RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit049l.rwl LOG FILE PROCESSED: brit049l.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_LATE 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 1.101 0.466 0.663 3.675 0.347 0.562 2 392012 1917 1968 52 1.068 0.345 -0.185 3.172 0.304 0.451 3 392021 1904 1976 73 0.908 0.300 -0.043 2.716 0.307 0.274 4 392022 1906 1976 71 1.169 0.404 1.324 6.137 0.240 0.446 5 392031 1930 1976 47 0.916 0.393 0.752 3.337 0.316 0.615 6 392032 1921 1976 56 1.093 0.428 0.497 3.252 0.291 0.504 7 392041 1950 1976 27 1.233 0.369 0.247 2.839 0.261 0.419 8 392042 1937 1976 40 1.182 0.786 2.039 5.834 0.355 0.767 9 392051 1933 1976 44 1.391 0.419 0.579 4.502 0.208 0.664 10 392052 1928 1976 49 1.433 0.653 1.359 6.545 0.330 0.546 11 392061 1938 1976 39 1.335 0.505 1.039 4.167 0.303 0.441 12 392062 1920 1976 57 1.276 0.460 0.106 2.300 0.309 0.439 13 393071 1922 1976 55 1.957 0.846 0.376 3.661 0.377 0.501 14 393072 1921 1976 56 1.723 0.561 -0.063 2.824 0.228 0.667 15 393081 1914 1976 63 0.786 0.526 0.846 3.262 0.373 0.710 16 393082 1904 1976 73 0.861 0.482 0.775 2.864 0.344 0.724 17 393091 1916 1976 61 0.998 0.380 0.202 3.298 0.263 0.568 18 393092 1921 1976 56 1.076 0.418 -0.010 3.665 0.277 0.600 19 393101 1903 1976 74 0.865 0.547 0.643 2.783 0.405 0.798 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 1.039 0.615 0.583 2.424 0.393 0.748 21 394111 1931 1976 46 1.074 0.462 0.749 4.391 0.297 0.546 22 394112 1934 1976 43 1.623 1.029 0.939 3.217 0.316 0.833 23 394121 1913 1976 64 0.578 0.666 3.247 14.106 0.708 0.640 24 394122 1916 1976 61 1.079 0.817 0.822 2.567 0.388 0.829 25 394131 1934 1976 43 1.700 0.467 0.869 4.134 0.299 0.085 26 394132 1932 1976 45 1.350 0.415 0.711 3.152 0.304 0.308 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 1.185 0.529 0.733 4.032 0.329 0.565 STANDARD DEVIATION 12 0.317 0.176 0.713 2.332 0.092 0.181 MEDIAN (50TH QUANTILE) 56 1.097 0.467 0.687 3.280 0.308 0.565 INTERQUARTILE RANGE 18 0.353 0.200 0.622 1.328 0.064 0.264 MINIMUM VALUE 26 0.578 0.300 -0.185 2.300 0.208 0.085 LOWER HINGE (25TH QUANTILE) 45 0.998 0.415 0.247 2.839 0.291 0.446 UPPER HINGE (75TH QUANTILE) 63 1.350 0.615 0.869 4.167 0.355 0.710 MAXIMUM VALUE 74 1.957 1.029 3.247 14.106 0.708 0.833 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 324 0.344 0.223 0.012 -0.167 2.730 -0.265 0.880 MINIMUM CORRELATION: -0.265 SERIES 392041 AND 394111 27 YEARS MAXIMUM CORRELATION: 0.880 SERIES 393081 AND 393102 63 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 1.145 0.327 0.651 4.526 0.204 0.420 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.332 0.170 0.314 31 43 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.43 1.01 1.16 1.59 8.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.00 0.87 0.96 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 0.414 0.224 0.220 0.181 0.128 0.032 0.178 0.306 0.015 0.019 PACF 0.414 0.064 0.129 0.051 0.015 -0.072 0.191 0.210 -0.251 0.016 95% C.L. 0.232 0.269 0.279 0.289 0.295 0.298 0.298 0.304 0.320 0.320 |------------------ 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 1 0.197 0.443 |================== 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 0.00058202 1.08466232 2 392012 3 0.00000000 0.00000000 -0.00392854 1.17237556 3 392021 3 0.00000000 0.00000000 0.00083765 0.87722605 4 392022 3 0.00000000 0.00000000 -0.00946982 1.50950503 5 392031 3 0.00000000 0.00000000 -0.01197387 1.20354307 6 392032 3 0.00000000 0.00000000 0.00914457 0.83205843 7 392041 3 0.00000000 0.00000000 0.02926129 0.82367522 8 392042 1 3.44292426 0.17772904 0.00000000 0.73983550 9 392051 3 0.00000000 0.00000000 -0.01084214 1.63508451 10 392052 3 0.00000000 0.00000000 -0.01957143 1.92255104 11 392061 1 0.94977278 0.05137349 0.00000000 0.93495011 12 392062 3 0.00000000 0.00000000 -0.00487685 1.41704261 13 393071 3 0.00000000 0.00000000 -0.02969120 2.78844452 14 393072 3 0.00000000 0.00000000 -0.01975222 2.28597403 15 393081 3 0.00000000 0.00000000 -0.02194124 1.48815155 16 393082 3 0.00000000 0.00000000 -0.00914970 1.19936073 17 393091 3 0.00000000 0.00000000 -0.00821999 1.25268853 18 393092 3 0.00000000 0.00000000 -0.01426111 1.48251295 19 393101 1 1.83096576 0.03323675 0.00000000 0.19574386 SERIES IDENT OPTION A B C D 20 393102 3 0.00000000 0.00000000 -0.02336620 1.88033807 21 394111 3 0.00000000 0.00000000 -0.01802035 1.49782610 22 394112 3 0.00000000 0.00000000 -0.05696617 2.87581396 23 394121 1 4.40909052 0.30396515 0.00000000 0.38449731 24 394122 1 2.62038302 0.05722317 0.00000000 0.37200528 25 394131 1 0.28307006 0.03816342 0.00000000 1.56380224 26 394132 1 0.73299235 0.47372049 0.00000000 1.32356358 |-------------------- 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 0.425 0.681 3.692 0.340 0.554 2 392012 1917 1968 52 1.000 0.316 -0.241 3.189 0.298 0.402 3 392021 1904 1976 73 1.000 0.331 -0.013 2.715 0.302 0.269 4 392022 1906 1976 71 0.999 0.288 0.608 3.435 0.237 0.277 5 392031 1930 1976 47 0.998 0.398 0.819 2.918 0.310 0.426 6 392032 1921 1976 56 0.999 0.375 0.605 3.570 0.284 0.478 7 392041 1950 1976 27 0.998 0.227 -0.085 2.395 0.248 0.100 8 392042 1937 1976 40 1.001 0.302 0.501 4.819 0.349 0.105 9 392051 1933 1976 44 1.000 0.288 0.544 3.625 0.204 0.591 10 392052 1928 1976 49 0.998 0.409 1.179 5.789 0.323 0.452 11 392061 1938 1976 39 1.000 0.326 0.426 3.273 0.293 0.364 12 392062 1920 1976 57 0.999 0.364 0.318 2.354 0.304 0.428 13 393071 1922 1976 55 0.996 0.362 0.646 5.323 0.370 0.263 14 393072 1921 1976 56 0.998 0.280 0.216 3.227 0.223 0.548 15 393081 1914 1976 63 1.078 0.818 4.253 23.388 0.370 0.394 16 393082 1904 1976 73 0.991 0.492 0.453 2.348 0.341 0.643 17 393091 1916 1976 61 0.998 0.378 0.768 4.009 0.260 0.531 18 393092 1921 1976 56 0.993 0.352 0.333 3.540 0.271 0.517 19 393101 1903 1976 74 0.994 0.453 0.718 3.988 0.398 0.360 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 1.048 0.550 2.181 8.953 0.385 0.422 21 394111 1931 1976 46 0.991 0.352 0.514 3.778 0.291 0.426 22 394112 1934 1976 43 0.990 0.427 0.601 3.569 0.314 0.516 23 394121 1913 1976 64 0.993 0.734 1.235 4.730 0.695 0.425 24 394122 1916 1976 61 1.013 0.702 2.838 12.491 0.379 0.672 25 394131 1934 1976 43 1.000 0.274 0.909 3.942 0.292 0.079 26 394132 1932 1976 45 1.000 0.302 0.700 3.015 0.298 0.273 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 1.003 0.405 0.835 4.926 0.322 0.404 STANDARD DEVIATION 12 0.019 0.147 0.944 4.341 0.091 0.158 MEDIAN (50TH QUANTILE) 56 0.999 0.363 0.606 3.598 0.303 0.426 INTERQUARTILE RANGE 18 0.004 0.125 0.393 1.541 0.064 0.240 MINIMUM VALUE 26 0.990 0.227 -0.241 2.348 0.204 0.079 LOWER HINGE (25TH QUANTILE) 45 0.996 0.302 0.426 3.189 0.284 0.277 UPPER HINGE (75TH QUANTILE) 63 1.000 0.427 0.819 4.730 0.349 0.517 MAXIMUM VALUE 74 1.078 0.818 4.253 23.388 0.695 0.672 |------------------------ 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 0.987 0.344 0.392 2.895 0.345 0.260 2 392012 1917 1968 52 0.993 0.269 -0.345 3.417 0.294 0.141 3 392021 1904 1976 73 0.998 0.309 -0.097 3.083 0.302 0.201 4 392022 1906 1976 71 0.999 0.283 0.769 4.175 0.237 0.257 5 392031 1930 1976 47 0.992 0.357 0.830 3.458 0.307 0.256 6 392032 1921 1976 56 0.987 0.306 0.659 3.401 0.275 0.230 7 392041 1950 1976 27 0.998 0.208 -0.203 2.630 0.245 -0.038 8 392042 1937 1976 40 0.997 0.290 0.483 4.852 0.349 0.025 9 392051 1933 1976 44 0.995 0.264 0.406 3.525 0.201 0.550 10 392052 1928 1976 49 0.991 0.361 0.761 4.108 0.318 0.384 11 392061 1938 1976 39 0.996 0.310 0.323 3.114 0.291 0.319 12 392062 1920 1976 57 0.995 0.302 -0.015 2.709 0.302 0.252 13 393071 1922 1976 55 0.996 0.334 0.526 6.050 0.370 0.152 14 393072 1921 1976 56 0.996 0.250 0.251 3.326 0.222 0.414 15 393081 1914 1976 63 0.990 0.500 1.252 4.470 0.367 0.374 16 393082 1904 1976 73 0.985 0.394 0.378 2.916 0.342 0.481 17 393091 1916 1976 61 0.997 0.355 0.937 4.370 0.261 0.458 18 393092 1921 1976 56 0.990 0.290 0.926 4.391 0.272 0.332 19 393101 1903 1976 74 0.993 0.435 0.898 4.917 0.397 0.221 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 0.989 0.367 0.222 2.715 0.386 0.264 21 394111 1931 1976 46 0.997 0.298 0.692 3.649 0.291 0.130 22 394112 1934 1976 43 0.981 0.360 0.411 3.366 0.306 0.441 23 394121 1913 1976 64 0.951 0.597 0.670 3.655 0.701 0.170 24 394122 1916 1976 61 0.985 0.447 0.670 3.320 0.380 0.473 25 394131 1934 1976 43 0.999 0.270 0.919 3.976 0.290 0.058 26 394132 1932 1976 45 0.996 0.276 0.469 2.943 0.297 0.197 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 0.991 0.338 0.507 3.670 0.321 0.269 STANDARD DEVIATION 12 0.010 0.084 0.384 0.815 0.093 0.149 MEDIAN (50TH QUANTILE) 56 0.994 0.310 0.505 3.437 0.302 0.257 INTERQUARTILE RANGE 18 0.008 0.078 0.446 1.093 0.074 0.214 MINIMUM VALUE 26 0.951 0.208 -0.345 2.630 0.201 -0.038 LOWER HINGE (25TH QUANTILE) 45 0.989 0.283 0.323 3.083 0.275 0.170 UPPER HINGE (75TH QUANTILE) 63 0.997 0.361 0.769 4.175 0.349 0.384 MAXIMUM VALUE 74 0.999 0.597 1.252 6.050 0.701 0.550 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 324 0.338 0.182 0.010 -0.133 3.039 -0.201 0.813 MINIMUM CORRELATION: -0.201 SERIES 392012 AND 393072 48 YEARS MAXIMUM CORRELATION: 0.813 SERIES 392051 AND 392052 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 0.986 0.195 0.294 3.538 0.191 0.260 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.326 0.162 0.098 24 50 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.41 0.61 1.01 1.10 1.71 297.37 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.08 0.00 0.89 0.97 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 0.256 -0.112 -0.184 -0.109 -0.148 -0.222 0.082 0.186 -0.160 -0.197 PACF 0.256 -0.190 -0.112 -0.052 -0.164 -0.212 0.152 0.028 -0.342 -0.074 95% C.L. 0.232 0.247 0.250 0.257 0.260 0.264 0.274 0.275 0.282 0.287 |------------------ 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 0.115 0.310 -0.189 |======================= 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 0.333 -0.103 -0.183 -0.054 -0.212 -0.243 -0.029 0.138 -0.114 -0.163 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 0.333 2 0.414 -0.241 3 0.397 -0.211 -0.071 4 0.398 -0.206 -0.081 0.024 5 0.405 -0.230 -0.142 0.141 -0.294 6 0.374 -0.215 -0.157 0.116 -0.250 -0.109 7 0.379 -0.202 -0.163 0.125 -0.239 -0.128 0.052 8 0.379 -0.202 -0.164 0.125 -0.239 -0.129 0.053 -0.002 9 0.379 -0.187 -0.201 0.056 -0.203 -0.176 -0.005 0.107 -0.288 10 0.365 -0.182 -0.201 0.048 -0.213 -0.173 -0.015 0.098 -0.271 -0.047 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) 541.64 534.91 532.49 534.11 536.07 531.38 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 532.50 534.30 536.30 531.87 533.70 SELECTED AUTOREGRESSION ORDER: 2 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 0.414 -0.241 R-SQUARED DUE TO POOLED AUTOREGRESSION: 16.27 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 119.44 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.414 -0.070 -0.128 -0.036 0.016 0.015 0.003 -0.003 -0.002 -.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 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 2 0.090 0.277 -0.032 2 392012 2 0.073 0.187 -0.226 3 392021 2 0.193 0.253 -0.253 4 392022 2 0.129 0.272 -0.049 5 392031 2 0.075 0.276 -0.060 6 392032 2 0.068 0.264 -0.099 7 392041 2 0.099 -0.049 -0.242 8 392042 2 0.033 0.030 -0.177 9 392051 2 0.394 0.724 -0.278 10 392052 2 0.194 0.358 0.112 11 392061 2 0.198 0.324 -0.007 12 392062 2 0.069 0.264 -0.048 13 393071 2 0.077 0.189 -0.227 14 393072 2 0.188 0.457 -0.064 15 393081 2 0.225 0.463 -0.126 16 393082 2 0.270 0.500 0.012 17 393091 2 0.315 0.538 -0.150 18 393092 2 0.228 0.452 -0.348 19 393101 2 0.097 0.265 -0.201 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 393102 2 0.103 0.309 -0.154 21 394111 2 0.089 0.166 -0.264 22 394112 2 0.295 0.613 -0.252 23 394121 2 0.160 0.151 0.120 24 394122 2 0.277 0.567 -0.192 25 394131 2 0.052 0.069 -0.179 26 394132 2 0.114 0.239 -0.186 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.158 0.314 -0.137 STANDARD DEVIATION 0 0.095 0.184 0.119 MEDIAN 2 0.122 0.274 -0.166 INTERQUARTILE RANGE 0 0.148 0.268 0.177 MINIMUM VALUE 2 0.033 -0.049 -0.348 LOWER HINGE 2 0.077 0.189 -0.227 UPPER HINGE 2 0.225 0.457 -0.049 MAXIMUM VALUE 2 0.394 0.724 0.120 |------------------- 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 0.331 0.795 3.392 0.352 0.003 2 392012 1917 1968 52 1.000 0.258 -0.019 3.162 0.282 -0.015 3 392021 1904 1976 73 1.000 0.293 0.182 3.762 0.327 -0.080 4 392022 1906 1976 71 1.000 0.273 0.693 3.925 0.273 -0.014 5 392031 1930 1976 47 1.000 0.344 0.907 4.025 0.332 0.007 6 392032 1921 1976 56 1.000 0.295 0.544 3.156 0.308 -0.002 7 392041 1950 1976 27 1.000 0.202 -0.024 2.593 0.237 -0.050 8 392042 1937 1976 40 1.000 0.285 0.464 4.774 0.335 -0.005 9 392051 1933 1976 44 1.000 0.209 0.754 4.104 0.215 -0.032 10 392052 1928 1976 49 1.000 0.328 1.203 5.346 0.344 0.025 11 392061 1938 1976 39 1.000 0.294 0.362 3.211 0.327 -0.005 12 392062 1920 1976 57 1.000 0.292 0.131 3.080 0.337 -0.003 13 393071 1922 1976 55 1.000 0.321 0.171 5.472 0.389 0.009 14 393072 1921 1976 56 1.000 0.225 0.292 3.025 0.257 0.015 15 393081 1914 1976 63 1.000 0.452 1.303 5.009 0.429 0.011 16 393082 1904 1976 73 1.000 0.340 0.327 2.658 0.388 0.026 17 393091 1916 1976 61 1.000 0.311 0.961 4.358 0.321 -0.038 18 393092 1921 1976 56 1.000 0.256 0.866 4.058 0.282 0.039 19 393101 1903 1976 74 1.000 0.416 0.844 5.046 0.417 0.025 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 393102 1906 1976 71 1.000 0.350 0.515 3.025 0.395 0.014 21 394111 1931 1976 46 1.000 0.285 0.745 3.805 0.304 -0.019 22 394112 1934 1976 43 1.000 0.302 0.550 2.859 0.332 0.054 23 394121 1913 1976 64 1.002 0.580 0.718 3.611 0.727 0.038 24 394122 1916 1976 61 1.000 0.386 0.371 2.747 0.468 -0.031 25 394131 1934 1976 43 1.000 0.265 0.919 4.152 0.293 -0.022 26 394132 1932 1976 45 1.000 0.265 0.397 2.530 0.319 -0.025 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 55 1.000 0.314 0.576 3.726 0.346 -0.003 STANDARD DEVIATION 12 0.000 0.079 0.353 0.875 0.097 0.030 MEDIAN (50TH QUANTILE) 56 1.000 0.294 0.547 3.686 0.329 -0.003 INTERQUARTILE RANGE 18 0.000 0.075 0.517 1.126 0.095 0.037 MINIMUM VALUE 26 1.000 0.202 -0.024 2.530 0.215 -0.080 LOWER HINGE (25TH QUANTILE) 45 1.000 0.265 0.327 3.025 0.293 -0.022 UPPER HINGE (75TH QUANTILE) 63 1.000 0.340 0.844 4.152 0.388 0.015 MAXIMUM VALUE 74 1.002 0.580 1.303 5.472 0.727 0.054 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 324 0.313 0.171 0.009 -0.170 2.806 -0.203 0.721 MINIMUM CORRELATION: -0.203 SERIES 392012 AND 393071 47 YEARS MAXIMUM CORRELATION: 0.721 SERIES 392052 AND 394112 43 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 0.995 0.178 0.391 3.309 0.204 0.015 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.318 0.157 0.086 30 44 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.63 1.00 1.11 1.73 5.04 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.10 0.00 0.88 0.98 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 0.015 -0.060 -0.135 -0.035 -0.081 -0.222 0.055 0.209 -0.192 -0.084 PACF 0.015 -0.060 -0.134 -0.036 -0.099 -0.252 0.030 0.164 -0.293 -0.092 95% C.L. 0.232 0.233 0.233 0.238 0.238 0.239 0.250 0.251 0.260 0.268 |------------------ 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 -0.002 -0.140 -0.048 -0.080 -0.212 0.041 0.199 -0.204 -0.057 PACF -0.010 -0.002 -0.140 -0.052 -0.084 -0.242 0.012 0.181 -0.303 -0.101 95% C.L. 0.232 0.233 0.233 0.237 0.238 0.239 0.249 0.249 0.258 0.266 |----------------- 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 2 0.021 -0.010 -0.002 |========================= 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 0.995 0.196 0.195 3.554 0.181 0.335 |------------ 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 0.331 -0.130 -0.228 -0.130 -0.161 -0.189 0.103 0.205 -0.142 -0.260 PACF 0.331 -0.269 -0.102 -0.044 -0.197 -0.154 0.184 -0.010 -0.347 -0.071 95% C.L. 0.232 0.257 0.260 0.271 0.274 0.279 0.286 0.288 0.296 0.299 |------------------- 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 2 0.190 0.429 -0.269 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.23 MINUTES