RUN: SPAI001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SPAI005L.rwl.conv LOG FILE PROCESSED: SPAI005L.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: 495 1 Alcala de Selva WIDTH_LATE PIMU - 495 2 Spain krummholz pine 1960 4023-40 1820 1977 - 495 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 11 495081 MISSING VALUES FOUND: 1 IN 1 GAPS / 1884 1884 / -------------------------------------------------------------------- 15 495101 MISSING VALUES FOUND: 3 IN 1 GAPS / 1939 1941 / -------------------------------------------------------------------- 16 495102 MISSING VALUES FOUND: 3 IN 1 GAPS / 1939 1941 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 0.441 0.221 0.914 4.325 0.370 0.598 2 495012 1914 1977 64 0.526 0.205 0.151 2.981 0.365 0.428 3 495021 1882 1977 96 0.452 0.412 1.922 6.373 0.492 0.759 4 495022 1886 1977 92 0.420 0.310 1.477 4.556 0.539 0.638 5 495031 1917 1977 61 0.622 0.282 0.668 3.096 0.405 0.355 6 495032 1922 1977 56 0.572 0.259 0.547 2.624 0.436 0.498 7 495041 1889 1977 89 0.433 0.182 0.676 3.336 0.395 0.400 8 495042 1885 1977 93 0.485 0.205 0.449 2.655 0.336 0.548 9 495051 1868 1977 110 0.433 0.334 2.070 7.595 0.374 0.653 10 495052 1864 1977 114 0.328 0.187 1.052 4.082 0.335 0.635 11 495081 1884 1977 94 0.410 0.199 1.181 4.248 0.404 0.421 12 495082 1868 1977 110 0.356 0.160 0.545 3.490 0.410 0.457 13 495091 1836 1977 142 0.293 0.161 1.290 6.264 0.414 0.608 14 495092 1854 1977 124 0.305 0.184 1.410 4.889 0.452 0.583 15 495101 1918 1977 60 0.706 0.308 0.607 2.832 0.375 0.431 16 495102 1917 1977 61 0.597 0.266 0.285 2.811 0.398 0.439 17 495111 1881 1977 97 0.518 0.222 -0.042 1.953 0.318 0.610 18 495112 1893 1977 85 0.557 0.259 1.031 5.104 0.320 0.562 19 495141 1831 1977 147 0.325 0.262 1.683 6.979 0.752 0.395 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 0.307 0.227 1.511 6.911 0.766 0.373 21 495151 1900 1977 78 0.522 0.270 0.353 2.642 0.397 0.624 22 495152 1897 1977 81 0.340 0.182 0.471 2.725 0.469 0.460 NUMBER OF SERIES READ IN: 22 FROM 1820 TO 1977 158 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 0.452 0.241 0.920 4.203 0.433 0.522 STANDARD DEVIATION 29 0.116 0.063 0.586 1.681 0.119 0.111 MEDIAN (50TH QUANTILE) 92 0.437 0.224 0.795 3.786 0.401 0.523 INTERQUARTILE RANGE 45 0.186 0.083 0.940 2.294 0.081 0.182 MINIMUM VALUE 56 0.293 0.160 -0.042 1.953 0.318 0.355 LOWER HINGE (25TH QUANTILE) 65 0.340 0.187 0.471 2.811 0.370 0.428 UPPER HINGE (75TH QUANTILE) 110 0.526 0.270 1.410 5.104 0.452 0.610 MAXIMUM VALUE 158 0.706 0.412 2.070 7.595 0.766 0.759 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.367 0.208 0.014 -0.250 2.987 -0.319 0.918 MINIMUM CORRELATION: -0.319 SERIES 495012 AND 495081 64 YEARS MAXIMUM CORRELATION: 0.918 SERIES 495021 AND 495022 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.340 0.182 0.338 SDEV 0.246 0.234 0.192 SERR 0.100 0.051 0.018 EPS 0.827 0.782 0.913 NSS 9.3 16.0 20.6 |======================== 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 1820 1977 158 0.376 0.157 0.058 3.025 0.428 0.401 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.625 0.386 0.035 42 116 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.52 1.31 1.01 1.15 2.46 150.84 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.93 0.13 0.00 0.87 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 92. 45. 56. 65. 110. 158. |----------- 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 0.399 0.380 0.348 0.349 0.315 0.377 0.297 0.286 0.153 0.134 PACF 0.399 0.262 0.168 0.149 0.086 0.172 0.029 0.029 -0.139 -0.097 95% C.L. 0.159 0.183 0.202 0.216 0.230 0.241 0.255 0.264 0.272 0.274 |------------------ 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 0.269 0.219 0.181 0.136 0.157 |================== 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 495011 3 0.00000000 0.00000000 -0.00664598 0.66039425 2 495012 3 0.00000000 0.00000000 -0.00492102 0.68571430 3 495021 1 1.16238070 0.03687837 0.00000000 0.13881740 4 495022 1 1.01291144 0.07316618 0.00000000 0.27491936 5 495031 3 0.00000000 0.00000000 -0.00774352 0.86201638 6 495032 1 0.69595003 0.04404883 0.00000000 0.31923869 7 495041 1 0.52788293 0.00961601 0.00000000 0.08037840 8 495042 1 0.46773881 0.03304873 0.00000000 0.34230304 9 495051 1 1.14969528 0.04822120 0.00000000 0.22276588 10 495052 3 0.00000000 0.00000000 -0.00462733 0.59387827 11 495081 1 0.27288404 0.05400800 0.00000000 0.35815665 12 495082 3 0.00000000 0.00000000 0.00004256 0.35327441 13 495091 3 0.00000000 0.00000000 -0.00184255 0.42434821 14 495092 3 0.00000000 0.00000000 -0.00288834 0.48576316 15 495101 3 0.00000000 0.00000000 -0.00638646 0.89809090 16 495102 1 0.30534422 0.08087947 0.00000000 0.52676016 17 495111 3 0.00000000 0.00000000 -0.00551297 0.78838271 18 495112 3 0.00000000 0.00000000 -0.00685187 0.85157144 19 495141 3 0.00000000 0.00000000 -0.00050934 0.36299694 SERIES IDENT OPTION A B C D 20 495142 3 0.00000000 0.00000000 0.00019247 0.29153430 21 495151 3 0.00000000 0.00000000 -0.00608923 0.76244754 22 495152 3 0.00000000 0.00000000 -0.00458898 0.52802467 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 0.991 0.401 1.200 6.050 0.366 0.406 2 495012 1914 1977 64 0.998 0.360 0.217 2.988 0.360 0.311 3 495021 1882 1977 96 1.013 0.673 2.304 9.054 0.489 0.433 4 495022 1886 1977 92 1.002 0.560 1.086 3.427 0.534 0.272 5 495031 1917 1977 61 0.996 0.393 0.706 3.383 0.397 0.176 6 495032 1922 1977 56 1.000 0.347 0.055 2.674 0.428 -0.010 7 495041 1889 1977 89 1.001 0.374 0.623 3.505 0.389 0.248 8 495042 1885 1977 93 1.000 0.356 0.273 2.800 0.333 0.362 9 495051 1868 1977 110 0.995 0.416 1.609 7.455 0.370 0.329 10 495052 1864 1977 114 1.040 0.422 1.888 7.903 0.332 0.418 11 495081 1884 1977 94 0.999 0.461 1.270 4.711 0.399 0.361 12 495082 1868 1977 110 1.000 0.449 0.555 3.509 0.406 0.454 13 495091 1836 1977 142 0.988 0.467 1.093 5.674 0.411 0.433 14 495092 1854 1977 124 1.006 0.486 1.253 4.740 0.448 0.327 15 495101 1918 1977 60 0.998 0.390 0.457 3.010 0.383 0.361 16 495102 1917 1977 61 1.000 0.447 0.430 3.132 0.399 0.480 17 495111 1881 1977 97 0.986 0.308 0.313 2.906 0.315 0.261 18 495112 1893 1977 85 0.992 0.339 0.274 2.596 0.317 0.336 19 495141 1831 1977 147 0.999 0.820 1.891 8.137 0.747 0.410 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 1.000 0.736 1.426 6.448 0.761 0.360 21 495151 1900 1977 78 0.992 0.490 0.977 3.761 0.392 0.484 22 495152 1897 1977 81 0.995 0.466 1.137 5.633 0.462 0.207 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.462 0.956 4.704 0.429 0.337 STANDARD DEVIATION 29 0.011 0.131 0.620 2.024 0.118 0.115 MEDIAN (50TH QUANTILE) 92 0.999 0.434 1.032 3.635 0.398 0.360 INTERQUARTILE RANGE 45 0.006 0.112 0.840 3.040 0.082 0.145 MINIMUM VALUE 56 0.986 0.308 0.055 2.596 0.315 -0.010 LOWER HINGE (25TH QUANTILE) 65 0.995 0.374 0.430 3.010 0.366 0.272 UPPER HINGE (75TH QUANTILE) 110 1.000 0.486 1.270 6.050 0.448 0.418 MAXIMUM VALUE 158 1.040 0.820 2.304 9.054 0.761 0.484 |------------------------ 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 495011 -67 43 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 495012 -67 42 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 495021 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 495022 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 495031 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 495032 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 495041 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 495042 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 495051 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 495052 -67 76 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 495081 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 495082 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 495091 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 495092 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 495101 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 495102 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 495111 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 495112 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 495141 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 495142 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 495151 -67 52 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 495152 -67 54 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 495011 1913 1977 65 0.997 0.352 0.326 3.929 0.365 0.253 2 495012 1914 1977 64 0.997 0.339 0.113 2.861 0.358 0.229 3 495021 1882 1977 96 0.982 0.554 1.639 5.837 0.488 0.335 4 495022 1886 1977 92 0.991 0.508 0.859 3.096 0.535 0.198 5 495031 1917 1977 61 0.993 0.354 0.560 3.104 0.395 0.039 6 495032 1922 1977 56 0.999 0.345 0.145 2.868 0.427 -0.045 7 495041 1889 1977 89 0.991 0.317 0.329 2.970 0.391 0.021 8 495042 1885 1977 93 0.996 0.342 0.353 3.208 0.332 0.270 9 495051 1868 1977 110 0.996 0.389 1.245 5.351 0.369 0.240 10 495052 1864 1977 114 0.995 0.306 0.295 2.905 0.332 0.101 11 495081 1884 1977 94 0.993 0.395 1.044 3.951 0.399 0.216 12 495082 1868 1977 110 0.992 0.387 0.077 2.979 0.406 0.265 13 495091 1836 1977 142 0.995 0.431 1.043 4.783 0.410 0.275 14 495092 1854 1977 124 0.995 0.453 1.099 4.523 0.448 0.263 15 495101 1918 1977 60 0.993 0.341 -0.021 2.718 0.384 0.202 16 495102 1917 1977 61 0.987 0.392 -0.090 2.555 0.396 0.303 17 495111 1881 1977 97 0.998 0.262 0.261 3.625 0.315 -0.061 18 495112 1893 1977 85 0.991 0.287 0.382 2.589 0.317 0.129 19 495141 1831 1977 147 0.989 0.729 1.308 4.830 0.746 0.265 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 0.989 0.690 1.113 4.588 0.762 0.239 21 495151 1900 1977 78 0.981 0.431 1.454 6.213 0.392 0.308 22 495152 1897 1977 81 0.995 0.455 1.102 5.385 0.462 0.172 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 0.992 0.412 0.665 3.858 0.429 0.192 STANDARD DEVIATION 29 0.005 0.119 0.530 1.144 0.118 0.114 MEDIAN (50TH QUANTILE) 92 0.993 0.388 0.471 3.417 0.396 0.234 INTERQUARTILE RANGE 45 0.005 0.112 0.840 1.878 0.083 0.137 MINIMUM VALUE 56 0.981 0.262 -0.090 2.555 0.315 -0.061 LOWER HINGE (25TH QUANTILE) 65 0.991 0.341 0.261 2.905 0.365 0.129 UPPER HINGE (75TH QUANTILE) 110 0.996 0.453 1.102 4.783 0.448 0.265 MAXIMUM VALUE 158 0.999 0.729 1.639 6.213 0.762 0.335 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.272 0.210 0.014 -0.527 3.011 -0.382 0.820 MINIMUM CORRELATION: -0.382 SERIES 495011 AND 495032 56 YEARS MAXIMUM CORRELATION: 0.820 SERIES 495021 AND 495022 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.334 0.212 0.350 SDEV 0.257 0.210 0.165 SERR 0.105 0.046 0.015 EPS 0.823 0.812 0.917 NSS 9.3 16.0 20.6 |======================== 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 1820 1977 158 0.961 0.366 0.576 3.805 0.424 0.073 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.352 0.162 0.147 39 119 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.42 1.00 1.00 1.09 2.10 8.66 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.13 0.00 0.87 1.00 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 0.072 -0.027 0.044 -0.045 -0.026 0.069 0.067 0.066 -0.135 -0.172 PACF 0.072 -0.032 0.048 -0.053 -0.016 0.068 0.061 0.062 -0.153 -0.153 95% C.L. 0.159 0.160 0.160 0.160 0.161 0.161 0.162 0.162 0.163 0.166 |------------------ 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 0.052 -0.171 0.116 0.084 -0.077 -0.056 -0.011 0.007 -0.105 -0.080 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 0.052 2 0.061 -0.174 3 0.085 -0.183 0.140 4 0.080 -0.176 0.136 0.037 5 0.081 -0.170 0.129 0.041 -0.044 6 0.079 -0.168 0.134 0.033 -0.041 -0.044 7 0.077 -0.170 0.136 0.039 -0.048 -0.040 -0.042 8 0.078 -0.169 0.136 0.039 -0.049 -0.039 -0.043 0.006 9 0.078 -0.174 0.132 0.034 -0.045 -0.025 -0.060 0.014 -0.102 10 0.073 -0.173 0.128 0.032 -0.047 -0.023 -0.052 0.004 -0.097 -0.058 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) 1227.63 1229.21 1226.34 1225.23 1227.01 1228.70 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1230.40 1232.12 1234.11 1234.47 1235.93 SELECTED AUTOREGRESSION ORDER: 3 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 0.085 -0.183 0.140 R-SQUARED DUE TO POOLED AUTOREGRESSION: 5.18 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 105.46 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.085 -0.175 0.109 0.053 -0.040 0.002 0.015 -0.005 -0.003 0.0027 0.000 -0.001 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 495011 3 0.097 0.282 -0.103 0.058 2 495012 3 0.101 0.256 -0.158 -0.114 3 495021 3 0.185 0.424 -0.241 0.187 4 495022 3 0.094 0.264 -0.217 0.157 5 495031 3 0.068 0.061 -0.257 0.046 6 495032 3 0.056 -0.057 -0.199 -0.012 7 495041 3 0.058 0.012 0.033 0.232 8 495042 3 0.107 0.221 0.084 0.150 9 495051 3 0.076 0.209 0.122 0.024 10 495052 3 0.072 0.055 0.146 0.187 11 495081 3 0.074 0.210 0.020 0.042 12 495082 3 0.100 0.225 0.134 0.025 13 495091 3 0.088 0.298 -0.083 0.094 14 495092 3 0.103 0.211 0.117 0.107 15 495101 3 0.056 0.202 -0.022 0.122 16 495102 3 0.151 0.218 0.156 0.154 17 495111 3 0.052 -0.056 -0.133 0.097 18 495112 3 0.017 0.131 -0.005 0.012 19 495141 3 0.108 0.299 -0.112 0.181 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 495142 3 0.086 0.266 -0.093 0.148 21 495151 3 0.144 0.325 -0.029 0.051 22 495152 3 0.064 0.219 -0.181 0.067 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.089 0.194 -0.046 0.092 STANDARD DEVIATION 0 0.037 0.123 0.134 0.081 MEDIAN 3 0.087 0.219 -0.056 0.095 INTERQUARTILE RANGE 0 0.040 0.135 0.241 0.112 MINIMUM VALUE 3 0.017 -0.057 -0.257 -0.114 LOWER HINGE 3 0.064 0.131 -0.158 0.042 UPPER HINGE 3 0.103 0.266 0.084 0.154 MAXIMUM VALUE 3 0.185 0.424 0.156 0.232 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 495011 1913 1977 65 1.000 0.338 0.475 4.405 0.384 0.008 2 495012 1914 1977 64 1.000 0.321 -0.128 3.057 0.393 0.008 3 495021 1882 1977 96 1.000 0.505 1.188 4.402 0.546 -0.027 4 495022 1886 1977 92 1.000 0.484 0.870 3.567 0.537 -0.003 5 495031 1917 1977 61 1.000 0.342 0.650 3.113 0.376 -0.001 6 495032 1922 1977 56 1.000 0.337 0.464 3.191 0.396 -0.002 7 495041 1889 1977 89 1.000 0.308 0.285 2.716 0.380 -0.010 8 495042 1885 1977 93 1.000 0.323 0.433 3.869 0.373 0.001 9 495051 1868 1977 110 1.000 0.374 1.034 4.334 0.404 -0.002 10 495052 1864 1977 114 1.000 0.295 0.310 2.851 0.336 -0.009 11 495081 1884 1977 94 1.000 0.385 1.082 3.932 0.435 -0.006 12 495082 1868 1977 110 1.000 0.369 0.078 2.935 0.429 -0.003 13 495091 1836 1977 142 1.000 0.411 1.173 5.145 0.444 -0.003 14 495092 1854 1977 124 1.000 0.430 0.853 4.223 0.494 -0.007 15 495101 1918 1977 60 1.000 0.331 0.215 3.005 0.410 0.003 16 495102 1917 1977 61 1.000 0.361 -0.208 2.771 0.434 -0.010 17 495111 1881 1977 97 1.000 0.258 0.278 3.865 0.298 0.014 18 495112 1893 1977 85 1.000 0.285 0.324 2.568 0.330 0.000 19 495141 1831 1977 147 1.001 0.686 1.234 4.550 0.768 0.009 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 495142 1820 1977 158 1.003 0.656 1.071 4.592 0.790 0.013 21 495151 1900 1977 78 1.000 0.408 1.682 7.607 0.423 -0.001 22 495152 1897 1977 81 1.000 0.440 1.367 6.028 0.440 -0.003 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 94 1.000 0.393 0.669 3.942 0.446 -0.001 STANDARD DEVIATION 29 0.001 0.109 0.514 1.209 0.123 0.009 MEDIAN (50TH QUANTILE) 92 1.000 0.365 0.563 3.867 0.416 -0.002 INTERQUARTILE RANGE 45 0.000 0.107 0.796 1.400 0.063 0.009 MINIMUM VALUE 56 1.000 0.258 -0.208 2.568 0.298 -0.027 LOWER HINGE (25TH QUANTILE) 65 1.000 0.323 0.285 3.005 0.380 -0.006 UPPER HINGE (75TH QUANTILE) 110 1.000 0.430 1.082 4.405 0.444 0.003 MAXIMUM VALUE 158 1.003 0.686 1.682 7.607 0.790 0.014 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 231 0.281 0.209 0.014 -0.702 3.203 -0.409 0.786 MINIMUM CORRELATION: -0.409 SERIES 495011 AND 495032 56 YEARS MAXIMUM CORRELATION: 0.786 SERIES 495021 AND 495022 92 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 49.16 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1880. 1905. 1930. CORR 6. 21. 120. RBAR 0.357 0.249 0.372 SDEV 0.238 0.191 0.145 SERR 0.097 0.042 0.013 EPS 0.837 0.842 0.924 NSS 9.3 16.0 20.6 |======================== 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 1820 1977 158 0.972 0.361 0.634 4.010 0.452 -0.122 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.392 0.181 0.111 37 121 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.39 0.80 1.00 1.13 1.93 42.74 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 1.00 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 -0.121 0.026 -0.045 -0.083 -0.032 0.065 0.019 0.094 -0.108 -0.081 PACF -0.121 0.012 -0.041 -0.095 -0.053 0.057 0.027 0.088 -0.091 -0.101 95% C.L. 0.159 0.161 0.162 0.162 0.163 0.163 0.164 0.164 0.165 0.167 |------------------ 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 1 0.015 -0.122 |---------- 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 -0.003 -0.003 -0.008 -0.100 -0.030 0.059 0.032 0.078 -0.106 -0.120 PACF -0.003 -0.003 -0.008 -0.100 -0.031 0.058 0.031 0.069 -0.113 -0.114 95% C.L. 0.159 0.159 0.159 0.159 0.161 0.161 0.161 0.162 0.162 0.164 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.011 -0.003 -0.003 -0.008 |========================= 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 1820 1977 158 0.973 0.367 0.630 4.070 0.421 0.039 |------------ 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 0.039 -0.158 0.110 -0.056 -0.064 0.047 0.043 0.059 -0.093 -0.154 PACF 0.039 -0.160 0.127 -0.099 -0.015 0.013 0.045 0.072 -0.108 -0.132 95% C.L. 0.159 0.159 0.163 0.165 0.166 0.166 0.167 0.167 0.167 0.169 |------------------- ARSTAN CHRONOLOGY AUTOREGRESSIVE MODEL -------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 3 0.057 0.068 -0.171 0.134 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.24 MINUTES