RUN: SPAI001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SPAI006E.rwl.conv LOG FILE PROCESSED: SPAI006E.rwl.conv_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: 491 1 El Quintar WIDTH_EARLY PISY - 491 2 Spain Scots pine, Scotch pine 1900 4202-242 1842 1977 - 491 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 491051 MISSING VALUES FOUND: 2 IN 1 GAPS / 1898 1899 / -------------------------------------------------------------------- 8 491052 MISSING VALUES FOUND: 3 IN 1 GAPS / 1898 1900 / -------------------------------------------------------------------- 15 491091 MISSING VALUES FOUND: 2 IN 1 GAPS / 1898 1899 / -------------------------------------------------------------------- 16 491092 MISSING VALUES FOUND: 1 IN 1 GAPS / 1897 1897 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 491011 1881 1977 97 1.427 0.538 1.426 7.288 0.267 0.629 2 491012 1892 1977 86 2.258 0.554 0.026 2.880 0.179 0.625 3 491021 1894 1977 84 1.131 0.357 0.217 4.080 0.211 0.689 4 491022 1890 1977 88 1.971 0.486 0.136 2.403 0.165 0.672 5 491031 1872 1977 106 1.930 0.594 0.230 3.284 0.202 0.717 6 491032 1888 1977 90 1.992 0.599 -0.503 2.870 0.190 0.748 7 491051 1843 1977 135 0.983 0.500 1.017 3.871 0.304 0.642 8 491052 1862 1977 116 1.795 0.766 0.651 4.177 0.241 0.689 9 491061 1874 1977 104 1.868 0.650 1.055 4.991 0.229 0.665 10 491062 1842 1977 136 1.227 0.602 1.220 4.583 0.288 0.655 11 491071 1858 1977 120 1.493 0.864 1.511 5.515 0.281 0.857 12 491072 1867 1977 111 1.340 0.614 0.532 3.142 0.253 0.754 13 491081 1862 1977 116 1.558 0.779 1.426 5.341 0.191 0.800 14 491082 1876 1977 102 1.564 0.663 0.812 3.639 0.230 0.714 15 491091 1860 1977 118 1.285 0.769 1.663 6.020 0.283 0.769 16 491092 1857 1977 121 1.683 1.019 1.078 3.345 0.263 0.808 17 491101 1865 1977 113 1.304 0.404 0.120 2.778 0.234 0.584 18 491102 1859 1977 119 1.660 0.518 0.132 2.842 0.200 0.713 19 491111 1875 1977 103 1.441 0.724 0.696 2.718 0.251 0.695 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 491112 1876 1977 102 1.869 0.725 1.117 6.512 0.248 0.721 21 491121 1861 1977 117 1.256 0.704 1.184 4.486 0.266 0.762 22 491122 1865 1977 113 1.595 0.737 1.473 5.614 0.217 0.753 NUMBER OF SERIES READ IN: 22 FROM 1842 TO 1977 136 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 109 1.574 0.644 0.783 4.199 0.236 0.712 STANDARD DEVIATION 14 0.323 0.153 0.598 1.380 0.038 0.066 MEDIAN (50TH QUANTILE) 112 1.561 0.632 0.914 3.975 0.237 0.714 INTERQUARTILE RANGE 15 0.564 0.199 1.003 2.461 0.064 0.089 MINIMUM VALUE 84 0.983 0.357 -0.503 2.403 0.165 0.584 LOWER HINGE (25TH QUANTILE) 102 1.304 0.538 0.217 2.880 0.202 0.665 UPPER HINGE (75TH QUANTILE) 117 1.868 0.737 1.220 5.341 0.266 0.754 MAXIMUM VALUE 136 2.258 1.019 1.663 7.288 0.304 0.857 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.420 0.227 0.015 -0.487 2.580 -0.223 0.868 MINIMUM CORRELATION: -0.223 SERIES 491032 AND 491062 90 YEARS MAXIMUM CORRELATION: 0.868 SERIES 491081 AND 491121 116 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 74.06 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 105. 231. 231. RBAR 0.508 0.398 0.420 SDEV 0.170 0.289 0.225 SERR 0.017 0.019 0.015 EPS 0.955 0.936 0.941 NSS 20.6 22.0 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 1842 1977 136 1.538 0.502 0.722 3.803 0.200 0.658 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.460 0.190 0.293 40 96 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.54 1.00 1.08 1.63 55.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.00 0.88 0.97 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 112. 16. 84. 102. 118. 136. |----------- 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 0.653 0.406 0.337 0.181 0.055 -0.035 -0.080 -0.097 -0.025 0.048 PACF 0.653 -0.036 0.151 -0.164 -0.033 -0.100 0.008 -0.017 0.147 0.053 95% C.L. 0.171 0.233 0.253 0.266 0.270 0.270 0.270 0.271 0.272 0.272 |------------------ 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 0.445 0.665 |================== 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 491011 1 3.35955548 0.32358986 0.00000000 1.33667278 2 491012 3 0.00000000 0.00000000 -0.00146903 2.32192612 3 491021 3 0.00000000 0.00000000 0.00160352 1.06304073 4 491022 3 0.00000000 0.00000000 0.00536156 1.73254704 5 491031 3 0.00000000 0.00000000 -0.00180724 2.02640438 6 491032 3 0.00000000 0.00000000 0.00537350 1.74706113 7 491051 1 0.95837557 0.03821372 0.00000000 0.79200101 8 491052 3 0.00000000 0.00000000 -0.00038533 1.78966653 9 491061 3 0.00000000 0.00000000 -0.00647087 2.20770168 10 491062 1 1.19356108 0.00864955 0.00000000 0.52877522 11 491071 1 3.13701987 0.09198998 0.00000000 1.22152996 12 491072 3 0.00000000 0.00000000 -0.01071674 1.94058800 13 491081 1 2.19649911 0.01980628 0.00000000 0.70625252 14 491082 3 0.00000000 0.00000000 -0.01725396 2.45210838 15 491091 3 0.00000000 0.00000000 -0.01282472 2.03896403 16 491092 3 0.00000000 0.00000000 -0.01805374 2.77630424 17 491101 3 0.00000000 0.00000000 -0.00489953 1.58298993 18 491102 3 0.00000000 0.00000000 -0.00805726 2.14368749 19 491111 3 0.00000000 0.00000000 -0.01717249 2.33384347 SERIES IDENT OPTION A B C D 20 491112 3 0.00000000 0.00000000 -0.00825067 2.29353714 21 491121 3 0.00000000 0.00000000 -0.01515271 2.15033460 22 491122 1 2.30559134 0.09899069 0.00000000 1.39843655 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 491011 1881 1977 97 1.000 0.295 -0.127 3.411 0.264 0.519 2 491012 1892 1977 86 1.000 0.244 -0.029 2.815 0.177 0.616 3 491021 1894 1977 84 1.000 0.316 0.388 5.008 0.208 0.673 4 491022 1890 1977 88 1.000 0.237 0.158 2.702 0.163 0.612 5 491031 1872 1977 106 1.000 0.304 0.154 3.333 0.200 0.707 6 491032 1888 1977 90 0.999 0.298 -0.422 2.738 0.187 0.718 7 491051 1843 1977 135 1.000 0.434 0.334 2.800 0.305 0.630 8 491052 1862 1977 116 1.000 0.437 0.628 3.988 0.243 0.720 9 491061 1874 1977 104 1.000 0.318 0.514 3.656 0.228 0.600 10 491062 1842 1977 136 1.000 0.415 0.584 3.221 0.285 0.615 11 491071 1858 1977 120 1.001 0.444 0.773 4.207 0.280 0.731 12 491072 1867 1977 111 1.001 0.371 -0.137 2.734 0.250 0.664 13 491081 1862 1977 116 0.998 0.326 0.659 4.718 0.189 0.709 14 491082 1876 1977 102 1.004 0.270 0.568 3.447 0.227 0.371 15 491091 1860 1977 118 1.010 0.449 1.358 6.953 0.289 0.679 16 491092 1857 1977 121 1.011 0.450 0.673 3.037 0.266 0.690 17 491101 1865 1977 113 1.000 0.286 0.071 3.067 0.232 0.521 18 491102 1859 1977 119 0.998 0.264 0.047 3.206 0.198 0.605 19 491111 1875 1977 103 1.006 0.349 0.491 3.567 0.248 0.540 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 491112 1876 1977 102 0.999 0.345 0.724 6.237 0.245 0.655 21 491121 1861 1977 117 1.007 0.335 0.393 3.783 0.264 0.507 22 491122 1865 1977 113 1.001 0.393 1.628 8.377 0.213 0.714 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 109 1.002 0.345 0.429 3.955 0.235 0.627 STANDARD DEVIATION 14 0.004 0.070 0.474 1.490 0.039 0.091 MEDIAN (50TH QUANTILE) 112 1.000 0.331 0.442 3.429 0.238 0.642 INTERQUARTILE RANGE 16 0.001 0.121 0.588 1.170 0.064 0.107 MINIMUM VALUE 84 0.998 0.237 -0.422 2.702 0.163 0.371 LOWER HINGE (25TH QUANTILE) 102 1.000 0.295 0.071 3.037 0.200 0.600 UPPER HINGE (75TH QUANTILE) 118 1.001 0.415 0.659 4.207 0.264 0.707 MAXIMUM VALUE 136 1.011 0.450 1.628 8.377 0.305 0.731 |------------------------ 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 491011 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 491012 -67 57 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 491021 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 491022 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 491031 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 491032 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 491051 -67 90 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 491052 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 491061 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 491062 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 491071 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 491072 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 491081 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 491082 -67 68 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 491091 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 491092 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 491101 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 491102 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 491111 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 491112 -67 68 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 491121 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 491122 -67 75 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 491011 1881 1977 97 0.998 0.286 -0.176 3.688 0.264 0.489 2 491012 1892 1977 86 0.999 0.242 0.022 2.828 0.177 0.612 3 491021 1894 1977 84 0.997 0.293 0.047 3.592 0.208 0.644 4 491022 1890 1977 88 0.999 0.228 0.004 2.736 0.163 0.588 5 491031 1872 1977 106 0.998 0.261 -0.255 3.322 0.199 0.574 6 491032 1888 1977 90 0.997 0.264 -0.128 3.968 0.187 0.566 7 491051 1843 1977 135 0.997 0.430 0.373 2.841 0.305 0.625 8 491052 1862 1977 116 0.993 0.415 1.187 7.319 0.242 0.688 9 491061 1874 1977 104 0.996 0.297 0.271 3.270 0.227 0.561 10 491062 1842 1977 136 0.993 0.379 0.575 3.816 0.285 0.527 11 491071 1858 1977 120 0.997 0.411 0.304 3.037 0.279 0.710 12 491072 1867 1977 111 0.996 0.358 -0.150 2.774 0.250 0.646 13 491081 1862 1977 116 0.995 0.301 0.516 4.073 0.188 0.673 14 491082 1876 1977 102 0.998 0.254 0.451 3.562 0.227 0.319 15 491091 1860 1977 118 0.991 0.402 1.402 7.872 0.289 0.619 16 491092 1857 1977 121 0.986 0.368 0.496 3.243 0.266 0.566 17 491101 1865 1977 113 0.998 0.276 0.010 3.154 0.232 0.483 18 491102 1859 1977 119 0.998 0.246 0.004 3.010 0.198 0.536 19 491111 1875 1977 103 0.993 0.287 -0.170 3.138 0.247 0.376 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 491112 1876 1977 102 0.996 0.318 0.457 5.676 0.244 0.597 21 491121 1861 1977 117 0.997 0.321 0.292 3.710 0.264 0.486 22 491122 1865 1977 113 0.996 0.348 1.068 6.991 0.213 0.667 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 109 0.996 0.318 0.300 3.983 0.234 0.571 STANDARD DEVIATION 14 0.003 0.062 0.455 1.529 0.039 0.097 MEDIAN (50TH QUANTILE) 112 0.997 0.299 0.281 3.442 0.237 0.581 INTERQUARTILE RANGE 16 0.003 0.103 0.492 0.931 0.064 0.117 MINIMUM VALUE 84 0.986 0.228 -0.255 2.736 0.163 0.319 LOWER HINGE (25TH QUANTILE) 102 0.995 0.264 0.004 3.037 0.199 0.527 UPPER HINGE (75TH QUANTILE) 118 0.998 0.368 0.496 3.968 0.264 0.644 MAXIMUM VALUE 136 0.999 0.430 1.402 7.872 0.305 0.710 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.454 0.150 0.010 -0.436 2.831 0.004 0.780 MINIMUM CORRELATION: 0.004 SERIES 491021 AND 491062 84 YEARS MAXIMUM CORRELATION: 0.780 SERIES 491011 AND 491012 86 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 74.06 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 105. 231. 231. RBAR 0.533 0.421 0.462 SDEV 0.166 0.222 0.172 SERR 0.016 0.015 0.011 EPS 0.959 0.941 0.950 NSS 20.6 22.0 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 1842 1977 136 0.979 0.259 0.000 3.844 0.197 0.553 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.226 0.102 0.147 46 90 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.20 0.60 1.00 1.04 1.65 5.07 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.10 0.00 0.89 0.99 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 0.549 0.226 0.118 -0.056 -0.191 -0.298 -0.304 -0.320 -0.243 -0.098 PACF 0.549 -0.108 0.058 -0.186 -0.109 -0.186 -0.054 -0.167 0.007 0.010 95% C.L. 0.171 0.217 0.224 0.226 0.226 0.231 0.242 0.253 0.265 0.271 |------------------ 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 0.328 0.634 -0.138 |======================= 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 0.651 0.316 0.095 -0.114 -0.257 -0.341 -0.349 -0.291 -0.224 -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 0.651 2 0.773 -0.187 3 0.764 -0.149 -0.049 4 0.754 -0.178 0.099 -0.194 5 0.733 -0.167 0.079 -0.111 -0.110 6 0.718 -0.182 0.090 -0.134 -0.008 -0.139 7 0.708 -0.183 0.081 -0.128 -0.021 -0.091 -0.067 8 0.705 -0.187 0.080 -0.134 -0.017 -0.100 -0.031 -0.051 9 0.701 -0.190 0.072 -0.136 -0.027 -0.093 -0.046 0.005 -0.079 10 0.708 -0.190 0.076 -0.127 -0.025 -0.081 -0.053 0.023 -0.145 0.093 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) 1059.95 986.90 984.06 985.72 982.52 982.86 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 982.22 983.60 985.25 986.39 987.21 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 0.773 -0.187 R-SQUARED DUE TO POOLED AUTOREGRESSION: 44.43 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 179.94 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.773 0.411 0.173 0.057 0.012 -0.002 -0.003 -0.002 -0.001 -.0005 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 491011 2 0.242 0.510 -0.040 2 491012 2 0.386 0.681 -0.109 3 491021 2 0.436 0.696 -0.074 4 491022 2 0.352 0.628 -0.067 5 491031 2 0.374 0.675 -0.153 6 491032 2 0.408 0.718 -0.195 7 491051 2 0.409 0.703 -0.110 8 491052 2 0.501 0.750 -0.091 9 491061 2 0.324 0.511 0.092 10 491062 2 0.325 0.643 -0.206 11 491071 2 0.542 0.899 -0.262 12 491072 2 0.443 0.685 -0.059 13 491081 2 0.479 0.772 -0.127 14 491082 2 0.119 0.336 -0.051 15 491091 2 0.415 0.698 -0.124 16 491092 2 0.324 0.586 -0.034 17 491101 2 0.242 0.501 -0.035 18 491102 2 0.292 0.568 -0.056 19 491111 2 0.158 0.403 -0.069 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 491112 2 0.364 0.633 -0.052 21 491121 2 0.268 0.490 -0.002 22 491122 2 0.466 0.767 -0.146 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.358 0.630 -0.090 STANDARD DEVIATION 0 0.108 0.132 0.076 MEDIAN 2 0.369 0.659 -0.072 INTERQUARTILE RANGE 0 0.144 0.192 0.077 MINIMUM VALUE 2 0.119 0.336 -0.262 LOWER HINGE 2 0.292 0.511 -0.127 UPPER HINGE 2 0.436 0.703 -0.051 MAXIMUM VALUE 2 0.542 0.899 0.092 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 491011 1881 1977 97 1.000 0.249 -0.531 4.501 0.296 0.000 2 491012 1892 1977 86 1.000 0.190 -0.198 3.558 0.228 -0.002 3 491021 1894 1977 84 1.000 0.221 0.087 3.487 0.251 -0.014 4 491022 1890 1977 88 1.000 0.184 -0.066 3.510 0.206 -0.003 5 491031 1872 1977 106 1.000 0.208 -0.617 4.627 0.247 -0.032 6 491032 1888 1977 90 1.000 0.202 -0.443 4.307 0.236 -0.055 7 491051 1843 1977 135 1.000 0.329 0.451 3.322 0.369 -0.001 8 491052 1862 1977 116 1.000 0.300 1.216 7.556 0.298 -0.017 9 491061 1874 1977 104 1.000 0.244 0.253 4.194 0.282 -0.006 10 491062 1842 1977 136 1.000 0.312 0.873 6.334 0.336 0.019 11 491071 1858 1977 120 1.000 0.278 -0.088 3.751 0.326 -0.006 12 491072 1867 1977 111 1.000 0.273 0.069 3.095 0.317 -0.011 13 491081 1862 1977 116 1.000 0.216 0.341 4.241 0.242 -0.018 14 491082 1876 1977 102 1.000 0.241 0.234 3.062 0.262 0.007 15 491091 1860 1977 118 1.000 0.312 0.963 5.971 0.350 -0.024 16 491092 1857 1977 121 1.000 0.303 0.275 3.188 0.356 -0.001 17 491101 1865 1977 113 1.000 0.241 0.032 4.000 0.283 -0.004 18 491102 1859 1977 119 1.000 0.207 0.002 3.344 0.246 0.002 19 491111 1875 1977 103 1.000 0.265 -0.492 4.932 0.279 0.012 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 491112 1876 1977 102 1.000 0.253 0.384 5.598 0.300 -0.005 21 491121 1861 1977 117 1.000 0.280 0.317 4.187 0.318 -0.003 22 491122 1865 1977 113 1.000 0.256 0.818 7.120 0.268 -0.014 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 109 1.000 0.253 0.176 4.449 0.286 -0.008 STANDARD DEVIATION 14 0.000 0.042 0.492 1.301 0.045 0.015 MEDIAN (50TH QUANTILE) 112 1.000 0.251 0.161 4.190 0.283 -0.004 INTERQUARTILE RANGE 16 0.000 0.064 0.473 1.445 0.071 0.013 MINIMUM VALUE 84 1.000 0.184 -0.617 3.062 0.206 -0.055 LOWER HINGE (25TH QUANTILE) 102 1.000 0.216 -0.088 3.487 0.247 -0.014 UPPER HINGE (75TH QUANTILE) 118 1.000 0.280 0.384 4.932 0.318 -0.001 MAXIMUM VALUE 136 1.000 0.329 1.216 7.556 0.369 0.019 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.389 0.122 0.008 -0.175 3.197 0.055 0.744 MINIMUM CORRELATION: 0.055 SERIES 491021 AND 491032 84 YEARS MAXIMUM CORRELATION: 0.744 SERIES 491011 AND 491012 86 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 74.06 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 105. 231. 231. RBAR 0.431 0.357 0.414 SDEV 0.137 0.145 0.135 SERR 0.013 0.010 0.009 EPS 0.940 0.924 0.939 NSS 20.6 22.0 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 1842 1977 136 0.992 0.212 0.132 5.927 0.240 0.005 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.231 0.110 0.092 44 92 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.58 1.00 1.04 1.63 4.91 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.09 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 0.005 -0.112 0.131 -0.093 -0.044 -0.117 -0.121 -0.129 -0.121 0.019 PACF 0.005 -0.112 0.134 -0.112 -0.009 -0.164 -0.098 -0.177 -0.129 -0.033 95% C.L. 0.171 0.172 0.174 0.177 0.178 0.178 0.181 0.183 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 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 0.017 -0.012 0.133 -0.123 -0.043 -0.144 -0.142 -0.143 -0.133 0.013 PACF 0.017 -0.013 0.133 -0.130 -0.034 -0.169 -0.108 -0.163 -0.118 -0.010 95% C.L. 0.171 0.172 0.172 0.175 0.177 0.177 0.181 0.184 0.187 0.190 |----------------- 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 0.019 0.017 -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 1842 1977 136 0.995 0.291 -0.171 3.198 0.194 0.668 |------------ 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 0.663 0.342 0.133 -0.097 -0.232 -0.330 -0.359 -0.346 -0.256 -0.112 PACF 0.663 -0.176 -0.032 -0.234 -0.056 -0.172 -0.057 -0.125 0.024 0.016 95% C.L. 0.171 0.235 0.249 0.251 0.253 0.259 0.271 0.284 0.297 0.303 |------------------- 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 0.472 0.804 -0.197 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.30 MINUTES