RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN015E.rwl LOG FILE PROCESSED: FRAN015E.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_EARLY 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 1.033 0.371 0.346 3.611 0.169 0.843 2 256020 1772 1975 204 0.886 0.247 1.022 4.605 0.167 0.724 3 256040 1845 1975 131 0.906 0.605 0.516 1.939 0.182 0.956 4 256080 1828 1975 148 0.900 0.521 0.307 1.696 0.177 0.922 5 256130 1819 1975 157 0.834 0.600 0.595 1.994 0.172 0.963 6 256170 1889 1975 87 0.942 0.646 0.151 1.842 0.168 0.942 7 256190 1771 1975 205 0.794 0.359 0.084 1.799 0.164 0.915 8 256200 1799 1975 177 0.801 0.345 0.540 2.141 0.149 0.921 9 256240 1831 1975 145 0.884 0.399 -0.103 2.432 0.245 0.817 10 256250 1846 1975 130 1.094 0.299 0.386 2.865 0.137 0.739 11 256270 1827 1975 149 1.056 0.394 0.685 3.059 0.179 0.842 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 0.921 0.435 0.412 2.544 0.173 0.871 STANDARD DEVIATION 33 0.101 0.135 0.311 0.915 0.027 0.084 MEDIAN (50TH QUANTILE) 149 0.900 0.394 0.386 2.141 0.169 0.915 INTERQUARTILE RANGE 29 0.128 0.208 0.338 1.071 0.012 0.102 MINIMUM VALUE 87 0.794 0.247 -0.103 1.696 0.137 0.724 LOWER HINGE (25TH QUANTILE) 138 0.859 0.352 0.229 1.891 0.165 0.830 UPPER HINGE (75TH QUANTILE) 167 0.988 0.560 0.567 2.962 0.178 0.932 MAXIMUM VALUE 205 1.094 0.646 1.022 4.605 0.245 0.963 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.415 0.381 0.051 -0.401 1.897 -0.395 0.922 MINIMUM CORRELATION: -0.395 SERIES 256020 AND 256170 87 YEARS MAXIMUM CORRELATION: 0.922 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 0.203 0.116 0.259 0.235 0.279 0.553 0.558 0.296 0.477 0.207 SDEV 0.000 0.443 0.140 0.491 0.370 0.268 0.203 0.389 0.275 0.420 SERR 0.000 0.255 0.081 0.201 0.081 0.051 0.030 0.058 0.041 0.063 EPS 0.394 0.287 0.591 0.668 0.765 0.921 0.927 0.808 0.901 0.733 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 0.289 0.408 0.269 0.645 0.516 0.385 0.331 SDEV 0.325 0.302 0.470 0.186 0.271 0.223 0.254 SERR 0.044 0.041 0.063 0.025 0.036 0.030 0.034 EPS 0.818 0.883 0.802 0.952 0.921 0.873 0.845 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 0.908 0.277 0.250 2.481 0.133 0.860 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.101 -0.065 0.370 36 169 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.93 1.01 1.07 2.00 11.60 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.14 0.00 0.86 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 0.856 0.844 0.821 0.781 0.781 0.728 0.713 0.680 0.642 0.635 PACF 0.856 0.418 0.192 0.007 0.126 -0.094 0.011 -0.038 -0.056 0.052 95% C.L. 0.140 0.219 0.276 0.320 0.355 0.387 0.413 0.436 0.456 0.474 |------------------ 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 0.797 0.396 0.326 0.215 |================== 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 0.00197935 0.88098902 2 256020 3 0.00000000 0.00000000 -0.00064202 0.95188546 3 256040 -67 87 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 256080 3 0.00000000 0.00000000 0.00463902 0.55479866 5 256130 -67 105 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 256170 3 0.00000000 0.00000000 0.01800886 0.14944935 7 256190 1 0.68101460 0.03687892 0.00000000 0.70518100 8 256200 3 0.00000000 0.00000000 0.00092324 0.71901768 9 256240 3 0.00000000 0.00000000 0.00484290 0.53060633 10 256250 3 0.00000000 0.00000000 0.00232372 0.94210374 11 256270 3 0.00000000 0.00000000 0.00256895 0.86377198 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 0.999 0.358 0.581 4.043 0.168 0.832 2 256020 1772 1975 204 1.000 0.274 1.010 4.877 0.166 0.719 3 256040 1845 1975 131 0.984 0.233 0.511 3.488 0.181 0.556 4 256080 1828 1975 148 1.023 0.641 1.287 5.326 0.176 0.878 5 256130 1819 1975 157 0.995 0.269 0.299 4.858 0.172 0.592 6 256170 1889 1975 87 0.955 0.520 1.025 3.560 0.172 0.876 7 256190 1771 1975 205 0.999 0.454 0.637 2.697 0.163 0.908 8 256200 1799 1975 177 1.001 0.426 0.482 2.093 0.148 0.910 9 256240 1831 1975 145 1.007 0.445 0.272 2.923 0.244 0.773 10 256250 1846 1975 130 1.001 0.268 0.771 4.946 0.136 0.663 11 256270 1827 1975 149 1.000 0.370 1.045 3.792 0.178 0.823 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 0.997 0.387 0.720 3.873 0.173 0.776 STANDARD DEVIATION 33 0.017 0.125 0.333 1.047 0.027 0.126 MEDIAN (50TH QUANTILE) 149 1.000 0.370 0.637 3.792 0.172 0.823 INTERQUARTILE RANGE 29 0.004 0.178 0.521 1.662 0.012 0.186 MINIMUM VALUE 87 0.955 0.233 0.272 2.093 0.136 0.556 LOWER HINGE (25TH QUANTILE) 138 0.997 0.272 0.496 3.205 0.165 0.691 UPPER HINGE (75TH QUANTILE) 167 1.001 0.450 1.017 4.868 0.177 0.877 MAXIMUM VALUE 205 1.023 0.641 1.287 5.326 0.244 0.910 |------------------------ 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 0.312 0.219 3.897 0.168 0.778 2 256020 1772 1975 204 0.998 0.257 0.729 4.142 0.166 0.683 3 256040 1845 1975 131 0.997 0.209 0.264 3.527 0.181 0.435 4 256080 1828 1975 148 0.973 0.256 0.431 3.147 0.176 0.635 5 256130 1819 1975 157 0.997 0.259 0.237 4.756 0.172 0.535 6 256170 1889 1975 87 0.962 0.336 0.646 4.025 0.169 0.740 7 256190 1771 1975 205 0.978 0.242 0.433 4.073 0.163 0.675 8 256200 1799 1975 177 0.989 0.195 0.242 2.808 0.148 0.574 9 256240 1831 1975 145 0.980 0.348 -0.213 2.886 0.242 0.697 10 256250 1846 1975 130 0.996 0.217 0.623 3.335 0.135 0.618 11 256270 1827 1975 149 0.988 0.304 0.554 3.164 0.178 0.755 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 0.987 0.267 0.379 3.614 0.173 0.648 STANDARD DEVIATION 33 0.012 0.052 0.268 0.611 0.027 0.103 MEDIAN (50TH QUANTILE) 149 0.989 0.257 0.431 3.527 0.169 0.675 INTERQUARTILE RANGE 29 0.017 0.078 0.349 0.894 0.013 0.123 MINIMUM VALUE 87 0.962 0.195 -0.213 2.808 0.135 0.435 LOWER HINGE (25TH QUANTILE) 138 0.979 0.230 0.239 3.155 0.164 0.596 UPPER HINGE (75TH QUANTILE) 167 0.996 0.308 0.589 4.049 0.177 0.719 MAXIMUM VALUE 205 0.998 0.348 0.729 4.756 0.242 0.778 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.395 0.153 0.021 -0.335 3.194 -0.013 0.736 MINIMUM CORRELATION: -0.013 SERIES 256130 AND 256270 149 YEARS MAXIMUM CORRELATION: 0.736 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 0.104 0.362 0.112 0.403 0.426 0.583 0.471 0.369 0.511 0.258 SDEV 0.000 0.309 0.185 0.214 0.317 0.209 0.268 0.297 0.238 0.341 SERR 0.000 0.178 0.107 0.087 0.069 0.039 0.040 0.044 0.035 0.051 EPS 0.229 0.633 0.343 0.816 0.862 0.930 0.899 0.854 0.913 0.785 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 0.476 0.439 0.289 0.548 0.476 0.431 0.330 SDEV 0.233 0.276 0.409 0.218 0.278 0.206 0.283 SERR 0.031 0.037 0.055 0.029 0.037 0.028 0.038 EPS 0.909 0.896 0.817 0.930 0.909 0.893 0.844 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 0.987 0.165 -0.050 3.342 0.130 0.521 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.137 0.081 0.114 25 180 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.46 1.02 1.09 1.55 5.48 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.15 0.00 0.85 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 0.518 0.516 0.477 0.373 0.363 0.226 0.211 0.137 0.099 0.045 PACF 0.518 0.338 0.193 0.001 0.048 -0.124 -0.019 -0.056 -0.009 -0.053 95% C.L. 0.140 0.173 0.201 0.222 0.234 0.245 0.249 0.252 0.254 0.254 |------------------ 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 0.377 0.279 0.273 0.192 |======================= 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 0.577 0.548 0.502 0.390 0.335 0.228 0.202 0.149 0.089 0.034 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 0.577 2 0.391 0.322 3 0.337 0.256 0.169 4 0.342 0.263 0.179 -0.030 5 0.341 0.267 0.184 -0.023 -0.020 6 0.339 0.265 0.203 0.004 0.015 -0.102 7 0.340 0.265 0.203 0.002 0.012 -0.105 0.010 8 0.340 0.264 0.203 0.002 0.013 -0.104 0.012 -0.006 9 0.340 0.264 0.200 0.003 0.013 -0.097 0.021 0.005 -0.033 10 0.338 0.265 0.201 -0.004 0.014 -0.097 0.034 0.022 -0.010 -0.065 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) 1285.83 1204.68 1184.22 1180.27 1182.09 1184.01 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1183.87 1185.85 1187.84 1189.62 1190.75 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 0.337 0.256 0.169 R-SQUARED DUE TO POOLED AUTOREGRESSION: 41.97 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 172.32 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.337 0.369 0.380 0.280 0.254 0.221 0.187 0.163 0.140 0.1204 0.104 0.089 0.077 0.066 0.057 0.049 0.043 0.037 0.032 0.0272 0.023 0.020 0.017 0.015 0.013 0.011 0.010 0.008 0.007 0.0061 0.005 0.005 0.004 0.003 0.003 0.003 0.002 0.002 0.002 0.0014 0.001 0.001 0.001 0.001 0.001 0.001 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 256010 3 0.651 0.507 0.248 0.108 2 256020 3 0.523 0.484 0.339 -0.051 3 256040 3 0.285 0.271 0.285 0.090 4 256080 3 0.466 0.521 0.268 -0.090 5 256130 3 0.356 0.390 0.173 0.139 6 256170 3 0.583 0.685 0.177 -0.100 7 256190 3 0.514 0.461 0.267 0.057 8 256200 3 0.380 0.434 0.138 0.138 9 256240 3 0.568 0.410 0.301 0.118 10 256250 3 0.451 0.485 0.272 -0.036 11 256270 3 0.619 0.563 0.165 0.108 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.490 0.474 0.239 0.044 STANDARD DEVIATION 0 0.115 0.105 0.065 0.094 MEDIAN 3 0.514 0.484 0.267 0.090 INTERQUARTILE RANGE 0 0.159 0.092 0.104 0.157 MINIMUM VALUE 3 0.285 0.271 0.138 -0.100 LOWER HINGE 3 0.416 0.422 0.175 -0.044 UPPER HINGE 3 0.575 0.514 0.279 0.113 MAXIMUM VALUE 3 0.651 0.685 0.339 0.139 |------------------- 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 0.185 0.200 4.359 0.196 0.010 2 256020 1772 1975 204 1.000 0.177 0.626 3.600 0.200 -0.006 3 256040 1845 1975 131 1.000 0.178 0.251 4.016 0.205 0.010 4 256080 1828 1975 148 1.000 0.189 0.626 3.741 0.205 -0.023 5 256130 1819 1975 157 1.000 0.208 0.063 5.464 0.207 -0.014 6 256170 1889 1975 87 1.000 0.215 1.356 6.489 0.215 -0.015 7 256190 1771 1975 205 1.000 0.170 0.147 3.545 0.191 -0.007 8 256200 1799 1975 177 1.000 0.154 -0.014 2.920 0.180 -0.010 9 256240 1831 1975 145 1.000 0.231 -0.023 3.920 0.250 0.013 10 256250 1846 1975 130 1.000 0.160 0.270 3.345 0.169 -0.024 11 256270 1827 1975 149 1.000 0.189 -0.196 4.098 0.215 0.008 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.187 0.301 4.136 0.203 -0.005 STANDARD DEVIATION 33 0.000 0.023 0.432 1.015 0.021 0.014 MEDIAN (50TH QUANTILE) 149 1.000 0.185 0.200 3.920 0.205 -0.007 INTERQUARTILE RANGE 29 0.000 0.025 0.423 0.656 0.018 0.024 MINIMUM VALUE 87 1.000 0.154 -0.196 2.920 0.169 -0.024 LOWER HINGE (25TH QUANTILE) 138 1.000 0.174 0.025 3.572 0.193 -0.015 UPPER HINGE (75TH QUANTILE) 167 1.000 0.198 0.448 4.229 0.211 0.009 MAXIMUM VALUE 205 1.000 0.231 1.356 6.489 0.250 0.013 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.485 0.097 0.013 -0.583 2.773 0.246 0.659 MINIMUM CORRELATION: 0.246 SERIES 256040 AND 256170 87 YEARS MAXIMUM CORRELATION: 0.659 SERIES 256080 AND 256240 145 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 0.214 0.403 0.271 0.258 0.679 0.715 0.529 0.497 0.545 0.521 SDEV 0.000 0.308 0.060 0.268 0.107 0.107 0.190 0.201 0.187 0.143 SERR 0.000 0.178 0.035 0.109 0.023 0.020 0.028 0.030 0.028 0.021 EPS 0.410 0.673 0.607 0.695 0.947 0.959 0.918 0.908 0.923 0.920 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 0.445 0.536 0.438 0.471 0.521 0.395 0.436 SDEV 0.203 0.179 0.170 0.191 0.192 0.193 0.187 SERR 0.027 0.024 0.023 0.026 0.026 0.026 0.025 EPS 0.898 0.927 0.895 0.907 0.923 0.878 0.895 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 0.129 0.202 3.559 0.151 -0.159 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.140 0.071 0.056 27 178 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.39 1.44 1.01 1.11 2.54 8.39 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 -0.158 -0.033 0.088 0.000 0.117 -0.084 0.007 0.043 -0.052 -0.006 PACF -0.158 -0.059 0.075 0.026 0.133 -0.052 -0.009 0.016 -0.038 -0.029 95% C.L. 0.140 0.143 0.143 0.144 0.144 0.146 0.147 0.147 0.147 0.148 |------------------ 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 0.029 -0.159 |---------- 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 -0.009 0.016 0.044 0.114 -0.072 0.003 0.030 -0.045 -0.025 PACF -0.003 -0.009 0.016 0.044 0.114 -0.071 0.003 0.024 -0.053 -0.032 95% C.L. 0.140 0.140 0.140 0.140 0.140 0.142 0.142 0.142 0.143 0.143 |----------------- 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 0.002 -0.003 -0.009 0.016 |========================= 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 1.001 0.168 -0.065 3.060 0.121 0.584 |------------ 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 0.581 0.553 0.510 0.421 0.391 0.252 0.220 0.173 0.090 0.057 PACF 0.581 0.325 0.176 0.011 0.035 -0.149 -0.035 -0.012 -0.062 -0.027 95% C.L. 0.140 0.181 0.211 0.234 0.248 0.260 0.265 0.268 0.271 0.271 |------------------- 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 0.427 0.337 0.257 0.174 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 1.46 MINUTES