RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN022L.rwl.conv LOG FILE PROCESSED: FRAN022L.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: 481 1 Llipodre WIDTH_LATE PIMU - 481 2 France krummholz pine 1950 4227-223 1839 1977 - 481 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 481011 1848 1977 130 0.397 0.265 0.913 2.826 0.396 0.798 2 481012 1848 1977 130 0.412 0.283 1.258 5.126 0.353 0.773 3 481021 1870 1977 108 0.429 0.221 1.404 6.198 0.371 0.459 4 481022 1862 1977 116 0.427 0.307 2.755 15.328 0.419 0.530 5 481031 1850 1977 128 0.223 0.115 0.575 2.889 0.390 0.535 6 481032 1853 1977 125 0.200 0.128 1.235 4.739 0.524 0.582 7 481051 1861 1977 117 0.348 0.191 1.925 8.564 0.394 0.424 8 481052 1858 1977 120 0.314 0.153 1.782 7.394 0.346 0.575 9 481061 1886 1977 92 0.367 0.225 1.256 4.029 0.334 0.674 10 481062 1868 1977 110 0.320 0.140 0.653 3.123 0.348 0.481 11 481081 1844 1977 134 0.287 0.170 0.801 3.350 0.398 0.687 12 481082 1839 1977 139 0.273 0.148 0.876 3.954 0.365 0.609 13 481091 1860 1977 118 0.238 0.185 1.615 6.180 0.602 0.470 14 481092 1855 1977 123 0.212 0.124 0.582 3.148 0.650 0.113 15 481101 1842 1977 136 0.238 0.163 1.859 7.308 0.314 0.834 16 481102 1853 1977 125 0.319 0.163 1.041 3.652 0.302 0.698 17 481111 1862 1977 116 0.252 0.143 1.901 8.850 0.439 0.390 18 481112 1877 1977 101 0.267 0.130 1.403 5.784 0.481 0.109 19 481131 1853 1977 125 0.511 0.205 0.412 2.469 0.307 0.613 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 0.589 0.390 1.579 5.354 0.308 0.752 NUMBER OF SERIES READ IN: 20 FROM 1839 TO 1977 139 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 0.331 0.192 1.291 5.513 0.402 0.555 STANDARD DEVIATION 11 0.104 0.072 0.586 3.015 0.096 0.198 MEDIAN (50TH QUANTILE) 121 0.316 0.167 1.257 4.932 0.380 0.578 INTERQUARTILE RANGE 15 0.159 0.082 0.860 3.504 0.089 0.228 MINIMUM VALUE 92 0.200 0.115 0.412 2.469 0.302 0.109 LOWER HINGE (25TH QUANTILE) 114 0.245 0.141 0.838 3.249 0.340 0.465 UPPER HINGE (75TH QUANTILE) 129 0.404 0.223 1.699 6.753 0.429 0.692 MAXIMUM VALUE 139 0.589 0.390 2.755 15.328 0.650 0.834 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.420 0.159 0.012 -0.255 2.672 -0.019 0.755 MINIMUM CORRELATION: -0.019 SERIES 481061 AND 481132 92 YEARS MAXIMUM CORRELATION: 0.755 SERIES 481012 AND 481061 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 81.64 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 105. 190. 190. RBAR 0.242 0.330 0.360 SDEV 0.214 0.219 0.197 SERR 0.021 0.016 0.014 EPS 0.860 0.908 0.918 NSS 19.2 20.0 20.0 |======================== 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 1839 1977 139 0.329 0.136 0.510 3.046 0.282 0.645 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.632 0.363 0.032 69 70 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.54 1.71 1.01 1.13 2.84 8.68 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.00 0.86 0.95 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 122. 15. 92. 114. 129. 139. |----------- 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 0.640 0.587 0.604 0.599 0.566 0.511 0.563 0.515 0.539 0.515 PACF 0.640 0.301 0.276 0.198 0.101 -0.006 0.156 0.001 0.122 0.027 95% C.L. 0.170 0.229 0.269 0.305 0.337 0.364 0.384 0.407 0.425 0.444 |------------------ 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 4 0.560 0.296 0.157 0.211 0.205 |================== 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 481011 1 0.76106125 0.02019821 0.00000000 0.13045825 2 481012 3 0.00000000 0.00000000 -0.00493266 0.73501253 3 481021 3 0.00000000 0.00000000 -0.00349686 0.61937523 4 481022 3 0.00000000 0.00000000 -0.00533733 0.73947525 5 481031 3 0.00000000 0.00000000 -0.00170670 0.33320743 6 481032 1 0.38184327 0.03646875 0.00000000 0.11853636 7 481051 1 0.42043200 0.00607523 0.00000000 0.04770046 8 481052 3 0.00000000 0.00000000 -0.00094708 0.37146500 9 481061 1 0.70770234 0.02275544 0.00000000 0.07437836 10 481062 3 0.00000000 0.00000000 -0.00221374 0.44268057 11 481081 3 0.00000000 0.00000000 -0.00352952 0.52510828 12 481082 3 0.00000000 0.00000000 -0.00251486 0.44884580 13 481091 3 0.00000000 0.00000000 -0.00269433 0.39827901 14 481092 3 0.00000000 0.00000000 -0.00020366 0.22490337 15 481101 1 0.53205407 0.02454343 0.00000000 0.08623539 16 481102 1 0.46863458 0.04086764 0.00000000 0.22930805 17 481111 3 0.00000000 0.00000000 -0.00206750 0.37250075 18 481112 3 0.00000000 0.00000000 -0.00171124 0.35410497 19 481131 3 0.00000000 0.00000000 -0.00245026 0.66516644 SERIES IDENT OPTION A B C D 20 481132 1 1.43788755 0.09046087 0.00000000 0.45342630 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 481011 1848 1977 130 1.001 0.488 0.726 3.479 0.393 0.601 2 481012 1848 1977 130 1.000 0.487 1.389 6.707 0.351 0.498 3 481021 1870 1977 108 1.004 0.438 0.719 3.460 0.368 0.302 4 481022 1862 1977 116 1.003 0.537 1.725 6.512 0.417 0.288 5 481031 1850 1977 128 0.992 0.458 1.059 5.296 0.387 0.396 6 481032 1853 1977 125 1.001 0.475 0.461 4.017 0.520 0.132 7 481051 1861 1977 117 1.000 0.501 1.292 4.800 0.390 0.386 8 481052 1858 1977 120 0.999 0.461 1.415 5.521 0.343 0.543 9 481061 1886 1977 92 1.003 0.387 0.805 3.859 0.330 0.421 10 481062 1868 1977 110 0.998 0.370 0.303 2.470 0.346 0.342 11 481081 1844 1977 134 1.027 0.415 1.030 4.911 0.393 0.164 12 481082 1839 1977 139 0.995 0.417 0.577 3.279 0.363 0.265 13 481091 1860 1977 118 1.009 0.692 1.324 4.554 0.598 0.362 14 481092 1855 1977 123 1.000 0.577 0.505 3.007 0.645 0.119 15 481101 1842 1977 136 1.006 0.372 1.608 8.271 0.312 0.348 16 481102 1853 1977 125 1.000 0.412 1.583 7.508 0.299 0.540 17 481111 1862 1977 116 0.999 0.459 1.242 5.512 0.436 0.285 18 481112 1877 1977 101 1.000 0.417 0.670 3.630 0.477 -0.004 19 481131 1853 1977 125 0.999 0.383 0.952 4.304 0.305 0.536 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 0.999 0.510 1.346 6.321 0.305 0.691 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.002 0.463 1.037 4.871 0.399 0.361 STANDARD DEVIATION 11 0.007 0.078 0.424 1.575 0.096 0.177 MEDIAN (50TH QUANTILE) 121 1.000 0.459 1.044 4.677 0.378 0.355 INTERQUARTILE RANGE 15 0.004 0.081 0.673 2.367 0.090 0.241 MINIMUM VALUE 92 0.992 0.370 0.303 2.470 0.299 -0.004 LOWER HINGE (25TH QUANTILE) 114 0.999 0.414 0.695 3.554 0.337 0.275 UPPER HINGE (75TH QUANTILE) 129 1.003 0.495 1.367 5.921 0.426 0.517 MAXIMUM VALUE 139 1.027 0.692 1.725 8.271 0.645 0.691 |------------------------ 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 481011 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 481012 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 481021 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 481022 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 481031 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 481032 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 481051 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 481052 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 481061 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 481062 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 481081 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 481082 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 481091 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 481092 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 481101 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 481102 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 481111 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 481112 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 481131 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 481132 -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 481011 1848 1977 130 0.992 0.462 0.618 3.261 0.393 0.568 2 481012 1848 1977 130 0.986 0.410 0.799 4.721 0.351 0.355 3 481021 1870 1977 108 0.990 0.392 0.809 3.743 0.367 0.197 4 481022 1862 1977 116 0.996 0.506 1.403 5.157 0.417 0.266 5 481031 1850 1977 128 0.987 0.417 0.832 4.604 0.387 0.278 6 481032 1853 1977 125 0.990 0.451 0.401 3.892 0.520 0.002 7 481051 1861 1977 117 0.993 0.485 1.383 5.345 0.390 0.350 8 481052 1858 1977 120 0.997 0.448 1.520 6.388 0.344 0.514 9 481061 1886 1977 92 0.996 0.358 0.528 2.844 0.329 0.347 10 481062 1868 1977 110 0.997 0.357 0.231 2.230 0.345 0.277 11 481081 1844 1977 134 0.997 0.363 0.459 3.160 0.394 0.072 12 481082 1839 1977 139 0.995 0.415 0.643 3.410 0.364 0.232 13 481091 1860 1977 118 0.992 0.653 1.202 4.305 0.598 0.323 14 481092 1855 1977 123 0.996 0.576 0.710 3.645 0.644 0.059 15 481101 1842 1977 136 0.997 0.325 0.939 5.550 0.312 0.244 16 481102 1853 1977 125 0.998 0.395 1.354 6.338 0.298 0.504 17 481111 1862 1977 116 0.997 0.442 1.148 5.437 0.436 0.221 18 481112 1877 1977 101 0.998 0.406 0.529 3.243 0.476 -0.032 19 481131 1853 1977 125 0.997 0.366 0.825 3.906 0.304 0.498 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 0.987 0.444 0.959 4.692 0.305 0.619 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 0.994 0.434 0.865 4.294 0.399 0.295 STANDARD DEVIATION 11 0.004 0.078 0.369 1.156 0.096 0.184 MEDIAN (50TH QUANTILE) 121 0.996 0.416 0.817 4.106 0.377 0.277 INTERQUARTILE RANGE 15 0.006 0.078 0.602 1.915 0.090 0.217 MINIMUM VALUE 92 0.986 0.325 0.231 2.230 0.298 -0.032 LOWER HINGE (25TH QUANTILE) 114 0.991 0.379 0.573 3.336 0.337 0.209 UPPER HINGE (75TH QUANTILE) 129 0.997 0.457 1.175 5.251 0.426 0.426 MAXIMUM VALUE 139 0.998 0.653 1.520 6.388 0.644 0.619 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.323 0.122 0.009 -0.029 3.278 -0.058 0.711 MINIMUM CORRELATION: -0.058 SERIES 481011 AND 481031 128 YEARS MAXIMUM CORRELATION: 0.711 SERIES 481111 AND 481112 101 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 81.64 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 105. 190. 190. RBAR 0.211 0.324 0.389 SDEV 0.190 0.181 0.172 SERR 0.019 0.013 0.013 EPS 0.836 0.906 0.927 NSS 19.2 20.0 20.0 |======================== 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 1839 1977 139 0.969 0.246 0.221 3.055 0.278 0.042 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.488 0.252 0.069 51 88 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.37 0.72 1.01 1.12 1.84 4.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.00 0.88 0.96 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 0.041 -0.100 0.096 0.053 -0.014 -0.135 -0.045 -0.089 0.028 -0.080 PACF 0.041 -0.102 0.106 0.034 0.002 -0.139 -0.043 -0.118 0.061 -0.091 95% C.L. 0.170 0.170 0.172 0.173 0.174 0.174 0.177 0.177 0.178 0.178 |------------------ 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 0 0.000 |======================= 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 0.057 -0.104 0.118 0.072 -0.005 -0.138 -0.045 -0.069 0.042 -0.065 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 0.057 2 0.064 -0.108 3 0.078 -0.116 0.132 4 0.072 -0.111 0.129 0.044 5 0.071 -0.113 0.131 0.043 0.014 6 0.073 -0.106 0.150 0.027 0.025 -0.146 7 0.067 -0.105 0.151 0.033 0.020 -0.144 -0.041 8 0.063 -0.120 0.153 0.036 0.036 -0.154 -0.034 -0.103 9 0.072 -0.117 0.166 0.033 0.033 -0.168 -0.023 -0.109 0.086 10 0.078 -0.125 0.165 0.021 0.035 -0.165 -0.012 -0.117 0.091 -0.070 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) 1118.07 1119.61 1119.99 1119.53 1121.26 1123.23 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1122.21 1123.99 1124.49 1125.46 1126.77 SELECTED AUTOREGRESSION ORDER: 0 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 481011 0 0.328 2 481012 0 0.128 3 481021 0 0.039 4 481022 0 0.071 5 481031 0 0.080 6 481032 0 0.000 7 481051 0 0.125 8 481052 0 0.266 9 481061 0 0.122 10 481062 0 0.078 11 481081 0 0.005 12 481082 0 0.056 13 481091 0 0.106 14 481092 0 0.004 15 481101 0 0.062 16 481102 0 0.258 17 481111 0 0.050 18 481112 0 0.001 19 481131 0 0.250 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 481132 0 0.383 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.121 STANDARD DEVIATION 0 0.115 MEDIAN 0 0.079 INTERQUARTILE RANGE 0 0.144 MINIMUM VALUE 0 0.000 LOWER HINGE 0 0.044 UPPER HINGE 0 0.189 MAXIMUM VALUE 0 0.383 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 481011 1848 1977 130 1.000 0.462 0.618 3.261 0.388 0.568 2 481012 1848 1977 130 1.000 0.410 0.799 4.721 0.345 0.355 3 481021 1870 1977 108 1.000 0.392 0.809 3.743 0.363 0.197 4 481022 1862 1977 116 1.000 0.506 1.403 5.157 0.415 0.266 5 481031 1850 1977 128 1.000 0.417 0.832 4.604 0.381 0.278 6 481032 1853 1977 125 1.000 0.451 0.401 3.892 0.514 0.002 7 481051 1861 1977 117 1.000 0.485 1.383 5.345 0.387 0.350 8 481052 1858 1977 120 1.000 0.448 1.520 6.388 0.343 0.514 9 481061 1886 1977 92 1.000 0.358 0.528 2.844 0.328 0.347 10 481062 1868 1977 110 1.000 0.357 0.231 2.230 0.344 0.277 11 481081 1844 1977 134 1.000 0.363 0.459 3.160 0.393 0.072 12 481082 1839 1977 139 1.000 0.415 0.643 3.410 0.362 0.232 13 481091 1860 1977 118 1.000 0.653 1.202 4.305 0.592 0.323 14 481092 1855 1977 123 1.000 0.576 0.710 3.645 0.641 0.059 15 481101 1842 1977 136 1.000 0.325 0.939 5.550 0.311 0.244 16 481102 1853 1977 125 1.000 0.395 1.354 6.338 0.298 0.504 17 481111 1862 1977 116 1.000 0.442 1.148 5.437 0.434 0.221 18 481112 1877 1977 101 1.000 0.406 0.529 3.243 0.475 -0.032 19 481131 1853 1977 125 1.000 0.366 0.825 3.906 0.303 0.498 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 481132 1866 1977 112 1.000 0.444 0.959 4.692 0.300 0.619 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 120 1.000 0.434 0.865 4.294 0.396 0.295 STANDARD DEVIATION 11 0.000 0.078 0.369 1.156 0.095 0.184 MEDIAN (50TH QUANTILE) 121 1.000 0.416 0.817 4.106 0.372 0.277 INTERQUARTILE RANGE 15 0.000 0.078 0.602 1.915 0.089 0.217 MINIMUM VALUE 92 1.000 0.325 0.231 2.230 0.298 -0.032 LOWER HINGE (25TH QUANTILE) 114 1.000 0.379 0.573 3.336 0.335 0.209 UPPER HINGE (75TH QUANTILE) 129 1.000 0.457 1.175 5.251 0.424 0.426 MAXIMUM VALUE 139 1.000 0.653 1.520 6.388 0.641 0.619 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.323 0.122 0.009 -0.029 3.278 -0.058 0.711 MINIMUM CORRELATION: -0.058 SERIES 481011 AND 481031 128 YEARS MAXIMUM CORRELATION: 0.711 SERIES 481111 AND 481112 101 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 81.64 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 105. 190. 190. RBAR 0.211 0.324 0.389 SDEV 0.190 0.181 0.172 SERR 0.019 0.013 0.013 EPS 0.836 0.906 0.927 NSS 19.2 20.0 20.0 |======================== 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 1839 1977 139 0.975 0.246 0.216 3.044 0.277 0.041 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.477 0.252 0.068 51 88 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 0.77 1.01 1.14 1.92 4.87 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.08 0.00 0.88 0.96 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 0.041 -0.099 0.096 0.054 -0.014 -0.135 -0.046 -0.090 0.028 -0.081 PACF 0.041 -0.101 0.105 0.034 0.002 -0.139 -0.044 -0.118 0.061 -0.091 95% C.L. 0.170 0.170 0.172 0.173 0.174 0.174 0.177 0.177 0.178 0.178 |------------------ 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 |========================= 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 1839 1977 139 0.975 0.246 0.216 3.044 0.277 0.041 |------------ 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 0.041 -0.099 0.096 0.054 -0.014 -0.135 -0.046 -0.090 0.028 -0.081 PACF 0.041 -0.101 0.105 0.034 0.002 -0.139 -0.044 -0.118 0.061 -0.091 95% C.L. 0.170 0.170 0.172 0.173 0.174 0.174 0.177 0.177 0.178 0.178 |------------------- 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 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES