RUN: FRAN002 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN025L.rwl.conv LOG FILE PROCESSED: FRAN025L.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: 482 1 Miraules Refuge WIDTH_LATE ABAL - 482 2 France silver fir, European fir 1720 4228-224 1831 1977 - 482 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 482011 1838 1977 140 0.404 0.269 0.976 3.116 0.326 0.820 2 482012 1846 1977 132 0.294 0.226 1.934 7.551 0.316 0.780 3 482021 1891 1977 87 0.452 0.218 0.950 4.087 0.308 0.709 4 482022 1889 1977 89 0.562 0.282 0.833 3.699 0.328 0.751 5 482031 1849 1977 129 0.447 0.326 2.984 13.719 0.351 0.809 6 482032 1863 1977 115 0.410 0.202 0.989 4.043 0.364 0.646 7 482041 1831 1977 147 0.305 0.127 1.499 6.033 0.313 0.483 8 482042 1855 1977 123 0.351 0.143 0.755 3.167 0.281 0.589 9 482051 1883 1977 95 0.529 0.297 1.168 5.548 0.314 0.699 10 482052 1888 1977 90 0.705 0.419 0.793 3.245 0.326 0.708 11 482061 1836 1977 142 0.291 0.159 0.543 2.689 0.335 0.730 12 482062 1842 1977 136 0.299 0.147 0.303 2.378 0.314 0.722 13 482071 1879 1977 99 0.628 0.327 1.261 4.217 0.273 0.705 14 482072 1875 1977 103 0.651 0.340 1.444 5.561 0.332 0.601 15 482081 1853 1977 125 0.339 0.160 0.848 2.904 0.285 0.694 16 482082 1849 1977 129 0.347 0.119 0.788 3.992 0.287 0.426 17 482091 1846 1977 132 0.409 0.303 1.075 3.016 0.326 0.798 18 482092 1852 1977 126 0.337 0.249 0.897 2.686 0.283 0.878 19 482101 1838 1977 140 0.373 0.306 0.891 2.471 0.265 0.897 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.429 0.347 0.729 2.163 0.267 0.912 21 482111 1896 1977 82 0.632 0.169 0.419 3.703 0.267 0.324 22 482112 1889 1977 89 0.586 0.209 0.589 2.910 0.278 0.505 23 482121 1861 1977 117 0.301 0.259 1.061 3.031 0.307 0.890 24 482122 1842 1977 136 0.315 0.242 0.685 2.439 0.400 0.806 NUMBER OF SERIES READ IN: 24 FROM 1831 TO 1977 147 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.433 0.243 1.017 4.099 0.310 0.703 STANDARD DEVIATION 20 0.130 0.081 0.550 2.437 0.033 0.153 MEDIAN (50TH QUANTILE) 125 0.406 0.246 0.894 3.206 0.313 0.716 INTERQUARTILE RANGE 39 0.219 0.140 0.380 1.355 0.045 0.184 MINIMUM VALUE 82 0.291 0.119 0.303 2.163 0.265 0.324 LOWER HINGE (25TH QUANTILE) 97 0.326 0.165 0.742 2.797 0.282 0.624 UPPER HINGE (75TH QUANTILE) 136 0.545 0.305 1.122 4.152 0.327 0.808 MAXIMUM VALUE 147 0.705 0.419 2.984 13.719 0.400 0.912 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.562 0.203 0.012 -0.762 3.616 -0.123 0.948 MINIMUM CORRELATION: -0.123 SERIES 482091 AND 482112 89 YEARS MAXIMUM CORRELATION: 0.948 SERIES 482101 AND 482102 138 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.493 0.563 0.537 SDEV 0.224 0.262 0.160 SERR 0.020 0.017 0.010 EPS 0.953 0.968 0.965 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.416 0.177 0.549 2.604 0.272 0.685 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.425 0.173 0.115 73 74 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.54 1.04 1.01 1.18 2.22 6.22 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.11 0.00 0.83 0.95 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 126. 39. 82. 97. 136. 147. |----------- 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 0.680 0.686 0.686 0.635 0.644 0.578 0.547 0.557 0.513 0.482 PACF 0.680 0.414 0.295 0.101 0.132 -0.039 -0.047 0.053 0.002 -0.034 95% C.L. 0.165 0.229 0.279 0.322 0.354 0.385 0.408 0.427 0.447 0.462 |------------------ 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 3 0.609 0.258 0.326 0.289 |================== 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 482011 3 0.00000000 0.00000000 -0.00436325 0.71203804 2 482012 1 0.64674962 0.01733367 0.00000000 0.04270160 3 482021 1 0.65140361 0.02572413 0.00000000 0.19527455 4 482022 3 0.00000000 0.00000000 -0.00851992 0.94575590 5 482031 3 0.00000000 0.00000000 -0.00450302 0.73998302 6 482032 1 0.56995499 0.02383654 0.00000000 0.21779692 7 482041 1 0.33821163 0.03187394 0.00000000 0.23424470 8 482042 3 0.00000000 0.00000000 -0.00213405 0.48304278 9 482051 3 0.00000000 0.00000000 -0.00761030 0.89392608 10 482052 3 0.00000000 0.00000000 -0.01028555 1.17265916 11 482061 3 0.00000000 0.00000000 -0.00273737 0.48691937 12 482062 3 0.00000000 0.00000000 -0.00252433 0.47210783 13 482071 3 0.00000000 0.00000000 -0.00762325 1.00904143 14 482072 1 0.64037913 0.01681837 0.00000000 0.34924904 15 482081 1 0.56495583 0.01093812 0.00000000 0.03323379 16 482082 1 0.20932405 0.02542961 0.00000000 0.28626871 17 482091 1 0.73136532 0.02211979 0.00000000 0.17420894 18 482092 3 0.00000000 0.00000000 -0.00505671 0.65840256 19 482101 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 482102 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 482111 3 0.00000000 0.00000000 -0.00258759 0.73945796 22 482112 3 0.00000000 0.00000000 -0.00219118 0.68478292 23 482121 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 482122 -67 91 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 482011 1838 1977 140 1.020 0.538 1.576 7.549 0.324 0.684 2 482012 1846 1977 132 1.005 0.477 0.808 3.060 0.313 0.659 3 482021 1891 1977 87 1.000 0.336 0.248 2.918 0.305 0.431 4 482022 1889 1977 89 1.007 0.332 0.568 3.548 0.324 0.279 5 482031 1849 1977 129 1.026 0.543 1.709 6.782 0.349 0.656 6 482032 1863 1977 115 1.001 0.361 0.788 4.024 0.360 0.307 7 482041 1831 1977 147 1.000 0.304 0.737 3.655 0.310 0.202 8 482042 1855 1977 123 0.999 0.343 0.785 3.456 0.279 0.419 9 482051 1883 1977 95 0.991 0.373 0.902 4.228 0.312 0.463 10 482052 1888 1977 90 0.973 0.409 0.844 3.608 0.320 0.552 11 482061 1836 1977 142 1.013 0.507 2.370 11.607 0.334 0.616 12 482062 1842 1977 136 0.996 0.399 0.825 3.667 0.312 0.539 13 482071 1879 1977 99 1.011 0.366 0.639 2.931 0.271 0.530 14 482072 1875 1977 103 1.001 0.472 1.574 6.258 0.329 0.534 15 482081 1853 1977 125 1.003 0.323 1.124 6.298 0.283 0.339 16 482082 1849 1977 129 1.000 0.309 0.727 4.245 0.285 0.337 17 482091 1846 1977 132 1.005 0.725 3.280 18.154 0.324 0.773 18 482092 1852 1977 126 1.213 1.145 3.429 15.189 0.280 0.828 19 482101 1838 1977 140 0.973 0.323 0.964 4.086 0.263 0.507 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.993 0.321 1.148 6.226 0.264 0.464 21 482111 1896 1977 82 1.000 0.252 0.604 4.398 0.263 0.213 22 482112 1889 1977 89 0.999 0.340 0.534 2.691 0.275 0.444 23 482121 1861 1977 117 0.985 0.324 0.747 4.554 0.303 0.270 24 482122 1842 1977 136 0.975 0.372 -0.066 3.462 0.396 0.350 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.008 0.425 1.119 5.691 0.307 0.475 STANDARD DEVIATION 20 0.046 0.185 0.850 3.940 0.033 0.171 MEDIAN (50TH QUANTILE) 125 1.000 0.363 0.816 4.157 0.311 0.463 INTERQUARTILE RANGE 39 0.012 0.151 0.678 2.773 0.044 0.246 MINIMUM VALUE 82 0.973 0.252 -0.066 2.691 0.263 0.202 LOWER HINGE (25TH QUANTILE) 97 0.994 0.323 0.683 3.505 0.280 0.338 UPPER HINGE (75TH QUANTILE) 136 1.006 0.475 1.361 6.278 0.324 0.584 MAXIMUM VALUE 147 1.213 1.145 3.429 18.154 0.396 0.828 |------------------------ 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 482011 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 482012 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 482021 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 482022 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 482031 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 482032 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 482041 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 482042 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 482051 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 482052 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 482061 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 482062 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 482071 -67 66 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 482072 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 482081 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 482082 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 482091 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 482092 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 482101 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 482102 -67 92 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 482111 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 22 482112 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 23 482121 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 24 482122 -67 91 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 482011 1838 1977 140 0.987 0.445 0.823 3.325 0.323 0.573 2 482012 1846 1977 132 0.983 0.397 1.030 3.902 0.313 0.534 3 482021 1891 1977 87 0.996 0.324 0.217 2.792 0.304 0.399 4 482022 1889 1977 89 0.998 0.312 0.230 2.988 0.324 0.230 5 482031 1849 1977 129 0.989 0.433 1.437 6.808 0.348 0.490 6 482032 1863 1977 115 0.997 0.338 0.608 3.240 0.360 0.213 7 482041 1831 1977 147 0.998 0.292 0.654 3.474 0.311 0.148 8 482042 1855 1977 123 0.994 0.293 0.440 2.960 0.279 0.258 9 482051 1883 1977 95 0.994 0.351 0.894 4.343 0.312 0.400 10 482052 1888 1977 90 0.994 0.322 0.123 2.614 0.320 0.329 11 482061 1836 1977 142 0.988 0.396 0.898 4.405 0.333 0.487 12 482062 1842 1977 136 0.995 0.382 0.872 3.724 0.313 0.512 13 482071 1879 1977 99 0.988 0.299 0.616 2.991 0.271 0.344 14 482072 1875 1977 103 0.986 0.352 0.914 4.241 0.328 0.285 15 482081 1853 1977 125 0.995 0.272 0.501 3.646 0.282 0.154 16 482082 1849 1977 129 0.998 0.294 0.625 4.099 0.285 0.283 17 482091 1846 1977 132 0.981 0.409 0.731 4.061 0.324 0.542 18 482092 1852 1977 126 0.970 0.358 0.593 2.871 0.281 0.570 19 482101 1838 1977 140 0.995 0.303 1.066 5.138 0.263 0.429 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 0.995 0.289 0.977 5.796 0.264 0.354 21 482111 1896 1977 82 0.999 0.241 0.432 3.948 0.263 0.154 22 482112 1889 1977 89 0.992 0.282 0.617 3.483 0.275 0.205 23 482121 1861 1977 117 0.997 0.309 0.513 3.512 0.303 0.228 24 482122 1842 1977 136 0.995 0.374 0.194 4.233 0.396 0.298 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 0.992 0.336 0.667 3.858 0.307 0.351 STANDARD DEVIATION 20 0.007 0.054 0.316 0.981 0.033 0.140 MEDIAN (50TH QUANTILE) 125 0.994 0.323 0.621 3.685 0.311 0.337 INTERQUARTILE RANGE 39 0.009 0.085 0.425 1.122 0.044 0.259 MINIMUM VALUE 82 0.970 0.241 0.123 2.614 0.263 0.148 LOWER HINGE (25TH QUANTILE) 97 0.988 0.294 0.471 3.115 0.280 0.229 UPPER HINGE (75TH QUANTILE) 136 0.997 0.378 0.896 4.237 0.324 0.488 MAXIMUM VALUE 147 0.999 0.445 1.437 6.808 0.396 0.573 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.410 0.138 0.008 -0.287 3.067 -0.007 0.772 MINIMUM CORRELATION: -0.007 SERIES 482071 AND 482101 99 YEARS MAXIMUM CORRELATION: 0.772 SERIES 482021 AND 482022 87 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.423 0.512 0.470 SDEV 0.176 0.143 0.167 SERR 0.016 0.009 0.010 EPS 0.938 0.962 0.955 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.983 0.232 0.041 2.532 0.249 0.232 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.483 0.184 0.055 49 98 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.46 1.01 1.11 1.57 9.36 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.00 0.86 0.94 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 0.230 0.152 0.134 0.006 0.114 0.006 0.056 0.028 0.033 -0.091 PACF 0.230 0.104 0.084 -0.057 0.107 -0.046 0.053 -0.015 0.036 -0.143 95% C.L. 0.165 0.173 0.177 0.180 0.180 0.182 0.182 0.182 0.182 0.182 |------------------ 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 1 0.063 0.231 |======================= 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 0.212 0.100 0.075 -0.014 0.069 -0.031 0.116 0.061 0.109 -0.084 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 0.212 2 0.199 0.058 3 0.197 0.048 0.046 4 0.199 0.051 0.055 -0.045 5 0.202 0.046 0.051 -0.061 0.076 6 0.207 0.043 0.054 -0.058 0.089 -0.062 7 0.216 0.030 0.062 -0.065 0.083 -0.091 0.138 8 0.215 0.031 0.061 -0.065 0.083 -0.091 0.136 0.006 9 0.214 0.017 0.070 -0.073 0.089 -0.097 0.133 -0.015 0.099 10 0.231 0.015 0.093 -0.090 0.104 -0.110 0.145 -0.012 0.136 -0.170 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) 1185.38 1180.65 1182.16 1183.86 1185.55 1186.69 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1188.12 1187.31 1189.30 1189.84 1187.50 SELECTED AUTOREGRESSION ORDER: 1 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 0.212 R-SQUARED DUE TO POOLED AUTOREGRESSION: 4.48 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 104.69 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.212 0.045 0.009 0.002 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 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 482011 1 0.339 0.575 2 482012 1 0.309 0.550 3 482021 1 0.190 0.406 4 482022 1 0.054 0.232 5 482031 1 0.282 0.491 6 482032 1 0.087 0.213 7 482041 1 0.025 0.149 8 482042 1 0.072 0.259 9 482051 1 0.185 0.401 10 482052 1 0.115 0.335 11 482061 1 0.248 0.496 12 482062 1 0.309 0.535 13 482071 1 0.169 0.345 14 482072 1 0.095 0.289 15 482081 1 0.030 0.155 16 482082 1 0.102 0.286 17 482091 1 0.314 0.545 18 482092 1 0.374 0.581 19 482101 1 0.194 0.430 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 482102 1 0.131 0.354 21 482111 1 0.024 0.156 22 482112 1 0.072 0.209 23 482121 1 0.053 0.229 24 482122 1 0.106 0.299 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.162 0.355 STANDARD DEVIATION 0 0.111 0.143 MEDIAN 1 0.123 0.340 INTERQUARTILE RANGE 0 0.193 0.263 MINIMUM VALUE 1 0.024 0.149 LOWER HINGE 1 0.072 0.231 UPPER HINGE 1 0.265 0.493 MAXIMUM VALUE 1 0.374 0.581 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 482011 1838 1977 140 1.000 0.364 0.997 5.387 0.401 -0.062 2 482012 1846 1977 132 1.000 0.329 1.162 5.711 0.372 -0.071 3 482021 1891 1977 87 1.000 0.295 0.346 3.085 0.356 -0.069 4 482022 1889 1977 89 1.000 0.304 0.311 3.398 0.349 -0.006 5 482031 1849 1977 129 1.000 0.377 0.640 3.561 0.439 -0.114 6 482032 1863 1977 115 1.000 0.330 0.566 3.175 0.394 -0.045 7 482041 1831 1977 147 1.000 0.288 0.605 3.562 0.332 -0.008 8 482042 1855 1977 123 1.000 0.283 0.472 3.072 0.308 -0.017 9 482051 1883 1977 95 1.000 0.321 1.050 5.591 0.371 -0.067 10 482052 1888 1977 90 1.000 0.303 0.124 2.700 0.358 -0.024 11 482061 1836 1977 142 1.000 0.344 0.437 3.647 0.406 -0.022 12 482062 1842 1977 136 1.000 0.322 0.730 4.109 0.385 -0.074 13 482071 1879 1977 99 1.000 0.280 0.540 3.290 0.320 -0.082 14 482072 1875 1977 103 1.000 0.337 0.893 4.269 0.367 -0.031 15 482081 1853 1977 125 1.000 0.269 0.536 3.709 0.303 -0.012 16 482082 1849 1977 129 1.000 0.281 0.682 4.031 0.321 -0.043 17 482091 1846 1977 132 1.000 0.342 0.821 4.194 0.400 -0.087 18 482092 1852 1977 126 1.000 0.291 0.412 2.619 0.343 -0.123 19 482101 1838 1977 140 1.000 0.274 0.766 3.562 0.316 -0.045 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 482102 1840 1977 138 1.000 0.271 1.021 6.434 0.302 -0.027 21 482111 1896 1977 82 1.000 0.238 0.471 3.726 0.279 0.004 22 482112 1889 1977 89 1.000 0.276 0.669 3.606 0.303 -0.030 23 482121 1861 1977 117 1.000 0.301 0.771 4.459 0.325 0.000 24 482122 1842 1977 136 1.000 0.357 -0.071 3.684 0.451 -0.041 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 118 1.000 0.307 0.623 3.941 0.354 -0.046 STANDARD DEVIATION 20 0.000 0.035 0.294 0.967 0.046 0.035 MEDIAN (50TH QUANTILE) 125 1.000 0.302 0.622 3.665 0.353 -0.042 INTERQUARTILE RANGE 39 0.000 0.053 0.342 0.888 0.072 0.050 MINIMUM VALUE 82 1.000 0.238 -0.071 2.619 0.279 -0.123 LOWER HINGE (25TH QUANTILE) 97 1.000 0.281 0.454 3.344 0.318 -0.070 UPPER HINGE (75TH QUANTILE) 136 1.000 0.334 0.796 4.232 0.390 -0.020 MAXIMUM VALUE 147 1.000 0.377 1.162 6.434 0.451 0.004 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 276 0.477 0.103 0.006 -0.196 3.446 0.136 0.812 MINIMUM CORRELATION: 0.136 SERIES 482112 AND 482122 89 YEARS MAXIMUM CORRELATION: 0.812 SERIES 482021 AND 482022 87 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 72.39 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 120. 231. 276. RBAR 0.521 0.570 0.536 SDEV 0.111 0.117 0.117 SERR 0.010 0.008 0.007 EPS 0.957 0.969 0.965 NSS 20.6 23.9 24.0 |======================== 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 1831 1977 147 0.991 0.225 0.059 2.625 0.285 -0.166 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.402 0.135 0.061 62 85 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.55 1.00 1.10 1.64 13.95 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.00 0.88 0.94 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 -0.164 0.027 0.071 -0.085 0.130 -0.076 0.065 0.006 0.052 -0.056 PACF -0.164 0.000 0.078 -0.063 0.107 -0.043 0.055 0.005 0.080 -0.069 95% C.L. 0.165 0.169 0.169 0.170 0.171 0.174 0.175 0.176 0.176 0.176 |------------------ 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 0.027 -0.165 |---------- 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 0.000 0.012 0.067 -0.055 0.112 -0.048 0.057 0.027 0.047 -0.073 PACF 0.000 0.012 0.067 -0.055 0.111 -0.053 0.065 0.008 0.067 -0.105 95% C.L. 0.165 0.165 0.165 0.166 0.166 0.168 0.169 0.169 0.169 0.170 |----------------- 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 1 0.000 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 1831 1977 147 0.992 0.227 0.083 2.560 0.243 0.217 |------------ 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 0.216 0.070 0.075 -0.014 0.098 -0.013 0.058 0.044 0.032 -0.099 PACF 0.216 0.025 0.057 -0.045 0.111 -0.062 0.076 0.002 0.035 -0.148 95% C.L. 0.165 0.172 0.173 0.174 0.174 0.176 0.176 0.176 0.176 0.177 |------------------- 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 1 0.047 0.216 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 2.71 MINUTES