RUN: FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: ital006e.rwl LOG FILE PROCESSED: ital006e.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 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: 253 1 Cortina dAmpezzo (Nord) WIDTH_EARLY PCAB - 253 2 Italy Norway spruce 1820 4632-1204 1737 1975 - 253 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 253010 1873 1975 103 1.952 0.565 1.140 4.773 0.103 0.811 2 253030 1856 1975 120 1.335 0.419 0.284 2.283 0.122 0.853 3 253050 1905 1975 71 1.727 0.506 0.778 3.149 0.171 0.631 4 253070 1900 1975 76 1.111 0.306 0.221 2.297 0.197 0.593 5 253080 1737 1975 239 0.701 0.257 0.395 2.477 0.171 0.839 6 253100 1865 1975 111 2.154 0.355 0.266 3.495 0.121 0.535 7 253110 1847 1975 129 1.724 0.358 0.703 4.698 0.129 0.652 8 253120 1870 1975 106 1.921 0.420 0.415 3.055 0.156 0.569 9 254130 1746 1975 230 0.931 0.427 0.414 3.688 0.202 0.815 10 254150 1829 1975 147 1.205 0.268 0.560 4.306 0.135 0.695 NUMBER OF SERIES READ IN: 10 FROM 1737 TO 1975 239 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 1.476 0.388 0.518 3.422 0.151 0.699 STANDARD DEVIATION 57 0.487 0.100 0.285 0.941 0.034 0.121 MEDIAN (50TH QUANTILE) 115 1.530 0.389 0.415 3.322 0.146 0.673 INTERQUARTILE RANGE 44 0.810 0.121 0.419 1.829 0.049 0.222 MINIMUM VALUE 71 0.701 0.257 0.221 2.283 0.103 0.535 LOWER HINGE (25TH QUANTILE) 103 1.111 0.306 0.284 2.477 0.122 0.593 UPPER HINGE (75TH QUANTILE) 147 1.921 0.427 0.703 4.306 0.171 0.815 MAXIMUM VALUE 239 2.154 0.565 1.140 4.773 0.202 0.853 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.195 0.291 0.043 -0.285 2.892 -0.465 0.816 MINIMUM CORRELATION: -0.465 SERIES 253030 AND 254130 120 YEARS MAXIMUM CORRELATION: 0.816 SERIES 253010 AND 253030 103 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 42.31 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 1. 1. 1. 3. 15. 28. 45. RBAR 0.645 0.587 0.600 -0.059 0.258 0.294 0.296 SDEV 0.000 0.000 0.000 0.424 0.250 0.273 0.228 SERR 0.000 0.000 0.000 0.245 0.064 0.052 0.034 EPS 0.784 0.759 0.830 -0.474 0.742 0.798 0.808 NSS 2.0 2.2 3.3 5.8 8.2 9.5 10.0 |======================== 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 1737 1975 239 1.104 0.475 -0.258 2.074 0.143 0.921 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.728 0.406 -0.012 11 228 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.57 4.67 1.00 1.17 5.84 29.47 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 1.00 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 116. 44. 71. 103. 147. 239. |----------- 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 0.917 0.896 0.877 0.855 0.819 0.810 0.780 0.766 0.745 0.732 PACF 0.917 0.348 0.162 0.047 -0.096 0.099 -0.051 0.061 -0.005 0.031 95% C.L. 0.129 0.212 0.268 0.312 0.349 0.380 0.408 0.432 0.454 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 0.866 0.536 0.255 0.164 |================== 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 253010 1 2.03329682 0.01859649 0.00000000 1.05565834 2 253030 3 0.00000000 0.00000000 -0.01038135 1.96290481 3 253050 3 0.00000000 0.00000000 -0.00731791 1.99076867 4 253070 3 0.00000000 0.00000000 0.00300998 0.99490529 5 253080 3 0.00000000 0.00000000 0.00237374 0.41623923 6 253100 3 0.00000000 0.00000000 -0.00217278 2.27609015 7 253110 3 0.00000000 0.00000000 0.00268968 1.54966688 8 253120 3 0.00000000 0.00000000 0.00566456 1.61798382 9 254130 3 0.00000000 0.00000000 0.00220397 0.67691970 10 254150 3 0.00000000 0.00000000 -0.00010903 1.21317029 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 253010 1873 1975 103 1.000 0.140 0.502 3.773 0.101 0.517 2 253030 1856 1975 120 1.001 0.157 0.135 3.370 0.121 0.472 3 253050 1905 1975 71 1.000 0.284 0.986 3.344 0.168 0.627 4 253070 1900 1975 76 0.999 0.272 0.419 2.382 0.194 0.569 5 253080 1737 1975 239 1.000 0.290 0.585 3.660 0.170 0.708 6 253100 1865 1975 111 1.000 0.163 0.437 3.491 0.120 0.520 7 253110 1847 1975 129 1.000 0.199 0.529 3.841 0.128 0.631 8 253120 1870 1975 106 1.001 0.199 0.190 3.027 0.155 0.486 9 254130 1746 1975 230 0.997 0.483 1.225 5.768 0.201 0.802 10 254150 1829 1975 147 1.000 0.222 0.547 4.271 0.134 0.690 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 1.000 0.241 0.556 3.693 0.149 0.602 STANDARD DEVIATION 57 0.001 0.100 0.330 0.888 0.034 0.108 MEDIAN (50TH QUANTILE) 115 1.000 0.211 0.516 3.575 0.145 0.598 INTERQUARTILE RANGE 44 0.000 0.121 0.166 0.496 0.049 0.173 MINIMUM VALUE 71 0.997 0.140 0.135 2.382 0.101 0.472 LOWER HINGE (25TH QUANTILE) 103 1.000 0.163 0.419 3.344 0.121 0.517 UPPER HINGE (75TH QUANTILE) 147 1.000 0.284 0.585 3.841 0.170 0.690 MAXIMUM VALUE 239 1.001 0.483 1.225 5.768 0.201 0.802 |------------------------ 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 253010 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 253030 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 253050 -67 47 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 253070 -67 50 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 253080 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 253100 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 253110 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 253120 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 254130 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 254150 -67 98 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 253010 1873 1975 103 1.000 0.138 0.551 3.926 0.101 0.503 2 253030 1856 1975 120 0.999 0.148 0.509 3.852 0.121 0.397 3 253050 1905 1975 71 0.998 0.273 0.976 3.385 0.167 0.609 4 253070 1900 1975 76 0.998 0.190 -0.523 3.215 0.192 0.186 5 253080 1737 1975 239 0.995 0.257 0.289 3.103 0.170 0.645 6 253100 1865 1975 111 0.999 0.146 0.371 3.381 0.119 0.417 7 253110 1847 1975 129 0.998 0.168 0.304 3.428 0.128 0.491 8 253120 1870 1975 106 0.999 0.180 0.272 3.311 0.155 0.382 9 254130 1746 1975 230 0.987 0.396 1.038 5.785 0.200 0.705 10 254150 1829 1975 147 0.997 0.186 0.577 3.747 0.134 0.558 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 0.997 0.208 0.436 3.713 0.149 0.489 STANDARD DEVIATION 57 0.004 0.080 0.432 0.777 0.033 0.152 MEDIAN (50TH QUANTILE) 115 0.998 0.183 0.440 3.406 0.144 0.497 INTERQUARTILE RANGE 44 0.002 0.110 0.288 0.541 0.049 0.212 MINIMUM VALUE 71 0.987 0.138 -0.523 3.103 0.101 0.186 LOWER HINGE (25TH QUANTILE) 103 0.997 0.148 0.289 3.311 0.121 0.397 UPPER HINGE (75TH QUANTILE) 147 0.999 0.257 0.577 3.852 0.170 0.609 MAXIMUM VALUE 239 1.000 0.396 1.038 5.785 0.200 0.705 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.334 0.169 0.025 -0.361 2.470 -0.049 0.600 MINIMUM CORRELATION: -0.049 SERIES 253030 AND 253070 76 YEARS MAXIMUM CORRELATION: 0.600 SERIES 253010 AND 253110 103 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 42.31 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 1. 1. 1. 3. 15. 28. 45. RBAR 0.573 0.648 0.580 0.080 0.278 0.366 0.376 SDEV 0.000 0.000 0.000 0.230 0.147 0.213 0.226 SERR 0.000 0.000 0.000 0.133 0.038 0.040 0.034 EPS 0.729 0.804 0.818 0.335 0.760 0.846 0.858 NSS 2.0 2.2 3.3 5.8 8.2 9.5 10.0 |======================== 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 1737 1975 239 1.000 0.252 0.706 4.530 0.148 0.687 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.223 0.147 0.042 30 209 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 3.07 1.01 1.14 4.22 125.10 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 1.00 0.13 0.00 0.87 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 0.684 0.613 0.506 0.459 0.330 0.331 0.264 0.233 0.182 0.167 PACF 0.684 0.272 0.031 0.066 -0.122 0.104 -0.013 -0.007 -0.012 -0.004 95% C.L. 0.129 0.180 0.212 0.231 0.246 0.253 0.261 0.265 0.268 0.270 |------------------ 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 0.520 0.493 0.285 |======================= 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 0.485 0.397 0.241 0.150 0.000 -0.008 -0.133 -0.176 -0.142 -0.158 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 0.485 2 0.382 0.212 3 0.386 0.219 -0.018 4 0.386 0.225 -0.007 -0.029 5 0.382 0.224 0.022 0.022 -0.131 6 0.383 0.224 0.022 0.019 -0.135 0.012 7 0.385 0.207 0.024 0.022 -0.107 0.060 -0.125 8 0.373 0.212 0.015 0.024 -0.105 0.078 -0.090 -0.091 9 0.377 0.216 0.011 0.028 -0.106 0.078 -0.099 -0.106 0.041 10 0.379 0.212 0.007 0.032 -0.111 0.079 -0.099 -0.097 0.058 -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) 1260.15 1198.06 1189.08 1191.00 1192.80 1190.67 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1192.64 1190.86 1190.88 1192.47 1194.03 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 0.382 0.212 R-SQUARED DUE TO POOLED AUTOREGRESSION: 26.96 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 136.90 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.382 0.358 0.218 0.159 0.107 0.075 0.051 0.035 0.024 0.0168 0.012 0.008 0.006 0.004 0.003 0.002 0.001 0.001 0.001 0.0004 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 253010 2 0.276 0.462 0.103 2 253030 2 0.183 0.335 0.160 3 253050 2 0.444 0.660 -0.072 4 253070 2 0.073 0.172 0.091 5 253080 2 0.469 0.487 0.254 6 253100 2 0.193 0.370 0.123 7 253110 2 0.279 0.413 0.177 8 253120 2 0.171 0.322 0.161 9 254130 2 0.578 0.550 0.243 10 254150 2 0.335 0.513 0.104 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.300 0.428 0.134 STANDARD DEVIATION 0 0.157 0.137 0.092 MEDIAN 2 0.277 0.438 0.141 INTERQUARTILE RANGE 0 0.262 0.178 0.074 MINIMUM VALUE 2 0.073 0.172 -0.072 LOWER HINGE 2 0.183 0.335 0.103 UPPER HINGE 2 0.444 0.513 0.177 MAXIMUM VALUE 2 0.578 0.660 0.254 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 253010 1873 1975 103 1.000 0.117 0.568 4.783 0.121 0.005 2 253030 1856 1975 120 1.000 0.133 0.451 3.332 0.143 0.005 3 253050 1905 1975 71 1.000 0.215 0.884 4.766 0.205 -0.017 4 253070 1900 1975 76 1.000 0.186 -0.767 3.498 0.209 0.011 5 253080 1737 1975 239 1.000 0.187 0.199 3.296 0.210 -0.032 6 253100 1865 1975 111 1.000 0.132 0.551 2.879 0.143 0.007 7 253110 1847 1975 129 1.000 0.142 0.376 3.256 0.153 0.004 8 253120 1870 1975 106 1.000 0.164 0.136 3.169 0.176 0.008 9 254130 1746 1975 230 1.001 0.255 1.413 10.856 0.247 -0.051 10 254150 1829 1975 147 1.000 0.151 0.245 4.111 0.160 0.014 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 133 1.000 0.168 0.406 4.395 0.177 -0.005 STANDARD DEVIATION 57 0.000 0.043 0.559 2.365 0.039 0.022 MEDIAN (50TH QUANTILE) 115 1.000 0.158 0.414 3.415 0.168 0.005 INTERQUARTILE RANGE 44 0.000 0.053 0.369 1.510 0.066 0.025 MINIMUM VALUE 71 1.000 0.117 -0.767 2.879 0.121 -0.051 LOWER HINGE (25TH QUANTILE) 103 1.000 0.133 0.199 3.256 0.143 -0.017 UPPER HINGE (75TH QUANTILE) 147 1.000 0.187 0.568 4.766 0.209 0.008 MAXIMUM VALUE 239 1.001 0.255 1.413 10.856 0.247 0.014 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.390 0.147 0.022 -0.691 3.107 0.006 0.590 MINIMUM CORRELATION: 0.006 SERIES 253070 AND 254150 76 YEARS MAXIMUM CORRELATION: 0.590 SERIES 253050 AND 253100 71 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 42.31 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1790. 1815. 1840. 1865. 1890. 1915. 1940. CORR 1. 1. 1. 3. 15. 28. 45. RBAR 0.230 0.304 0.497 0.243 0.369 0.432 0.418 SDEV 0.000 0.000 0.000 0.070 0.134 0.127 0.196 SERR 0.000 0.000 0.000 0.040 0.034 0.024 0.029 EPS 0.374 0.492 0.763 0.650 0.828 0.878 0.878 NSS 2.0 2.2 3.3 5.8 8.2 9.5 10.0 |======================== 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 1737 1975 239 1.000 0.162 0.675 4.951 0.171 -0.012 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.227 0.184 -0.054 31 208 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.63 2.18 1.01 1.13 3.31 13.85 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 1.00 0.12 0.00 0.88 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 -0.012 -0.014 0.048 0.132 -0.116 0.086 -0.004 -0.009 -0.029 0.143 PACF -0.012 -0.014 0.047 0.134 -0.113 0.088 -0.020 -0.014 -0.007 0.112 95% C.L. 0.129 0.129 0.129 0.130 0.132 0.134 0.135 0.135 0.135 0.135 |------------------ 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 0.001 0.003 0.047 0.133 -0.113 0.086 -0.005 -0.006 -0.029 0.140 PACF 0.001 0.003 0.047 0.133 -0.115 0.087 -0.020 -0.013 -0.006 0.111 95% C.L. 0.129 0.129 0.129 0.130 0.132 0.134 0.134 0.134 0.134 0.135 |----------------- 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 0.001 0.003 |========================= 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 1737 1975 239 1.002 0.196 0.837 4.753 0.141 0.521 |------------ 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 0.519 0.447 0.329 0.300 0.129 0.171 0.089 0.072 0.031 0.075 PACF 0.519 0.243 0.040 0.076 -0.144 0.089 -0.030 -0.014 -0.002 0.047 95% C.L. 0.129 0.160 0.180 0.190 0.198 0.199 0.201 0.202 0.203 0.203 |------------------- 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 0.320 0.392 0.250 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.14 MINUTES