RUN: AZ001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: AZ551E.rwl.conv LOG FILE PROCESSED: AZ551E.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: 735 1 Fly Peak, Chiricahua Mts WIDTH_EARLY PSME - 735 2 United States of America bigcone Douglas-fir 2790 3151-10918 1703 19 735 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 3 735161 MISSING VALUES FOUND: 1 IN 1 GAPS / 1896 1896 / -------------------------------------------------------------------- 4 735162 MISSING VALUES FOUND: 1 IN 1 GAPS / 1739 1739 / -------------------------------------------------------------------- 11 735201 MISSING VALUES FOUND: 1 IN 1 GAPS / 1734 1734 / -------------------------------------------------------------------- 12 735202 MISSING VALUES FOUND: 1 IN 1 GAPS / 1925 1925 / -------------------------------------------------------------------- 13 735211 MISSING VALUES FOUND: 4 IN 1 GAPS / 1770 1773 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 735151 1857 1983 127 1.041 0.275 -0.226 2.771 0.243 0.380 2 735152 1852 1983 132 1.020 0.343 0.647 3.382 0.244 0.583 3 735161 1749 1983 235 0.748 0.425 0.924 2.955 0.264 0.871 4 735162 1719 1982 264 0.694 0.456 1.353 4.279 0.292 0.788 5 735171 1803 1983 181 0.789 0.359 -0.073 2.855 0.284 0.779 6 735172 1767 1983 217 0.569 0.334 0.913 3.231 0.278 0.875 7 735181 1703 1983 281 0.828 0.493 1.867 6.195 0.199 0.907 8 735182 1773 1983 211 0.773 0.254 0.447 2.492 0.198 0.778 9 735191 1725 1983 259 0.875 0.713 1.864 6.464 0.229 0.918 10 735192 1727 1983 257 0.810 0.616 1.900 6.496 0.220 0.914 11 735201 1724 1983 260 0.792 0.809 1.845 6.187 0.202 0.919 12 735202 1711 1983 273 0.847 0.836 1.549 4.851 0.189 0.967 13 735211 1753 1983 231 0.782 0.334 1.120 5.132 0.197 0.836 14 735212 1753 1983 231 0.597 0.323 0.954 3.288 0.212 0.893 15 735221 1724 1835 112 1.133 0.379 0.367 2.560 0.199 0.755 16 735222 1712 1983 272 0.563 0.281 0.949 3.563 0.242 0.842 NUMBER OF SERIES READ IN: 16 FROM 1703 TO 1983 281 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 0.804 0.452 1.025 4.169 0.231 0.813 STANDARD DEVIATION 55 0.162 0.190 0.681 1.493 0.034 0.148 MEDIAN (50TH QUANTILE) 232 0.790 0.369 0.952 3.472 0.224 0.857 INTERQUARTILE RANGE 65 0.140 0.226 1.150 2.754 0.055 0.132 MINIMUM VALUE 112 0.563 0.254 -0.226 2.492 0.189 0.380 LOWER HINGE (25TH QUANTILE) 196 0.721 0.328 0.547 2.905 0.199 0.778 UPPER HINGE (75TH QUANTILE) 261 0.861 0.554 1.697 5.660 0.254 0.911 MAXIMUM VALUE 281 1.133 0.836 1.900 6.496 0.292 0.967 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 118 0.565 0.235 0.022 -0.352 2.208 -0.014 0.964 MINIMUM CORRELATION: -0.014 SERIES 735152 AND 735201 132 YEARS MAXIMUM CORRELATION: 0.964 SERIES 735191 AND 735192 257 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 98.33 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 66.44 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 28. 55. 78. 78. 78. 105. 105. 105. RBAR 0.726 0.236 0.511 0.599 0.332 0.335 0.366 0.426 SDEV 0.142 0.273 0.204 0.136 0.224 0.236 0.258 0.333 SERR 0.027 0.037 0.023 0.015 0.025 0.023 0.025 0.032 EPS 0.966 0.798 0.935 0.954 0.876 0.883 0.896 0.917 NSS 10.6 12.7 13.6 13.7 14.2 15.0 15.0 15.0 |======================== 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 1703 1983 281 0.856 0.518 1.591 5.206 0.187 0.919 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.739 0.382 0.016 96 185 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.44 0.93 1.01 1.14 2.07 6.49 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.09 0.00 0.83 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 233. 66. 112. 196. 262. 281. |----------- 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 0.916 0.900 0.855 0.823 0.791 0.768 0.760 0.755 0.754 0.754 PACF 0.916 0.380 -0.025 -0.020 0.023 0.064 0.146 0.112 0.063 0.051 95% C.L. 0.119 0.195 0.247 0.286 0.318 0.345 0.369 0.390 0.411 0.430 |------------------ 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 0.863 0.563 0.385 |================== 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 735151 1 0.18170722 0.01623405 0.00000000 0.96512324 2 735152 3 0.00000000 0.00000000 -0.00285156 1.20962870 3 735161 3 0.00000000 0.00000000 -0.00498351 1.33523488 4 735162 1 1.43757510 0.00766265 0.00000000 0.08440509 5 735171 3 0.00000000 0.00000000 -0.00453856 1.20157278 6 735172 1 1.03068745 0.01322074 0.00000000 0.23223384 7 735181 1 1.51176858 0.01011426 0.00000000 0.32927415 8 735182 1 0.74455410 0.00745122 0.00000000 0.39924085 9 735191 1 2.90535855 0.02799424 0.00000000 0.48018533 10 735192 1 2.46297884 0.02622124 0.00000000 0.45011151 11 735201 1 3.25475979 0.02061623 0.00000000 0.20270622 12 735202 1 3.12935185 0.01559660 0.00000000 0.12523630 13 735211 3 0.00000000 0.00000000 -0.00126065 0.92473441 14 735212 3 0.00000000 0.00000000 -0.00231134 0.86538792 15 735221 1 0.68968564 0.04003578 0.00000000 0.98407853 16 735222 1 1.01367748 0.00570200 0.00000000 0.04957391 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 735151 1857 1983 127 1.000 0.263 -0.174 2.759 0.241 0.368 2 735152 1852 1983 132 0.999 0.311 0.399 2.959 0.242 0.507 3 735161 1749 1983 235 1.035 0.395 1.521 7.495 0.262 0.547 4 735162 1719 1982 264 1.009 0.402 0.851 4.154 0.290 0.541 5 735171 1803 1983 181 0.999 0.421 0.375 3.705 0.282 0.643 6 735172 1767 1983 217 1.004 0.404 0.480 2.952 0.276 0.634 7 735181 1703 1983 281 1.002 0.280 0.287 3.245 0.198 0.623 8 735182 1773 1983 211 1.000 0.250 0.155 2.753 0.197 0.553 9 735191 1725 1983 259 0.997 0.438 0.779 3.798 0.228 0.807 10 735192 1727 1983 257 0.998 0.352 0.013 2.810 0.219 0.768 11 735201 1724 1983 260 0.997 0.387 0.571 3.302 0.202 0.776 12 735202 1711 1983 273 0.982 0.481 0.886 3.995 0.191 0.878 13 735211 1753 1983 231 0.999 0.394 0.789 4.221 0.199 0.802 14 735212 1753 1983 231 0.994 0.415 0.317 2.583 0.211 0.807 15 735221 1724 1835 112 1.000 0.297 0.063 2.883 0.197 0.695 16 735222 1712 1983 272 1.000 0.289 0.237 2.902 0.241 0.497 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.001 0.361 0.472 3.532 0.230 0.653 STANDARD DEVIATION 55 0.011 0.070 0.420 1.187 0.033 0.144 MEDIAN (50TH QUANTILE) 233 1.000 0.391 0.387 3.102 0.223 0.638 INTERQUARTILE RANGE 66 0.004 0.117 0.588 1.051 0.053 0.245 MINIMUM VALUE 112 0.982 0.250 -0.174 2.583 0.191 0.368 LOWER HINGE (25TH QUANTILE) 196 0.997 0.293 0.196 2.846 0.199 0.544 UPPER HINGE (75TH QUANTILE) 262 1.001 0.410 0.784 3.897 0.252 0.789 MAXIMUM VALUE 281 1.035 0.481 1.521 7.495 0.290 0.878 |------------------------ 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 735151 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 735152 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 735161 -67 157 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 735162 -67 176 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 735171 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 735172 -67 145 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 735181 -67 188 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 735182 -67 141 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 735191 -67 173 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 735192 -67 172 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 735201 -67 174 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 735202 -67 182 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 735211 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 735212 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 735221 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 735222 -67 182 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 735151 1857 1983 127 0.997 0.246 -0.282 2.944 0.241 0.289 2 735152 1852 1983 132 0.992 0.244 -0.048 3.344 0.243 0.218 3 735161 1749 1983 235 0.997 0.306 0.268 3.164 0.262 0.426 4 735162 1719 1982 264 0.995 0.335 0.224 3.118 0.290 0.429 5 735171 1803 1983 181 0.987 0.389 0.358 4.130 0.282 0.590 6 735172 1767 1983 217 0.993 0.330 0.057 2.950 0.277 0.487 7 735181 1703 1983 281 0.998 0.263 0.134 3.346 0.198 0.583 8 735182 1773 1983 211 0.997 0.235 0.050 2.758 0.197 0.487 9 735191 1725 1983 259 0.997 0.305 0.339 3.293 0.228 0.575 10 735192 1727 1983 257 0.994 0.271 -0.232 2.845 0.219 0.576 11 735201 1724 1983 260 0.984 0.295 0.742 5.611 0.202 0.673 12 735202 1711 1983 273 0.967 0.392 0.998 4.647 0.191 0.840 13 735211 1753 1983 231 0.987 0.344 0.486 3.269 0.199 0.743 14 735212 1753 1983 231 0.984 0.363 0.263 2.589 0.210 0.744 15 735221 1724 1835 112 0.999 0.293 0.045 2.872 0.197 0.687 16 735222 1712 1983 272 1.000 0.286 0.195 2.842 0.241 0.490 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 0.992 0.306 0.225 3.358 0.230 0.552 STANDARD DEVIATION 55 0.009 0.050 0.327 0.796 0.034 0.167 MEDIAN (50TH QUANTILE) 233 0.995 0.300 0.210 3.141 0.224 0.575 INTERQUARTILE RANGE 66 0.011 0.073 0.301 0.486 0.054 0.222 MINIMUM VALUE 112 0.967 0.235 -0.282 2.589 0.191 0.218 LOWER HINGE (25TH QUANTILE) 196 0.987 0.267 0.047 2.858 0.199 0.458 UPPER HINGE (75TH QUANTILE) 262 0.997 0.339 0.348 3.345 0.252 0.680 MAXIMUM VALUE 281 1.000 0.392 0.998 5.611 0.290 0.840 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 118 0.381 0.153 0.014 -0.146 2.582 0.020 0.724 MINIMUM CORRELATION: 0.020 SERIES 735171 AND 735201 181 YEARS MAXIMUM CORRELATION: 0.724 SERIES 735191 AND 735192 257 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 98.33 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 66.44 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 28. 55. 78. 78. 78. 105. 105. 105. RBAR 0.567 0.417 0.479 0.462 0.366 0.309 0.408 0.434 SDEV 0.143 0.190 0.196 0.169 0.210 0.236 0.214 0.258 SERR 0.027 0.026 0.022 0.019 0.024 0.023 0.021 0.025 EPS 0.933 0.901 0.926 0.922 0.892 0.870 0.912 0.920 NSS 10.6 12.7 13.6 13.7 14.2 15.0 15.0 15.0 |======================== 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 1703 1983 281 0.972 0.212 -0.192 2.925 0.185 0.461 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.376 0.139 0.088 82 199 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.62 1.01 1.10 1.72 5.43 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 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 0.459 0.384 0.279 0.174 0.093 -0.008 -0.045 -0.074 -0.109 -0.083 PACF 0.459 0.219 0.054 -0.032 -0.048 -0.093 -0.038 -0.022 -0.042 0.018 95% C.L. 0.119 0.142 0.156 0.163 0.166 0.167 0.167 0.167 0.167 0.168 |------------------ 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 0.260 0.359 0.229 |======================= 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 0.422 0.339 0.257 0.154 0.110 0.008 -0.015 -0.053 -0.087 -0.083 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 0.422 2 0.340 0.195 3 0.325 0.170 0.075 4 0.327 0.174 0.082 -0.023 5 0.327 0.174 0.083 -0.022 -0.004 6 0.326 0.173 0.090 -0.007 0.024 -0.085 7 0.324 0.173 0.090 -0.005 0.028 -0.077 -0.027 8 0.323 0.170 0.091 -0.005 0.032 -0.070 -0.015 -0.036 9 0.321 0.170 0.088 -0.003 0.032 -0.066 -0.007 -0.022 -0.044 10 0.321 0.169 0.088 -0.004 0.032 -0.066 -0.006 -0.020 -0.040 -0.013 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) 2123.75 2070.63 2061.68 2062.11 2063.96 2065.96 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2065.91 2067.70 2069.33 2070.79 2072.74 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 0.340 0.195 R-SQUARED DUE TO POOLED AUTOREGRESSION: 20.95 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 126.50 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.340 0.311 0.172 0.119 0.074 0.048 0.031 0.020 0.013 0.0083 0.005 0.003 0.002 0.001 0.001 0.001 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 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 735151 2 0.134 0.222 0.233 2 735152 2 0.092 0.183 0.200 3 735161 2 0.227 0.375 0.145 4 735162 2 0.213 0.361 0.165 5 735171 2 0.416 0.470 0.221 6 735172 2 0.296 0.358 0.267 7 735181 2 0.387 0.461 0.217 8 735182 2 0.278 0.390 0.205 9 735191 2 0.381 0.451 0.223 10 735192 2 0.353 0.514 0.113 11 735201 2 0.481 0.533 0.210 12 735202 2 0.733 0.683 0.196 13 735211 2 0.589 0.588 0.219 14 735212 2 0.587 0.593 0.211 15 735221 2 0.491 0.786 -0.131 16 735222 2 0.273 0.393 0.201 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.371 0.460 0.181 STANDARD DEVIATION 0 0.175 0.157 0.091 MEDIAN 2 0.367 0.456 0.208 INTERQUARTILE RANGE 0 0.236 0.193 0.040 MINIMUM VALUE 2 0.092 0.183 -0.131 LOWER HINGE 2 0.250 0.368 0.180 UPPER HINGE 2 0.486 0.561 0.220 MAXIMUM VALUE 2 0.733 0.786 0.267 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 735151 1857 1983 127 1.000 0.229 -0.285 3.010 0.262 0.008 2 735152 1852 1983 132 1.000 0.232 -0.083 3.166 0.258 0.004 3 735161 1749 1983 235 1.000 0.271 0.213 3.217 0.303 -0.016 4 735162 1719 1982 264 1.000 0.298 0.020 3.485 0.348 -0.015 5 735171 1803 1983 181 1.000 0.303 0.205 4.119 0.334 -0.027 6 735172 1767 1983 217 1.000 0.277 0.170 3.857 0.302 -0.018 7 735181 1703 1983 281 1.000 0.207 -0.231 3.695 0.242 -0.030 8 735182 1773 1983 211 1.000 0.200 0.048 3.178 0.232 -0.020 9 735191 1725 1983 259 1.000 0.242 -0.028 3.041 0.279 -0.023 10 735192 1727 1983 257 1.000 0.219 -0.276 3.110 0.260 -0.011 11 735201 1724 1983 260 1.000 0.212 0.346 4.715 0.234 0.007 12 735202 1711 1983 273 1.000 0.203 0.248 3.455 0.223 0.017 13 735211 1753 1983 231 1.000 0.218 0.277 3.656 0.240 -0.009 14 735212 1753 1983 231 1.000 0.232 0.117 3.709 0.252 0.008 15 735221 1724 1835 112 1.000 0.208 0.325 3.161 0.230 0.002 16 735222 1712 1983 272 1.000 0.244 0.143 3.309 0.279 0.007 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.000 0.237 0.076 3.493 0.267 -0.007 STANDARD DEVIATION 55 0.000 0.033 0.207 0.458 0.038 0.015 MEDIAN (50TH QUANTILE) 233 1.000 0.230 0.130 3.382 0.259 -0.010 INTERQUARTILE RANGE 66 0.000 0.047 0.286 0.539 0.053 0.026 MINIMUM VALUE 112 1.000 0.200 -0.285 3.010 0.223 -0.030 LOWER HINGE (25TH QUANTILE) 196 1.000 0.210 -0.055 3.163 0.237 -0.019 UPPER HINGE (75TH QUANTILE) 262 1.000 0.258 0.231 3.702 0.290 0.007 MAXIMUM VALUE 281 1.000 0.303 0.346 4.715 0.348 0.017 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 118 0.489 0.119 0.011 -0.401 2.616 0.154 0.718 MINIMUM CORRELATION: 0.154 SERIES 735211 AND 735221 83 YEARS MAXIMUM CORRELATION: 0.718 SERIES 735181 AND 735182 211 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 98.33 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 66.44 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 28. 55. 78. 78. 78. 105. 105. 105. RBAR 0.588 0.397 0.459 0.489 0.439 0.434 0.544 0.605 SDEV 0.103 0.240 0.186 0.146 0.137 0.123 0.112 0.124 SERR 0.019 0.032 0.021 0.017 0.016 0.012 0.011 0.012 EPS 0.938 0.893 0.921 0.929 0.918 0.920 0.947 0.958 NSS 10.6 12.7 13.6 13.7 14.2 15.0 15.0 15.0 |======================== 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 1703 1983 281 0.990 0.172 -0.402 3.475 0.209 -0.084 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.297 0.102 0.050 84 197 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 1.24 1.01 1.14 2.38 15.31 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.10 0.00 0.82 0.92 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 -0.084 -0.037 0.037 -0.002 0.030 -0.049 -0.054 -0.013 -0.068 -0.038 PACF -0.084 -0.044 0.031 0.003 0.033 -0.046 -0.060 -0.029 -0.074 -0.050 95% C.L. 0.119 0.120 0.120 0.120 0.120 0.121 0.121 0.121 0.121 0.122 |------------------ 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 0.003 0.032 0.000 0.023 -0.055 -0.063 -0.029 -0.081 -0.051 PACF 0.001 0.003 0.032 0.000 0.023 -0.056 -0.063 -0.031 -0.078 -0.049 95% C.L. 0.119 0.119 0.119 0.119 0.119 0.119 0.120 0.120 0.120 0.121 |----------------- 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 0.001 0.001 0.003 |========================= 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 1703 1983 281 0.987 0.193 -0.259 2.933 0.173 0.419 |------------ 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 0.418 0.330 0.202 0.103 0.036 -0.061 -0.108 -0.115 -0.158 -0.131 PACF 0.418 0.189 0.014 -0.040 -0.038 -0.094 -0.070 -0.023 -0.070 -0.013 95% C.L. 0.119 0.139 0.149 0.153 0.154 0.154 0.155 0.156 0.157 0.159 |------------------- 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 0.210 0.340 0.196 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.25 MINUTES