RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN015W.rwl LOG FILE PROCESSED: FRAN015W.rwl_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 20 10 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: 256 1 Col dAllos WIDTH_RING ABAL - 256 2 France silver fir, European fir 1900 4416-634 1771 1975 - 256 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 256010 1823 1975 153 1.299 0.474 0.824 4.429 0.150 0.879 2 256020 1772 1975 204 1.091 0.318 1.194 5.413 0.155 0.779 3 256040 1845 1975 131 1.222 0.773 0.512 2.054 0.157 0.955 4 256080 1828 1975 148 1.179 0.649 0.309 1.669 0.158 0.925 5 256130 1819 1975 157 1.127 0.783 0.665 2.056 0.147 0.960 6 256170 1889 1975 87 1.206 0.788 0.231 1.952 0.142 0.954 7 256190 1771 1975 205 1.017 0.452 0.139 1.827 0.147 0.924 8 256200 1799 1975 177 0.969 0.386 0.522 2.092 0.136 0.917 9 256240 1831 1975 145 1.264 0.559 0.272 2.908 0.226 0.810 10 256250 1846 1975 130 1.307 0.329 0.445 3.231 0.129 0.718 11 256270 1827 1975 149 1.247 0.454 0.809 3.283 0.167 0.855 NUMBER OF SERIES READ IN: 11 FROM 1771 TO 1975 205 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.175 0.542 0.538 2.810 0.156 0.880 STANDARD DEVIATION 33 0.112 0.180 0.314 1.203 0.026 0.081 MEDIAN (50TH QUANTILE) 149 1.206 0.474 0.512 2.092 0.150 0.917 INTERQUARTILE RANGE 29 0.147 0.292 0.446 1.254 0.013 0.107 MINIMUM VALUE 87 0.969 0.318 0.139 1.669 0.129 0.718 LOWER HINGE (25TH QUANTILE) 138 1.109 0.419 0.290 2.003 0.144 0.833 UPPER HINGE (75TH QUANTILE) 167 1.255 0.711 0.737 3.257 0.157 0.940 MAXIMUM VALUE 205 1.307 0.788 1.194 5.413 0.226 0.960 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.371 0.403 0.054 -0.330 1.816 -0.468 0.907 MINIMUM CORRELATION: -0.468 SERIES 256020 AND 256170 87 YEARS MAXIMUM CORRELATION: 0.907 SERIES 256040 AND 256130 131 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.43 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. CORR 1. 3. 3. 6. 21. 28. 45. 45. 45. 45. RBAR 0.120 0.034 0.336 0.202 0.272 0.544 0.501 0.316 0.441 0.157 SDEV 0.000 0.519 0.148 0.593 0.390 0.277 0.210 0.392 0.287 0.442 SERR 0.000 0.300 0.086 0.242 0.085 0.052 0.031 0.059 0.043 0.066 EPS 0.258 0.096 0.677 0.624 0.758 0.919 0.910 0.822 0.888 0.663 NSS 2.5 3.0 4.2 6.6 8.4 9.4 10.0 10.0 10.1 10.6 YEAR 1900. 1910. 1920. 1930. 1940. 1950. 1960. CORR 55. 55. 55. 55. 55. 55. 55. RBAR 0.212 0.352 0.261 0.593 0.490 0.371 0.347 SDEV 0.376 0.341 0.493 0.208 0.283 0.269 0.286 SERR 0.051 0.046 0.066 0.028 0.038 0.036 0.039 EPS 0.748 0.857 0.795 0.941 0.914 0.867 0.854 NSS 11.0 11.0 11.0 11.0 11.0 11.0 11.0 |======================== 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 1771 1975 205 1.154 0.332 0.238 2.654 0.123 0.866 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.090 0.062 0.335 29 176 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.38 0.77 1.00 1.07 1.85 4.12 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.15 0.00 0.85 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 149. 29. 87. 138. 167. 205. |----------- 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 0.862 0.844 0.819 0.775 0.776 0.722 0.699 0.677 0.631 0.618 PACF 0.862 0.394 0.178 -0.015 0.142 -0.096 -0.011 0.013 -0.071 0.018 95% C.L. 0.140 0.220 0.276 0.320 0.355 0.387 0.412 0.435 0.455 0.471 |------------------ 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 0.799 0.427 0.311 0.198 |================== 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 256010 3 0.00000000 0.00000000 0.00148808 1.18437219 2 256020 3 0.00000000 0.00000000 -0.00089866 1.18289673 3 256040 3 0.00000000 0.00000000 0.01779827 0.04691721 4 256080 3 0.00000000 0.00000000 0.00610294 0.72465527 5 256130 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 256170 3 0.00000000 0.00000000 0.02079318 0.29107726 7 256190 1 0.90595227 0.03746417 0.00000000 0.90145987 8 256200 3 0.00000000 0.00000000 0.00079110 0.89880073 9 256240 3 0.00000000 0.00000000 0.00650327 0.78926152 10 256250 3 0.00000000 0.00000000 0.00155925 1.20440793 11 256270 3 0.00000000 0.00000000 0.00231155 1.07327771 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 1.000 0.367 0.979 4.754 0.149 0.874 2 256020 1772 1975 204 1.000 0.286 1.229 5.859 0.155 0.773 3 256040 1845 1975 131 1.268 1.330 4.145 20.326 0.154 0.827 4 256080 1828 1975 148 1.021 0.599 1.170 4.730 0.157 0.887 5 256130 1819 1975 157 0.997 0.233 0.487 4.027 0.146 0.654 6 256170 1889 1975 87 0.957 0.507 1.168 3.638 0.144 0.917 7 256190 1771 1975 205 0.999 0.441 0.702 2.813 0.146 0.914 8 256200 1799 1975 177 1.001 0.397 0.500 2.100 0.135 0.909 9 256240 1831 1975 145 1.004 0.414 0.251 2.561 0.224 0.757 10 256250 1846 1975 130 1.000 0.251 0.683 4.390 0.128 0.677 11 256270 1827 1975 149 1.000 0.366 1.112 3.834 0.166 0.843 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.022 0.472 1.130 5.367 0.155 0.821 STANDARD DEVIATION 33 0.083 0.304 1.053 5.079 0.025 0.094 MEDIAN (50TH QUANTILE) 149 1.000 0.397 0.979 4.027 0.149 0.843 INTERQUARTILE RANGE 29 0.003 0.148 0.578 1.517 0.011 0.133 MINIMUM VALUE 87 0.957 0.233 0.251 2.100 0.128 0.654 LOWER HINGE (25TH QUANTILE) 138 0.999 0.326 0.592 3.225 0.145 0.765 UPPER HINGE (75TH QUANTILE) 167 1.002 0.474 1.169 4.742 0.156 0.898 MAXIMUM VALUE 205 1.268 1.330 4.145 20.326 0.224 0.917 |------------------------ 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 256010 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 256020 -67 136 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 256040 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 256080 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 256130 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 256170 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 256190 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 256200 -67 118 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 256240 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 256250 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 256270 -67 99 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 256010 1823 1975 153 0.994 0.308 0.429 4.115 0.149 0.819 2 256020 1772 1975 204 0.997 0.262 0.864 4.928 0.154 0.735 3 256040 1845 1975 131 1.001 0.319 0.229 3.500 0.156 0.784 4 256080 1828 1975 148 0.974 0.246 0.932 4.975 0.157 0.673 5 256130 1819 1975 157 0.997 0.216 0.301 3.760 0.146 0.605 6 256170 1889 1975 87 0.970 0.305 0.482 3.601 0.140 0.800 7 256190 1771 1975 205 0.980 0.237 0.684 4.424 0.145 0.713 8 256200 1799 1975 177 0.990 0.180 0.312 2.958 0.135 0.561 9 256240 1831 1975 145 0.981 0.313 -0.166 2.843 0.224 0.653 10 256250 1846 1975 130 0.996 0.210 0.637 3.240 0.128 0.635 11 256270 1827 1975 149 0.987 0.295 0.645 3.217 0.166 0.774 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 0.988 0.263 0.486 3.778 0.155 0.705 STANDARD DEVIATION 33 0.010 0.048 0.314 0.745 0.025 0.086 MEDIAN (50TH QUANTILE) 149 0.990 0.262 0.482 3.601 0.149 0.713 INTERQUARTILE RANGE 29 0.016 0.080 0.358 1.041 0.014 0.135 MINIMUM VALUE 87 0.970 0.180 -0.166 2.843 0.128 0.561 LOWER HINGE (25TH QUANTILE) 138 0.980 0.226 0.307 3.228 0.143 0.644 UPPER HINGE (75TH QUANTILE) 167 0.997 0.307 0.665 4.269 0.157 0.779 MAXIMUM VALUE 205 1.001 0.319 0.932 4.975 0.224 0.819 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.366 0.181 0.024 -0.156 2.653 -0.100 0.748 MINIMUM CORRELATION: -0.100 SERIES 256130 AND 256270 149 YEARS MAXIMUM CORRELATION: 0.748 SERIES 256080 AND 256170 87 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.43 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. CORR 1. 3. 3. 6. 21. 28. 45. 45. 45. 45. RBAR -0.001 0.261 0.182 0.447 0.420 0.559 0.430 0.382 0.453 0.178 SDEV 0.000 0.403 0.140 0.209 0.321 0.227 0.283 0.342 0.302 0.385 SERR 0.000 0.232 0.081 0.085 0.070 0.043 0.042 0.051 0.045 0.057 EPS -0.002 0.519 0.479 0.841 0.859 0.923 0.883 0.861 0.893 0.695 NSS 2.5 3.0 4.2 6.6 8.4 9.4 10.0 10.0 10.1 10.6 YEAR 1900. 1910. 1920. 1930. 1940. 1950. 1960. CORR 55. 55. 55. 55. 55. 55. 55. RBAR 0.432 0.423 0.264 0.505 0.467 0.441 0.339 SDEV 0.266 0.300 0.434 0.245 0.305 0.223 0.309 SERR 0.036 0.040 0.059 0.033 0.041 0.030 0.042 EPS 0.893 0.890 0.798 0.918 0.906 0.897 0.849 NSS 11.0 11.0 11.0 11.0 11.0 11.0 11.0 |======================== 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 1771 1975 205 0.985 0.160 0.086 3.820 0.121 0.553 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.157 0.098 0.094 26 179 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.83 1.00 1.10 1.93 7.19 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.14 0.00 0.86 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 0.550 0.551 0.502 0.404 0.382 0.256 0.212 0.169 0.091 0.047 PACF 0.550 0.356 0.181 -0.003 0.033 -0.117 -0.057 -0.014 -0.054 -0.049 95% C.L. 0.140 0.177 0.208 0.230 0.244 0.255 0.260 0.263 0.266 0.266 |------------------ 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 3 0.412 0.291 0.292 0.180 |======================= 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 0.614 0.587 0.536 0.418 0.383 0.273 0.212 0.172 0.085 0.026 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 0.614 2 0.407 0.337 3 0.352 0.270 0.164 4 0.361 0.285 0.183 -0.054 5 0.361 0.283 0.180 -0.058 0.011 6 0.362 0.277 0.197 -0.030 0.046 -0.098 7 0.358 0.280 0.196 -0.021 0.060 -0.080 -0.050 8 0.357 0.279 0.196 -0.021 0.060 -0.080 -0.050 -0.001 9 0.357 0.276 0.191 -0.017 0.059 -0.067 -0.032 0.021 -0.064 10 0.353 0.278 0.188 -0.022 0.064 -0.068 -0.018 0.042 -0.037 -0.074 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) 1270.10 1175.22 1152.54 1148.99 1150.38 1152.36 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1152.38 1153.86 1155.86 1157.03 1157.90 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 0.352 0.270 0.164 R-SQUARED DUE TO POOLED AUTOREGRESSION: 46.21 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 185.90 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.352 0.394 0.397 0.304 0.279 0.245 0.211 0.186 0.163 0.1421 0.124 0.109 0.095 0.083 0.073 0.064 0.056 0.049 0.043 0.0373 0.033 0.029 0.025 0.022 0.019 0.017 0.015 0.013 0.011 0.0098 0.009 0.007 0.007 0.006 0.005 0.004 0.004 0.003 0.003 0.0026 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 256010 3 0.706 0.587 0.258 0.028 2 256020 3 0.590 0.529 0.343 -0.067 3 256040 3 0.709 0.481 0.388 0.014 4 256080 3 0.510 0.589 0.287 -0.186 5 256130 3 0.463 0.350 0.304 0.123 6 256170 3 0.662 0.811 0.021 -0.022 7 256190 3 0.569 0.458 0.306 0.056 8 256200 3 0.385 0.385 0.175 0.168 9 256240 3 0.499 0.422 0.291 0.069 10 256250 3 0.478 0.499 0.279 -0.045 11 256270 3 0.647 0.592 0.152 0.103 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.565 0.519 0.255 0.022 STANDARD DEVIATION 0 0.107 0.127 0.102 0.100 MEDIAN 3 0.569 0.499 0.287 0.028 INTERQUARTILE RANGE 0 0.166 0.148 0.088 0.120 MINIMUM VALUE 3 0.385 0.350 0.021 -0.186 LOWER HINGE 3 0.489 0.440 0.217 -0.034 UPPER HINGE 3 0.655 0.588 0.305 0.086 MAXIMUM VALUE 3 0.709 0.811 0.388 0.168 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 1.000 0.170 0.192 3.895 0.184 0.004 2 256020 1772 1975 204 1.000 0.169 0.788 4.796 0.187 -0.007 3 256040 1845 1975 131 1.000 0.170 0.560 4.978 0.193 -0.027 4 256080 1828 1975 148 1.000 0.173 0.839 5.041 0.188 -0.035 5 256130 1819 1975 157 1.000 0.159 0.303 3.821 0.171 0.009 6 256170 1889 1975 87 1.000 0.176 0.995 5.270 0.184 -0.015 7 256190 1771 1975 205 1.000 0.156 0.364 3.672 0.172 -0.006 8 256200 1799 1975 177 1.000 0.141 -0.044 2.783 0.163 -0.011 9 256240 1831 1975 145 1.000 0.224 0.192 4.235 0.251 0.008 10 256250 1846 1975 130 1.000 0.151 0.188 3.269 0.161 -0.027 11 256270 1827 1975 149 1.000 0.176 -0.227 3.825 0.201 0.005 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.170 0.377 4.144 0.187 -0.009 STANDARD DEVIATION 33 0.000 0.021 0.381 0.794 0.025 0.015 MEDIAN (50TH QUANTILE) 149 1.000 0.170 0.303 3.895 0.184 -0.007 INTERQUARTILE RANGE 29 0.000 0.017 0.484 1.140 0.019 0.026 MINIMUM VALUE 87 1.000 0.141 -0.227 2.783 0.161 -0.035 LOWER HINGE (25TH QUANTILE) 138 1.000 0.158 0.190 3.747 0.171 -0.021 UPPER HINGE (75TH QUANTILE) 167 1.000 0.174 0.674 4.887 0.191 0.004 MAXIMUM VALUE 205 1.000 0.224 0.995 5.270 0.251 0.009 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.481 0.104 0.014 -0.341 2.565 0.227 0.662 MINIMUM CORRELATION: 0.227 SERIES 256040 AND 256170 87 YEARS MAXIMUM CORRELATION: 0.662 SERIES 256080 AND 256170 87 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.43 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1810. 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. CORR 1. 3. 3. 6. 21. 28. 45. 45. 45. 45. RBAR 0.233 0.372 0.346 0.281 0.690 0.721 0.534 0.537 0.561 0.477 SDEV 0.000 0.365 0.124 0.246 0.091 0.101 0.180 0.185 0.168 0.204 SERR 0.000 0.211 0.071 0.100 0.020 0.019 0.027 0.028 0.025 0.030 EPS 0.437 0.644 0.687 0.719 0.949 0.961 0.920 0.921 0.928 0.906 NSS 2.5 3.0 4.2 6.6 8.4 9.4 10.0 10.0 10.1 10.6 YEAR 1900. 1910. 1920. 1930. 1940. 1950. 1960. CORR 55. 55. 55. 55. 55. 55. 55. RBAR 0.384 0.502 0.455 0.448 0.510 0.382 0.475 SDEV 0.228 0.218 0.173 0.197 0.192 0.199 0.202 SERR 0.031 0.029 0.023 0.027 0.026 0.027 0.027 EPS 0.873 0.917 0.902 0.899 0.920 0.872 0.909 NSS 11.0 11.0 11.0 11.0 11.0 11.0 11.0 |======================== 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 1771 1975 205 1.000 0.118 0.278 3.708 0.139 -0.184 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.201 0.103 0.009 32 173 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.78 1.00 1.06 1.84 23.45 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.15 0.00 0.85 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 -0.183 -0.033 0.085 -0.033 0.151 -0.057 -0.030 0.072 -0.062 -0.025 PACF -0.183 -0.069 0.069 -0.006 0.158 -0.008 -0.029 0.035 -0.041 -0.060 95% C.L. 0.140 0.144 0.144 0.145 0.146 0.149 0.149 0.149 0.150 0.150 |------------------ 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 0.038 -0.184 |---------- 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 -0.012 0.011 0.025 0.146 -0.039 -0.022 0.049 -0.060 -0.049 PACF -0.001 -0.012 0.011 0.025 0.146 -0.039 -0.020 0.045 -0.069 -0.069 95% C.L. 0.140 0.140 0.140 0.140 0.140 0.143 0.143 0.143 0.143 0.144 |----------------- 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 0.001 0.000 -0.012 0.011 |========================= 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 1771 1975 205 1.000 0.158 0.058 3.285 0.110 0.621 |------------ 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 0.618 0.591 0.544 0.454 0.441 0.307 0.247 0.212 0.114 0.074 PACF 0.618 0.338 0.172 -0.002 0.065 -0.141 -0.080 -0.005 -0.083 -0.044 95% C.L. 0.140 0.186 0.219 0.244 0.260 0.274 0.281 0.285 0.288 0.289 |------------------- 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 0.469 0.353 0.267 0.170 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.84 MINUTES