RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN015L.rwl LOG FILE PROCESSED: FRAN015L.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_LATE 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 4 256080 MISSING VALUES FOUND: 5 IN 1 GAPS / 1889 1893 / -------------------------------------------------------------------- 7 256190 MISSING VALUES FOUND: 6 IN 1 GAPS / 1881 1886 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 256010 1823 1975 153 0.266 0.131 2.398 9.569 0.205 0.845 2 256020 1772 1975 204 0.205 0.090 1.783 7.762 0.242 0.683 3 256040 1845 1975 131 0.315 0.187 0.995 3.929 0.190 0.881 4 256080 1828 1975 148 0.284 0.147 1.060 4.177 0.194 0.843 5 256130 1819 1975 157 0.292 0.212 1.486 4.348 0.210 0.866 6 256170 1889 1975 87 0.264 0.160 1.136 3.805 0.168 0.908 7 256190 1771 1975 205 0.228 0.103 0.547 2.247 0.186 0.857 8 256200 1799 1975 177 0.168 0.055 0.945 3.377 0.199 0.698 9 256240 1831 1975 145 0.380 0.207 1.541 5.081 0.270 0.706 10 256250 1846 1975 130 0.212 0.063 0.704 3.228 0.190 0.646 11 256270 1827 1975 149 0.190 0.079 1.559 5.062 0.199 0.810 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 152 0.255 0.130 1.287 4.780 0.205 0.795 STANDARD DEVIATION 32 0.062 0.057 0.531 2.122 0.028 0.093 MEDIAN (50TH QUANTILE) 149 0.264 0.131 1.136 4.177 0.199 0.843 INTERQUARTILE RANGE 30 0.080 0.089 0.580 1.481 0.018 0.159 MINIMUM VALUE 87 0.168 0.055 0.547 2.247 0.168 0.646 LOWER HINGE (25TH QUANTILE) 137 0.208 0.085 0.970 3.591 0.190 0.702 UPPER HINGE (75TH QUANTILE) 167 0.288 0.174 1.550 5.071 0.208 0.861 MAXIMUM VALUE 204 0.380 0.212 2.398 9.569 0.270 0.908 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.244 0.410 0.055 -0.090 1.449 -0.438 0.801 MINIMUM CORRELATION: -0.438 SERIES 256170 AND 256270 87 YEARS MAXIMUM CORRELATION: 0.801 SERIES 256130 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 0.041 0.025 0.399 0.390 0.417 0.447 0.252 0.323 0.356 0.272 SDEV 0.000 0.574 0.386 0.430 0.337 0.188 0.248 0.321 0.305 0.364 SERR 0.000 0.331 0.223 0.175 0.073 0.036 0.037 0.048 0.045 0.054 EPS 0.099 0.071 0.733 0.807 0.857 0.884 0.771 0.826 0.848 0.798 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 0.218 0.214 0.302 0.326 0.399 0.306 0.380 SDEV 0.335 0.279 0.350 0.315 0.242 0.263 0.351 SERR 0.045 0.038 0.047 0.042 0.033 0.035 0.047 EPS 0.754 0.750 0.827 0.842 0.880 0.829 0.871 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 0.240 0.070 0.892 3.791 0.162 0.763 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.691 0.677 -0.056 47 158 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.43 1.41 1.00 1.18 2.59 7.23 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.16 0.00 0.84 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 0.760 0.727 0.662 0.591 0.610 0.568 0.540 0.508 0.469 0.411 PACF 0.760 0.354 0.098 -0.020 0.190 0.044 -0.008 -0.015 0.001 -0.097 95% C.L. 0.140 0.205 0.250 0.282 0.306 0.328 0.347 0.363 0.377 0.388 |------------------ 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 2 0.641 0.477 0.373 |================== 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 -0.00049127 0.30338320 2 256020 3 0.00000000 0.00000000 -0.00025664 0.23101130 3 256040 3 0.00000000 0.00000000 0.00372839 0.06904052 4 256080 3 0.00000000 0.00000000 0.00146249 0.17018211 5 256130 3 0.00000000 0.00000000 0.00323287 0.03702352 6 256170 3 0.00000000 0.00000000 0.00278432 0.14162791 7 256190 1 0.22353823 0.03985074 0.00000000 0.19795297 8 256200 1 0.18344845 0.07351477 0.00000000 0.15443639 9 256240 3 0.00000000 0.00000000 0.00166037 0.25865516 10 256250 3 0.00000000 0.00000000 -0.00076448 0.26230413 11 256270 3 0.00000000 0.00000000 -0.00025739 0.20950572 |-------------------- 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 0.474 2.341 9.435 0.204 0.831 2 256020 1772 1975 204 1.000 0.434 1.865 8.363 0.241 0.681 3 256040 1845 1975 131 1.045 0.544 2.303 8.647 0.189 0.772 4 256080 1828 1975 148 1.015 0.517 1.197 4.388 0.193 0.847 5 256130 1819 1975 157 1.053 0.475 0.977 3.213 0.211 0.777 6 256170 1889 1975 87 0.980 0.546 1.764 5.156 0.167 0.893 7 256190 1771 1975 205 0.999 0.440 1.132 3.698 0.184 0.835 8 256200 1799 1975 177 1.000 0.280 1.002 3.630 0.198 0.580 9 256240 1831 1975 145 0.999 0.483 1.182 4.081 0.269 0.645 10 256250 1846 1975 130 1.000 0.261 0.736 3.654 0.189 0.586 11 256270 1827 1975 149 1.000 0.402 1.389 4.729 0.197 0.797 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.008 0.441 1.444 5.363 0.204 0.750 STANDARD DEVIATION 33 0.022 0.096 0.545 2.296 0.028 0.109 MEDIAN (50TH QUANTILE) 149 1.000 0.474 1.197 4.388 0.197 0.777 INTERQUARTILE RANGE 29 0.008 0.082 0.748 3.084 0.018 0.170 MINIMUM VALUE 87 0.980 0.261 0.736 3.213 0.167 0.580 LOWER HINGE (25TH QUANTILE) 138 0.999 0.418 1.067 3.676 0.189 0.663 UPPER HINGE (75TH QUANTILE) 167 1.008 0.500 1.814 6.759 0.207 0.833 MAXIMUM VALUE 205 1.053 0.546 2.341 9.435 0.269 0.893 |------------------------ 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 0.360 1.389 6.322 0.204 0.730 2 256020 1772 1975 204 0.992 0.381 1.464 7.013 0.241 0.611 3 256040 1845 1975 131 0.976 0.281 1.944 7.913 0.189 0.531 4 256080 1828 1975 148 0.977 0.298 2.577 12.988 0.194 0.647 5 256130 1819 1975 157 0.983 0.311 0.875 4.207 0.209 0.557 6 256170 1889 1975 87 0.983 0.289 0.730 3.498 0.166 0.704 7 256190 1771 1975 205 0.986 0.285 1.134 4.349 0.184 0.658 8 256200 1799 1975 177 0.996 0.206 0.543 2.989 0.199 0.250 9 256240 1831 1975 145 0.977 0.335 0.717 3.530 0.268 0.436 10 256250 1846 1975 130 0.996 0.237 0.534 3.172 0.189 0.495 11 256270 1827 1975 149 0.983 0.315 1.267 4.484 0.198 0.693 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 0.986 0.300 1.198 5.497 0.204 0.574 STANDARD DEVIATION 33 0.008 0.050 0.632 2.975 0.028 0.142 MEDIAN (50TH QUANTILE) 149 0.983 0.298 1.134 4.349 0.198 0.611 INTERQUARTILE RANGE 29 0.013 0.042 0.703 3.154 0.018 0.163 MINIMUM VALUE 87 0.976 0.206 0.534 2.989 0.166 0.250 LOWER HINGE (25TH QUANTILE) 138 0.980 0.283 0.723 3.514 0.189 0.513 UPPER HINGE (75TH QUANTILE) 167 0.993 0.325 1.426 6.668 0.207 0.676 MAXIMUM VALUE 205 0.996 0.381 2.577 12.988 0.268 0.730 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.316 0.177 0.024 -0.111 2.385 -0.064 0.645 MINIMUM CORRELATION: -0.064 SERIES 256130 AND 256270 149 YEARS MAXIMUM CORRELATION: 0.645 SERIES 256080 AND 256250 130 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 -0.026 0.197 0.256 0.701 0.515 0.413 0.258 0.369 0.380 0.343 SDEV 0.000 0.455 0.534 0.119 0.184 0.210 0.241 0.295 0.336 0.307 SERR 0.000 0.263 0.308 0.049 0.040 0.040 0.036 0.044 0.050 0.046 EPS -0.070 0.428 0.588 0.939 0.899 0.869 0.776 0.854 0.860 0.846 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 0.294 0.315 0.296 0.340 0.378 0.304 0.384 SDEV 0.296 0.246 0.295 0.278 0.270 0.266 0.340 SERR 0.040 0.033 0.040 0.037 0.036 0.036 0.046 EPS 0.821 0.835 0.822 0.850 0.870 0.828 0.873 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 0.979 0.182 0.519 3.098 0.160 0.405 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.421 0.302 -0.080 39 166 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.45 1.27 1.01 1.24 2.51 12.30 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 0.403 0.400 0.344 0.202 0.287 0.223 0.128 0.141 0.071 -0.037 PACF 0.403 0.284 0.148 -0.052 0.140 0.049 -0.078 -0.009 -0.022 -0.147 95% C.L. 0.140 0.161 0.179 0.192 0.196 0.204 0.208 0.210 0.212 0.212 |------------------ 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 0.253 0.244 0.246 0.150 |======================= 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 0.464 0.459 0.386 0.255 0.320 0.224 0.150 0.144 0.030 -0.042 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 0.464 2 0.320 0.311 3 0.279 0.268 0.133 4 0.286 0.283 0.148 -0.054 5 0.293 0.262 0.109 -0.093 0.136 6 0.293 0.263 0.109 -0.093 0.136 0.001 7 0.293 0.274 0.102 -0.084 0.157 0.025 -0.080 8 0.292 0.274 0.104 -0.085 0.158 0.028 -0.077 -0.011 9 0.291 0.267 0.106 -0.072 0.151 0.037 -0.053 0.014 -0.087 10 0.279 0.269 0.099 -0.066 0.172 0.027 -0.039 0.051 -0.047 -0.138 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) 1301.57 1253.76 1234.93 1233.27 1234.68 1232.83 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1234.83 1235.50 1237.48 1237.91 1235.98 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 0.279 0.268 0.133 R-SQUARED DUE TO POOLED AUTOREGRESSION: 30.40 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 143.68 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.279 0.346 0.304 0.215 0.187 0.150 0.121 0.099 0.080 0.0649 0.053 0.043 0.035 0.028 0.023 0.019 0.015 0.012 0.010 0.0080 0.007 0.005 0.004 0.003 0.003 0.002 0.002 0.002 0.001 0.0010 0.001 0.001 0.001 0.000 0.000 0.000 0.000 0.000 0.000 0.0001 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 3 0.587 0.543 0.214 0.050 2 256020 3 0.441 0.436 0.269 0.037 3 256040 3 0.319 0.407 0.192 0.055 4 256080 3 0.468 0.582 0.282 -0.226 5 256130 3 0.457 0.235 0.350 0.212 6 256170 3 0.576 0.459 0.330 0.025 7 256190 3 0.483 0.472 0.288 -0.003 8 256200 3 0.172 0.126 0.256 0.183 9 256240 3 0.230 0.346 0.215 -0.005 10 256250 3 0.313 0.361 0.231 0.062 11 256270 3 0.553 0.484 0.155 0.183 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.418 0.405 0.253 0.052 STANDARD DEVIATION 0 0.140 0.133 0.059 0.120 MEDIAN 3 0.457 0.436 0.256 0.050 INTERQUARTILE RANGE 0 0.202 0.125 0.071 0.111 MINIMUM VALUE 3 0.172 0.126 0.155 -0.226 LOWER HINGE 3 0.316 0.353 0.214 0.011 UPPER HINGE 3 0.518 0.478 0.285 0.123 MAXIMUM VALUE 3 0.587 0.582 0.350 0.212 |------------------- 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 0.237 0.513 4.108 0.262 0.009 2 256020 1772 1975 204 1.000 0.284 1.003 6.226 0.299 -0.011 3 256040 1845 1975 131 1.000 0.232 1.753 8.834 0.229 0.000 4 256080 1828 1975 148 1.000 0.218 1.195 7.251 0.247 -0.015 5 256130 1819 1975 157 1.000 0.229 0.565 5.370 0.230 -0.002 6 256170 1889 1975 87 1.000 0.190 1.073 3.922 0.201 -0.008 7 256190 1771 1975 205 1.000 0.205 0.823 3.910 0.215 -0.002 8 256200 1799 1975 177 1.000 0.188 0.369 3.105 0.209 -0.010 9 256240 1831 1975 145 1.000 0.294 0.580 3.707 0.319 -0.001 10 256250 1846 1975 130 1.000 0.196 0.064 3.110 0.222 -0.001 11 256270 1827 1975 149 1.000 0.209 0.434 3.555 0.236 -0.006 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 153 1.000 0.226 0.761 4.827 0.243 -0.004 STANDARD DEVIATION 33 0.000 0.035 0.470 1.875 0.037 0.007 MEDIAN (50TH QUANTILE) 149 1.000 0.218 0.580 3.922 0.230 -0.002 INTERQUARTILE RANGE 29 0.000 0.034 0.564 2.167 0.037 0.008 MINIMUM VALUE 87 1.000 0.188 0.064 3.105 0.201 -0.015 LOWER HINGE (25TH QUANTILE) 138 1.000 0.200 0.473 3.631 0.218 -0.009 UPPER HINGE (75TH QUANTILE) 167 1.000 0.235 1.038 5.798 0.255 -0.001 MAXIMUM VALUE 205 1.000 0.294 1.753 8.834 0.319 0.009 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 55 0.390 0.106 0.014 0.068 2.596 0.160 0.615 MINIMUM CORRELATION: 0.160 SERIES 256040 AND 256080 131 YEARS MAXIMUM CORRELATION: 0.615 SERIES 256010 AND 256020 153 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 0.381 0.259 0.421 0.575 0.542 0.488 0.410 0.463 0.532 0.483 SDEV 0.000 0.379 0.377 0.157 0.197 0.164 0.172 0.175 0.142 0.235 SERR 0.000 0.219 0.218 0.064 0.043 0.031 0.026 0.026 0.021 0.035 EPS 0.611 0.516 0.751 0.898 0.909 0.900 0.874 0.896 0.919 0.908 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 0.337 0.363 0.388 0.352 0.410 0.312 0.508 SDEV 0.191 0.176 0.199 0.197 0.192 0.204 0.267 SERR 0.026 0.024 0.027 0.027 0.026 0.028 0.036 EPS 0.848 0.862 0.874 0.857 0.884 0.833 0.919 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 0.994 0.153 0.174 2.951 0.183 -0.087 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.317 0.190 -0.029 44 161 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 1.54 1.00 1.09 2.63 14.98 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 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 -0.087 -0.068 -0.020 -0.151 0.134 0.070 -0.033 0.064 0.018 -0.056 PACF -0.087 -0.077 -0.033 -0.164 0.104 0.069 -0.011 0.058 0.070 -0.037 95% C.L. 0.140 0.141 0.141 0.141 0.145 0.147 0.148 0.148 0.148 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 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 -0.005 -0.010 -0.005 -0.147 0.125 0.076 -0.013 0.067 0.014 -0.054 PACF -0.005 -0.010 -0.005 -0.147 0.126 0.074 -0.014 0.050 0.053 -0.050 95% C.L. 0.140 0.140 0.140 0.140 0.143 0.145 0.146 0.146 0.146 0.146 |----------------- 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 0.023 -0.005 -0.010 -0.005 |========================= 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 0.991 0.179 0.501 3.169 0.156 0.441 |------------ 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 0.439 0.429 0.373 0.206 0.310 0.239 0.154 0.164 0.092 0.028 PACF 0.439 0.293 0.150 -0.090 0.163 0.053 -0.068 -0.015 -0.011 -0.087 95% C.L. 0.140 0.164 0.185 0.199 0.203 0.212 0.217 0.220 0.222 0.223 |------------------- 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 0.289 0.262 0.253 0.152 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.17 MINUTES