RUN: SWIT001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SWIT112L.rwl.conv LOG FILE PROCESSED: SWIT112L.rwl.conv_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 50 25 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 372 1 Lauenen BE BrŸchli WIDTH_LATE PCAB - 372 2 Switzerland Norway spruce 1500 4625-719 1701 1976 - 372 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 372011 1814 1976 163 0.373 0.100 0.079 2.704 0.218 0.507 2 372012 1810 1976 167 0.320 0.120 0.658 3.709 0.228 0.738 3 372021 1705 1976 272 0.238 0.113 1.584 5.774 0.212 0.788 4 372022 1726 1976 251 0.270 0.117 2.165 10.423 0.218 0.768 5 372031 1701 1976 276 0.169 0.046 2.206 14.582 0.169 0.546 6 372032 1709 1976 268 0.236 0.084 1.395 6.079 0.191 0.757 7 372041 1769 1976 208 0.231 0.102 0.698 2.925 0.196 0.792 8 372042 1748 1976 229 0.216 0.087 0.526 2.720 0.192 0.766 9 372051 1734 1976 243 0.162 0.086 1.525 5.897 0.232 0.839 10 372052 1755 1976 222 0.179 0.110 2.733 14.113 0.228 0.779 11 372091 1813 1976 164 0.212 0.079 0.838 4.599 0.304 0.478 12 372092 1788 1976 189 0.220 0.091 0.448 2.823 0.286 0.601 NUMBER OF SERIES READ IN: 12 FROM 1701 TO 1976 276 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 0.236 0.094 1.238 6.362 0.223 0.697 STANDARD DEVIATION 42 0.061 0.020 0.827 4.326 0.039 0.126 MEDIAN (50TH QUANTILE) 225 0.226 0.095 1.117 5.186 0.218 0.761 INTERQUARTILE RANGE 81 0.059 0.026 1.282 5.377 0.036 0.210 MINIMUM VALUE 163 0.162 0.046 0.079 2.704 0.169 0.478 LOWER HINGE (25TH QUANTILE) 178 0.195 0.085 0.592 2.874 0.194 0.573 UPPER HINGE (75TH QUANTILE) 259 0.254 0.111 1.875 8.251 0.230 0.784 MAXIMUM VALUE 276 0.373 0.120 2.733 14.582 0.304 0.839 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.404 0.213 0.026 -0.552 2.659 -0.094 0.759 MINIMUM CORRELATION: -0.094 SERIES 372021 AND 372042 229 YEARS MAXIMUM CORRELATION: 0.759 SERIES 372011 AND 372012 163 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 70.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 10. 21. 28. 45. 66. 66. 66. 66. RBAR 0.507 0.166 0.304 0.355 0.391 0.473 0.556 0.520 SDEV 0.277 0.366 0.200 0.241 0.191 0.259 0.177 0.137 SERR 0.087 0.080 0.038 0.036 0.024 0.032 0.022 0.017 EPS 0.872 0.621 0.818 0.867 0.885 0.915 0.938 0.929 NSS 6.7 8.3 10.3 11.9 12.0 12.0 12.0 12.0 |======================== 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 1701 1976 276 0.225 0.063 0.849 4.454 0.173 0.652 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.478 0.283 0.020 64 212 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.67 1.83 1.00 1.30 3.13 11.44 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.12 0.00 0.85 0.97 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 226. 82. 163. 178. 260. 276. |----------- 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 0.650 0.635 0.516 0.438 0.446 0.356 0.336 0.269 0.245 0.246 PACF 0.650 0.369 0.031 -0.028 0.148 -0.032 -0.012 -0.036 0.020 0.063 95% C.L. 0.120 0.163 0.196 0.215 0.227 0.240 0.247 0.254 0.258 0.261 |------------------ 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 0.508 0.406 0.378 |================== 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 372011 3 0.00000000 0.00000000 -0.00085585 0.44330832 2 372012 3 0.00000000 0.00000000 -0.00168152 0.46118751 3 372021 1 0.36141154 0.08081841 0.00000000 0.22233981 4 372022 3 0.00000000 0.00000000 -0.00029635 0.30765927 5 372031 1 0.11349466 0.03282456 0.00000000 0.15695406 6 372032 3 0.00000000 0.00000000 -0.00003405 0.24014004 7 372041 3 0.00000000 0.00000000 -0.00118840 0.35562989 8 372042 3 0.00000000 0.00000000 -0.00092462 0.32279360 9 372051 1 0.30611053 0.02328675 0.00000000 0.10832527 10 372052 1 0.42743409 0.04208085 0.00000000 0.13412558 11 372091 1 0.18470758 0.03448423 0.00000000 0.18008596 12 372092 1 0.33978108 0.00576970 0.00000000 0.01345352 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 372011 1814 1976 163 0.999 0.251 0.451 3.347 0.217 0.404 2 372012 1810 1976 167 0.997 0.264 0.545 3.724 0.227 0.436 3 372021 1705 1976 272 1.000 0.446 2.112 9.158 0.211 0.760 4 372022 1726 1976 251 1.000 0.429 2.494 13.223 0.217 0.763 5 372031 1701 1976 276 1.000 0.221 0.870 5.532 0.168 0.423 6 372032 1709 1976 268 1.000 0.359 1.448 6.273 0.190 0.755 7 372041 1769 1976 208 1.003 0.336 1.697 7.289 0.196 0.672 8 372042 1748 1976 229 1.003 0.305 0.871 3.704 0.192 0.635 9 372051 1734 1976 243 1.000 0.314 0.867 5.221 0.231 0.532 10 372052 1755 1976 222 1.001 0.363 0.913 4.189 0.228 0.622 11 372091 1813 1976 164 1.000 0.324 0.592 3.953 0.302 0.272 12 372092 1788 1976 189 0.999 0.316 0.909 5.334 0.285 0.232 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.000 0.327 1.147 5.912 0.222 0.542 STANDARD DEVIATION 42 0.002 0.067 0.649 2.861 0.038 0.188 MEDIAN (50TH QUANTILE) 225 1.000 0.320 0.890 5.277 0.217 0.577 INTERQUARTILE RANGE 81 0.001 0.076 0.842 2.942 0.035 0.300 MINIMUM VALUE 163 0.997 0.221 0.451 3.347 0.168 0.232 LOWER HINGE (25TH QUANTILE) 178 0.999 0.285 0.730 3.839 0.194 0.414 UPPER HINGE (75TH QUANTILE) 259 1.001 0.361 1.572 6.781 0.229 0.714 MAXIMUM VALUE 276 1.003 0.446 2.494 13.223 0.302 0.763 |------------------------ 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 372011 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 372012 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 372021 -67 182 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 372022 -67 168 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 372031 -67 184 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 372032 -67 179 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 372041 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 372042 -67 153 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 372051 -67 162 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 372052 -67 148 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 372091 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 372092 -67 126 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 372011 1814 1976 163 0.999 0.225 0.225 3.263 0.217 0.249 2 372012 1810 1976 167 0.998 0.249 0.467 3.354 0.227 0.343 3 372021 1705 1976 272 0.991 0.364 1.741 7.112 0.211 0.694 4 372022 1726 1976 251 0.993 0.381 2.077 10.949 0.217 0.717 5 372031 1701 1976 276 0.999 0.211 0.792 5.678 0.169 0.372 6 372032 1709 1976 268 0.993 0.292 1.166 5.244 0.190 0.645 7 372041 1769 1976 208 0.998 0.328 1.887 8.298 0.196 0.658 8 372042 1748 1976 229 0.997 0.290 1.257 5.307 0.192 0.611 9 372051 1734 1976 243 0.996 0.283 0.422 4.620 0.231 0.457 10 372052 1755 1976 222 0.997 0.316 0.861 4.600 0.228 0.505 11 372091 1813 1976 164 0.999 0.320 0.636 4.062 0.302 0.250 12 372092 1788 1976 189 0.996 0.280 0.589 4.812 0.285 0.109 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 0.996 0.295 1.010 5.608 0.222 0.468 STANDARD DEVIATION 42 0.003 0.051 0.616 2.212 0.038 0.203 MEDIAN (50TH QUANTILE) 225 0.997 0.291 0.826 5.028 0.217 0.481 INTERQUARTILE RANGE 81 0.004 0.059 0.971 2.064 0.036 0.355 MINIMUM VALUE 163 0.991 0.211 0.225 3.263 0.169 0.109 LOWER HINGE (25TH QUANTILE) 178 0.995 0.264 0.528 4.331 0.194 0.297 UPPER HINGE (75TH QUANTILE) 259 0.998 0.324 1.499 6.395 0.230 0.652 MAXIMUM VALUE 276 0.999 0.381 2.077 10.949 0.302 0.717 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.423 0.127 0.016 0.141 2.074 0.197 0.696 MINIMUM CORRELATION: 0.197 SERIES 372041 AND 372091 164 YEARS MAXIMUM CORRELATION: 0.696 SERIES 372011 AND 372012 163 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 70.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 10. 21. 28. 45. 66. 66. 66. 66. RBAR 0.731 0.208 0.295 0.384 0.427 0.527 0.547 0.454 SDEV 0.069 0.353 0.207 0.175 0.170 0.218 0.189 0.145 SERR 0.022 0.077 0.039 0.026 0.021 0.027 0.023 0.018 EPS 0.948 0.684 0.812 0.881 0.899 0.930 0.935 0.909 NSS 6.7 8.3 10.3 11.9 12.0 12.0 12.0 12.0 |======================== 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 1701 1976 276 0.984 0.204 0.800 4.831 0.162 0.503 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.544 0.287 -0.086 74 202 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.32 0.71 1.01 1.14 1.85 10.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.13 0.00 0.85 0.97 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 0.501 0.497 0.318 0.226 0.260 0.156 0.150 0.064 0.039 0.037 PACF 0.501 0.329 -0.021 -0.059 0.149 -0.029 -0.028 -0.057 -0.011 0.022 95% C.L. 0.120 0.148 0.170 0.178 0.183 0.188 0.190 0.191 0.192 0.192 |------------------ 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 0.336 0.336 0.332 |======================= 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 0.512 0.505 0.313 0.202 0.215 0.147 0.157 0.044 0.052 0.032 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 0.512 2 0.343 0.330 3 0.358 0.345 -0.045 4 0.354 0.377 -0.011 -0.093 5 0.365 0.378 -0.057 -0.136 0.121 6 0.362 0.382 -0.055 -0.145 0.112 0.025 7 0.362 0.380 -0.053 -0.144 0.106 0.020 0.014 8 0.363 0.383 -0.040 -0.162 0.100 0.067 0.059 -0.123 9 0.365 0.382 -0.041 -0.164 0.102 0.067 0.053 -0.128 0.014 10 0.364 0.388 -0.044 -0.167 0.097 0.075 0.055 -0.147 -0.004 0.050 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) 1969.77 1887.85 1858.12 1859.57 1859.17 1857.11 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1858.94 1860.88 1858.70 1860.64 1861.95 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 0.343 0.330 R-SQUARED DUE TO POOLED AUTOREGRESSION: 34.23 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 152.05 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.343 0.447 0.267 0.239 0.170 0.137 0.103 0.081 0.062 0.0477 0.037 0.028 0.022 0.017 0.013 0.010 0.008 0.006 0.005 0.0035 0.003 0.002 0.002 0.001 0.001 0.001 0.001 0.000 0.000 0.0003 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 372011 2 0.072 0.228 0.091 2 372012 2 0.154 0.297 0.155 3 372021 2 0.498 0.580 0.166 4 372022 2 0.542 0.569 0.211 5 372031 2 0.161 0.321 0.143 6 372032 2 0.461 0.472 0.268 7 372041 2 0.475 0.530 0.197 8 372042 2 0.384 0.536 0.123 9 372051 2 0.281 0.322 0.296 10 372052 2 0.338 0.341 0.327 11 372091 2 0.080 0.220 0.124 12 372092 2 0.037 0.096 0.122 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.290 0.376 0.185 STANDARD DEVIATION 0 0.184 0.158 0.076 MEDIAN 2 0.310 0.332 0.160 INTERQUARTILE RANGE 0 0.351 0.271 0.116 MINIMUM VALUE 2 0.037 0.096 0.091 LOWER HINGE 2 0.117 0.263 0.124 UPPER HINGE 2 0.468 0.533 0.240 MAXIMUM VALUE 2 0.542 0.580 0.327 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 372011 1814 1976 163 1.000 0.217 0.171 3.216 0.243 -0.005 2 372012 1810 1976 167 1.000 0.230 0.291 3.084 0.260 0.014 3 372021 1705 1976 272 1.000 0.258 1.015 7.941 0.268 -0.008 4 372022 1726 1976 251 1.000 0.256 1.012 6.565 0.271 -0.007 5 372031 1701 1976 276 1.000 0.193 0.573 6.063 0.198 -0.011 6 372032 1709 1976 268 1.000 0.214 0.664 4.381 0.238 -0.021 7 372041 1769 1976 208 1.000 0.241 1.063 6.308 0.254 0.033 8 372042 1748 1976 229 1.000 0.228 0.498 4.211 0.243 0.001 9 372051 1734 1976 243 1.001 0.237 -0.401 4.529 0.263 0.022 10 372052 1755 1976 222 1.001 0.253 0.425 5.138 0.261 0.022 11 372091 1813 1976 164 1.000 0.307 0.513 4.147 0.333 0.007 12 372092 1788 1976 189 1.000 0.276 0.438 4.711 0.297 0.013 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.000 0.242 0.522 5.024 0.261 0.005 STANDARD DEVIATION 42 0.000 0.030 0.410 1.441 0.033 0.016 MEDIAN (50TH QUANTILE) 225 1.000 0.239 0.505 4.620 0.261 0.004 INTERQUARTILE RANGE 81 0.000 0.035 0.480 2.006 0.027 0.025 MINIMUM VALUE 163 1.000 0.193 -0.401 3.084 0.198 -0.021 LOWER HINGE (25TH QUANTILE) 178 1.000 0.222 0.358 4.179 0.243 -0.007 UPPER HINGE (75TH QUANTILE) 259 1.000 0.257 0.838 6.185 0.270 0.018 MAXIMUM VALUE 276 1.001 0.307 1.063 7.941 0.333 0.033 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.402 0.099 0.012 0.623 3.877 0.195 0.710 MINIMUM CORRELATION: 0.195 SERIES 372012 AND 372022 167 YEARS MAXIMUM CORRELATION: 0.710 SERIES 372011 AND 372012 163 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 70.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 10. 21. 28. 45. 66. 66. 66. 66. RBAR 0.525 0.273 0.314 0.364 0.435 0.421 0.461 0.493 SDEV 0.105 0.167 0.210 0.137 0.138 0.159 0.147 0.119 SERR 0.033 0.037 0.040 0.020 0.017 0.020 0.018 0.015 EPS 0.880 0.757 0.825 0.872 0.902 0.897 0.911 0.921 NSS 6.7 8.3 10.3 11.9 12.0 12.0 12.0 12.0 |======================== 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 1701 1976 276 0.994 0.164 -0.112 3.713 0.188 -0.090 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.276 0.146 0.012 66 210 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.87 1.97 1.00 1.15 3.12 22.03 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.12 0.00 0.85 0.97 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 -0.090 0.105 -0.035 -0.110 0.131 -0.009 0.067 -0.047 -0.031 0.024 PACF -0.090 0.097 -0.018 -0.127 0.121 0.036 0.035 -0.049 -0.020 0.023 95% C.L. 0.120 0.121 0.123 0.123 0.124 0.126 0.126 0.127 0.127 0.127 |------------------ 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 2 0.018 -0.081 0.098 |---------- 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 0.002 0.011 -0.041 -0.116 0.123 0.021 0.056 -0.047 -0.038 0.022 PACF 0.002 0.011 -0.041 -0.116 0.126 0.022 0.043 -0.054 -0.008 0.018 95% C.L. 0.120 0.120 0.120 0.121 0.122 0.124 0.124 0.124 0.125 0.125 |----------------- 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 0.002 0.002 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 1701 1976 276 0.993 0.198 0.679 4.309 0.154 0.500 |------------ 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 0.498 0.483 0.314 0.218 0.264 0.163 0.150 0.062 0.034 0.032 PACF 0.498 0.312 -0.011 -0.055 0.158 -0.023 -0.033 -0.068 -0.009 0.018 95% C.L. 0.120 0.147 0.169 0.177 0.181 0.186 0.188 0.190 0.190 0.190 |------------------- 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 0.327 0.341 0.318 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.12 MINUTES