.009 0.049 -0.088 -0.138 95% C.L. 0.232 0.234 0.239 0.239 0.240 0.241 0.268 0.268 0.272 0.273 |------------------ 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 -0.001 0.000 -0.012 -0.026 -0.052 -0.336 -0.031 0.092 -0.081 -0.107 PACF -0.001 0.000 -0.012 -0.026 -0.052 -0.337 -0.044 0.096 -0.101 -0.155 95% C.L. 0.232 0.232 0.232 0.233 0.233 0.233 0.258 0.258 0.260 0.261 |----------------- 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 0.001 -0.001 0.000 -0.013 |========================= 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 1903 1976 74 0.998 0.127 -0.345 3.356 0.110 0.431 |------------ 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 0.425 -0.107 -0.047 0.062 -0.171 -0.401 -0.156 0.090 -0.059 -0.252 PACF 0.425 -0.351 0.228 -0.082 -0.254 -0.218 0.131 -0.062 -0.146 -0.163 95% C.L. 0.232 0.271 0.274 0.274 0.275 0.280 0.310 0.314 0.316 0.316 |------------------- 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 0.330 0.666 -0.487 0.231 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.23 MINUTES