RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN015P.rwl LOG FILE PROCESSED: FRAN015P.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 LATEWOOD_PERCENT 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 2.070 0.552 1.155 4.565 0.172 0.595 2 256020 1772 1975 204 1.845 0.433 1.098 5.954 0.193 0.323 3 256040 1845 1975 131 2.789 0.636 0.818 3.754 0.151 0.563 4 256080 1828 1975 148 2.519 0.526 0.310 2.448 0.138 0.633 5 256130 1819 1975 157 2.938 1.168 1.902 7.057 0.169 0.813 6 256170 1889 1975 87 2.581 0.828 0.380 2.000 0.156 0.826 7 256190 1771 1975 205 2.248 0.429 0.134 3.090 0.151 0.479 8 256200 1799 1975 177 1.837 0.426 0.033 2.395 0.166 0.609 9 256240 1831 1975 145 3.119 0.914 0.812 3.350 0.185 0.669 10 256250 1846 1975 130 1.664 0.417 -0.165 2.467 0.162 0.700 11 256270 1827 1975 149 1.563 0.391 0.504 3.051 0.171 0.602 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 2.288 0.611 0.635 3.648 0.165 0.619 STANDARD DEVIATION 33 0.535 0.254 0.600 1.602 0.016 0.142 MEDIAN (50TH QUANTILE) 149 2.248 0.526 0.504 3.090 0.166 0.609 INTERQUARTILE RANGE 29 0.844 0.305 0.736 1.702 0.018 0.106 MINIMUM VALUE 87 1.563 0.391 -0.165 2.000 0.138 0.323 LOWER HINGE (25TH QUANTILE) 138 1.841 0.427 0.222 2.457 0.154 0.579 UPPER HINGE (75TH QUANTILE) 167 2.685 0.732 0.958 4.159 0.171 0.685 MAXIMUM VALUE 205 3.119 1.168 1.902 7.057 0.193 0.826 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.493 0.166 0.022 -0.642 3.107 0.062 0.779 MINIMUM CORRELATION: 0.062 SERIES 256020 AND 256130 157 YEARS MAXIMUM CORRELATION: 0.779 SERIES 256170 AND 256200 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 0.500 0.445 0.186 0.620 0.573 0.466 0.503 0.290 0.383 0.501 SDEV 0.000 0.256 0.403 0.087 0.198 0.185 0.187 0.275 0.243 0.235 SERR 0.000 0.148 0.233 0.035 0.043 0.035 0.028 0.041 0.036 0.035 EPS 0.719 0.710 0.487 0.915 0.918 0.892 0.910 0.803 0.862 0.914 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 0.509 0.354 0.288 0.378 0.500 0.292 0.312 SDEV 0.172 0.267 0.238 0.228 0.179 0.205 0.255 SERR 0.023 0.036 0.032 0.031 0.024 0.028 0.034 EPS 0.919 0.857 0.817 0.870 0.917 0.819 0.833 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 2.168 0.375 0.406 2.747 0.119 0.571 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.508 0.366 -0.233 39 166 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.51 2.68 1.01 1.17 3.85 110.77 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 0.569 0.502 0.443 0.366 0.389 0.359 0.416 0.381 0.390 0.360 PACF 0.569 0.263 0.132 0.026 0.136 0.063 0.171 0.036 0.081 0.011 95% C.L. 0.140 0.179 0.205 0.223 0.234 0.246 0.256 0.269 0.280 0.290 |------------------ 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 0.383 0.384 0.210 0.132 |================== 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 -0.00709910 2.61656523 2 256020 1 0.31972077 0.03345535 0.00000000 1.79922950 3 256040 3 0.00000000 0.00000000 -0.00953852 3.41809154 4 256080 3 0.00000000 0.00000000 -0.00085120 2.58206296 5 256130 1 4.12593699 0.04685104 0.00000000 2.39088321 6 256170 3 0.00000000 0.00000000 -0.02736276 3.78488111 7 256190 3 0.00000000 0.00000000 0.00008059 2.23930836 8 256200 3 0.00000000 0.00000000 -0.00143921 1.96509504 9 256240 3 0.00000000 0.00000000 -0.00500130 3.48426723 10 256250 3 0.00000000 0.00000000 -0.00732043 2.14364219 11 256270 3 0.00000000 0.00000000 -0.00473343 1.91849720 |-------------------- 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 0.206 1.052 4.178 0.171 0.386 2 256020 1772 1975 204 1.000 0.229 0.852 4.516 0.192 0.328 3 256040 1845 1975 131 1.000 0.186 0.957 4.335 0.150 0.363 4 256080 1828 1975 148 1.000 0.208 0.309 2.504 0.137 0.624 5 256130 1819 1975 157 1.000 0.243 0.768 3.272 0.169 0.534 6 256170 1889 1975 87 1.001 0.172 0.398 3.010 0.155 0.401 7 256190 1771 1975 205 1.000 0.191 0.127 3.088 0.150 0.476 8 256200 1799 1975 177 1.000 0.231 0.230 2.433 0.165 0.606 9 256240 1831 1975 145 0.999 0.284 0.858 3.398 0.184 0.643 10 256250 1846 1975 130 0.997 0.189 0.163 2.732 0.160 0.474 11 256270 1827 1975 149 0.999 0.211 0.494 2.868 0.169 0.485 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.214 0.564 3.303 0.164 0.484 STANDARD DEVIATION 33 0.001 0.032 0.341 0.732 0.016 0.109 MEDIAN (50TH QUANTILE) 149 1.000 0.208 0.494 3.088 0.165 0.476 INTERQUARTILE RANGE 29 0.001 0.040 0.586 0.988 0.018 0.177 MINIMUM VALUE 87 0.997 0.172 0.127 2.433 0.137 0.328 LOWER HINGE (25TH QUANTILE) 138 0.999 0.190 0.269 2.800 0.153 0.393 UPPER HINGE (75TH QUANTILE) 167 1.000 0.230 0.855 3.788 0.170 0.570 MAXIMUM VALUE 205 1.001 0.284 1.052 4.516 0.192 0.643 |------------------------ 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 0.999 0.187 0.921 4.630 0.171 0.258 2 256020 1772 1975 204 0.998 0.215 0.872 5.313 0.192 0.244 3 256040 1845 1975 131 0.998 0.175 0.947 4.339 0.150 0.294 4 256080 1828 1975 148 0.998 0.160 0.449 3.192 0.137 0.381 5 256130 1819 1975 157 0.998 0.220 0.740 3.558 0.168 0.445 6 256170 1889 1975 87 0.998 0.150 0.286 3.203 0.155 0.231 7 256190 1771 1975 205 0.998 0.169 0.107 3.592 0.150 0.328 8 256200 1799 1975 177 0.997 0.166 0.030 2.906 0.165 0.232 9 256240 1831 1975 145 0.996 0.229 0.646 3.167 0.184 0.479 10 256250 1846 1975 130 0.999 0.156 0.183 2.813 0.160 0.213 11 256270 1827 1975 149 0.999 0.200 0.504 2.820 0.169 0.429 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 0.998 0.184 0.517 3.594 0.164 0.321 STANDARD DEVIATION 33 0.001 0.028 0.334 0.822 0.016 0.097 MEDIAN (50TH QUANTILE) 149 0.998 0.175 0.504 3.203 0.165 0.294 INTERQUARTILE RANGE 29 0.001 0.045 0.571 0.929 0.018 0.167 MINIMUM VALUE 87 0.996 0.150 0.030 2.813 0.137 0.213 LOWER HINGE (25TH QUANTILE) 138 0.998 0.163 0.235 3.036 0.152 0.238 UPPER HINGE (75TH QUANTILE) 167 0.999 0.208 0.806 3.966 0.170 0.405 MAXIMUM VALUE 205 0.999 0.229 0.947 5.313 0.192 0.479 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.415 0.096 0.013 -0.427 3.393 0.166 0.643 MINIMUM CORRELATION: 0.166 SERIES 256020 AND 256240 145 YEARS MAXIMUM CORRELATION: 0.643 SERIES 256080 AND 256270 148 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 0.536 0.416 0.221 0.572 0.639 0.505 0.455 0.303 0.388 0.512 SDEV 0.000 0.276 0.382 0.133 0.137 0.179 0.180 0.250 0.238 0.219 SERR 0.000 0.159 0.221 0.054 0.030 0.034 0.027 0.037 0.035 0.033 EPS 0.747 0.685 0.541 0.898 0.937 0.906 0.893 0.813 0.865 0.917 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 0.513 0.342 0.348 0.300 0.375 0.222 0.303 SDEV 0.172 0.242 0.221 0.198 0.212 0.237 0.239 SERR 0.023 0.033 0.030 0.027 0.029 0.032 0.032 EPS 0.921 0.851 0.855 0.825 0.869 0.758 0.827 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 0.995 0.134 0.533 3.793 0.116 0.368 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.262 0.143 -0.007 40 165 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.95 1.01 1.07 2.02 13.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 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 0.367 0.262 0.175 0.039 0.089 0.033 0.093 0.041 0.065 0.035 PACF 0.367 0.148 0.046 -0.079 0.074 -0.014 0.083 -0.032 0.045 -0.023 95% C.L. 0.140 0.157 0.166 0.169 0.169 0.170 0.170 0.171 0.172 0.172 |------------------ 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 2 0.158 0.314 0.151 |======================= 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 0.364 0.294 0.212 0.127 0.121 0.085 0.169 0.103 0.092 0.041 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 0.364 2 0.297 0.186 3 0.284 0.165 0.069 4 0.285 0.167 0.071 -0.009 5 0.285 0.164 0.065 -0.020 0.038 6 0.285 0.164 0.064 -0.021 0.036 0.010 7 0.283 0.159 0.067 -0.030 0.015 -0.027 0.129 8 0.284 0.159 0.067 -0.030 0.015 -0.026 0.130 -0.006 9 0.284 0.159 0.067 -0.030 0.015 -0.026 0.130 -0.006 0.001 10 0.284 0.159 0.073 -0.031 0.016 -0.027 0.133 0.001 0.013 -0.043 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) 1146.64 1119.41 1114.23 1115.26 1117.24 1118.94 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1120.92 1119.49 1121.48 1123.48 1125.10 SELECTED AUTOREGRESSION ORDER: 2 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 0.297 0.186 R-SQUARED DUE TO POOLED AUTOREGRESSION: 16.27 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 119.43 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.297 0.274 0.136 0.091 0.052 0.032 0.019 0.012 0.007 0.0043 0.003 0.002 0.001 0.001 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 256010 2 0.073 0.245 0.057 2 256020 2 0.103 0.205 0.194 3 256040 2 0.127 0.279 0.067 4 256080 2 0.197 0.304 0.224 5 256130 2 0.265 0.332 0.261 6 256170 2 0.138 0.166 0.284 7 256190 2 0.128 0.299 0.095 8 256200 2 0.069 0.204 0.125 9 256240 2 0.265 0.380 0.211 10 256250 2 0.054 0.202 0.075 11 256270 2 0.231 0.344 0.202 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.150 0.269 0.163 STANDARD DEVIATION 0 0.078 0.069 0.082 MEDIAN 2 0.128 0.279 0.194 INTERQUARTILE RANGE 0 0.126 0.113 0.133 MINIMUM VALUE 2 0.054 0.166 0.057 LOWER HINGE 2 0.088 0.204 0.085 UPPER HINGE 2 0.214 0.318 0.217 MAXIMUM VALUE 2 0.265 0.380 0.284 |------------------- 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 0.180 0.909 4.669 0.192 -0.004 2 256020 1772 1975 204 1.000 0.204 0.852 6.258 0.211 -0.019 3 256040 1845 1975 131 1.000 0.167 1.001 5.151 0.175 -0.010 4 256080 1828 1975 148 1.000 0.144 0.242 3.323 0.157 0.007 5 256130 1819 1975 157 1.000 0.190 0.802 4.123 0.198 -0.031 6 256170 1889 1975 87 1.000 0.140 0.159 3.679 0.161 0.028 7 256190 1771 1975 205 1.000 0.159 0.277 3.337 0.173 0.012 8 256200 1799 1975 177 1.000 0.160 -0.025 2.981 0.180 -0.002 9 256240 1831 1975 145 1.000 0.196 0.509 3.114 0.217 -0.005 10 256250 1846 1975 130 1.000 0.152 0.089 2.758 0.175 0.005 11 256270 1827 1975 149 1.000 0.177 0.515 3.436 0.201 -0.025 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.170 0.485 3.893 0.185 -0.004 STANDARD DEVIATION 33 0.000 0.021 0.362 1.070 0.020 0.017 MEDIAN (50TH QUANTILE) 149 1.000 0.167 0.509 3.436 0.180 -0.004 INTERQUARTILE RANGE 29 0.000 0.030 0.626 1.177 0.026 0.020 MINIMUM VALUE 87 1.000 0.140 -0.025 2.758 0.157 -0.031 LOWER HINGE (25TH QUANTILE) 138 1.000 0.155 0.201 3.218 0.174 -0.014 UPPER HINGE (75TH QUANTILE) 167 1.000 0.185 0.827 4.396 0.199 0.006 MAXIMUM VALUE 205 1.000 0.204 1.001 6.258 0.217 0.028 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.399 0.086 0.012 -0.215 3.273 0.178 0.601 MINIMUM CORRELATION: 0.178 SERIES 256020 AND 256240 145 YEARS MAXIMUM CORRELATION: 0.601 SERIES 256130 AND 256190 157 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 0.563 0.415 0.286 0.590 0.595 0.489 0.406 0.312 0.395 0.551 SDEV 0.000 0.262 0.312 0.100 0.170 0.199 0.182 0.236 0.187 0.158 SERR 0.000 0.151 0.180 0.041 0.037 0.038 0.027 0.035 0.028 0.024 EPS 0.767 0.684 0.624 0.904 0.925 0.901 0.872 0.819 0.868 0.928 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 0.498 0.364 0.300 0.334 0.366 0.273 0.376 SDEV 0.137 0.176 0.207 0.186 0.202 0.202 0.222 SERR 0.019 0.024 0.028 0.025 0.027 0.027 0.030 EPS 0.916 0.863 0.825 0.847 0.864 0.805 0.869 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 0.998 0.123 0.632 4.163 0.132 0.037 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.194 0.115 0.008 26 179 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.74 1.00 1.04 1.78 9.59 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.13 0.00 0.87 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 0.037 0.007 0.066 -0.084 0.040 -0.027 0.076 0.003 0.044 0.024 PACF 0.037 0.005 0.066 -0.089 0.047 -0.035 0.092 -0.020 0.060 -0.002 95% C.L. 0.140 0.140 0.140 0.140 0.141 0.142 0.142 0.143 0.143 0.143 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |---------- 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 -0.002 0.069 -0.088 0.044 -0.031 0.076 -0.002 0.043 0.023 PACF 0.000 -0.002 0.069 -0.088 0.046 -0.037 0.091 -0.019 0.059 0.000 95% C.L. 0.140 0.140 0.140 0.140 0.141 0.142 0.142 0.143 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 2 0.005 0.000 -0.002 |========================= 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 0.997 0.135 0.458 3.384 0.117 0.371 |------------ 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 0.369 0.288 0.197 0.051 0.096 0.034 0.102 0.055 0.079 0.055 PACF 0.369 0.176 0.053 -0.087 0.067 -0.014 0.094 -0.021 0.046 -0.014 95% C.L. 0.140 0.158 0.168 0.172 0.172 0.173 0.173 0.175 0.175 0.176 |------------------- 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 2 0.169 0.304 0.182 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.16 MINUTES