RUN: aust FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: aust007w.rwl LOG FILE PROCESSED: aust007w.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: 249 1 Stubaital, Milderaun Alm WIDTH_RING PCAB - 249 2 Austria Norway spruce 1850 4708-1117 1745 1975 - 249 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 249001 1796 1975 180 0.854 0.352 0.967 3.062 0.156 0.856 2 249002 1775 1975 201 0.657 0.272 1.499 5.245 0.187 0.816 3 249003 1795 1975 181 1.091 0.539 1.691 5.396 0.157 0.903 4 249004 1784 1975 192 0.972 0.266 0.837 3.768 0.141 0.784 5 249005 1800 1975 176 1.241 0.485 0.443 2.758 0.162 0.834 6 250007 1782 1975 194 1.047 0.459 1.431 5.321 0.154 0.880 7 250012 1824 1975 152 0.993 0.338 -0.107 2.605 0.194 0.735 8 250013 1782 1975 194 0.847 0.530 1.742 5.116 0.170 0.916 9 250015 1824 1975 152 0.864 0.393 0.741 3.129 0.174 0.872 10 250017 1850 1975 126 0.677 0.252 1.058 3.359 0.157 0.877 11 250019 1806 1975 170 0.727 0.181 0.892 3.996 0.150 0.656 12 250020 1745 1975 231 1.194 0.505 1.023 3.863 0.186 0.829 13 250021 1899 1975 77 1.371 0.265 1.281 5.891 0.150 0.488 NUMBER OF SERIES READ IN: 13 FROM 1745 TO 1975 231 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.964 0.372 1.038 4.116 0.164 0.804 STANDARD DEVIATION 38 0.221 0.121 0.514 1.137 0.016 0.119 MEDIAN (50TH QUANTILE) 180 0.972 0.352 1.023 3.863 0.157 0.834 INTERQUARTILE RANGE 42 0.243 0.219 0.593 2.116 0.021 0.094 MINIMUM VALUE 77 0.657 0.181 -0.107 2.605 0.141 0.488 LOWER HINGE (25TH QUANTILE) 152 0.847 0.266 0.837 3.129 0.154 0.784 UPPER HINGE (75TH QUANTILE) 194 1.091 0.485 1.431 5.245 0.174 0.877 MAXIMUM VALUE 231 1.371 0.539 1.742 5.891 0.194 0.916 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.573 0.206 0.023 -0.771 3.106 0.007 0.897 MINIMUM CORRELATION: 0.007 SERIES 249002 AND 250020 201 YEARS MAXIMUM CORRELATION: 0.897 SERIES 250007 AND 250013 194 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.01 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 1. 28. 55. 66. 66. 78. 78. RBAR -0.514 0.345 0.459 0.393 0.572 0.504 0.287 SDEV 0.000 0.348 0.223 0.164 0.158 0.194 0.225 SERR 0.000 0.066 0.030 0.020 0.019 0.022 0.025 EPS 1.798 0.839 0.907 0.886 0.944 0.930 0.840 NSS 6.6 9.9 11.5 12.0 12.5 13.0 13.0 |======================== 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 1745 1975 231 1.045 0.404 1.267 5.289 0.136 0.857 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.240 0.122 0.162 76 155 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.79 1.91 1.01 1.23 3.14 17.49 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.16 0.00 0.78 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 180. 42. 77. 152. 194. 231. |----------- 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 0.853 0.794 0.704 0.685 0.646 0.631 0.578 0.509 0.463 0.447 PACF 0.853 0.243 -0.066 0.193 0.045 0.051 -0.065 -0.145 0.031 0.095 95% C.L. 0.132 0.206 0.254 0.286 0.313 0.335 0.355 0.371 0.383 0.392 |------------------ 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 0.755 0.628 0.268 |================== 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 249001 1 1.37160838 0.00758540 0.00000000 0.10904744 2 249002 1 0.94595993 0.02672298 0.00000000 0.48395887 3 249003 1 2.08088684 0.03223067 0.00000000 0.74098611 4 249004 3 0.00000000 0.00000000 -0.00343797 1.30379581 5 249005 3 0.00000000 0.00000000 -0.00765904 1.91907465 6 250007 1 1.50409126 0.02015496 0.00000000 0.67379826 7 250012 3 0.00000000 0.00000000 -0.00498566 1.37436390 8 250013 1 2.05317450 0.02790672 0.00000000 0.47517887 9 250015 1 1.33567357 0.01574756 0.00000000 0.36121556 10 250017 1 0.79397547 0.02959307 0.00000000 0.47183403 11 250019 1 0.69361359 0.10155861 0.00000000 0.68900776 12 250020 3 0.00000000 0.00000000 -0.00337953 1.58596539 13 250021 3 0.00000000 0.00000000 0.00027236 1.36015725 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 249001 1796 1975 180 1.000 0.207 0.616 3.369 0.155 0.560 2 249002 1775 1975 201 1.000 0.219 0.069 3.119 0.186 0.473 3 249003 1795 1975 181 1.000 0.218 0.815 4.431 0.155 0.536 4 249004 1784 1975 192 1.000 0.181 0.546 3.351 0.140 0.506 5 249005 1800 1975 176 0.997 0.218 0.499 3.969 0.161 0.537 6 250007 1782 1975 194 1.000 0.238 0.967 4.833 0.152 0.650 7 250012 1824 1975 152 0.997 0.278 0.092 2.688 0.192 0.619 8 250013 1782 1975 194 1.001 0.199 -0.003 2.936 0.169 0.447 9 250015 1824 1975 152 1.001 0.276 0.965 5.415 0.172 0.699 10 250017 1850 1975 126 1.000 0.227 0.779 3.673 0.154 0.665 11 250019 1806 1975 170 1.000 0.207 0.607 4.323 0.149 0.523 12 250020 1745 1975 231 0.996 0.354 0.927 4.226 0.185 0.775 13 250021 1899 1975 77 1.000 0.193 1.299 6.013 0.148 0.481 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.999 0.232 0.629 4.027 0.163 0.575 STANDARD DEVIATION 38 0.002 0.047 0.392 0.985 0.016 0.099 MEDIAN (50TH QUANTILE) 180 1.000 0.218 0.616 3.969 0.155 0.537 INTERQUARTILE RANGE 42 0.000 0.031 0.427 1.080 0.020 0.144 MINIMUM VALUE 77 0.996 0.181 -0.003 2.688 0.140 0.447 LOWER HINGE (25TH QUANTILE) 152 1.000 0.207 0.499 3.351 0.152 0.506 UPPER HINGE (75TH QUANTILE) 194 1.000 0.238 0.927 4.431 0.172 0.650 MAXIMUM VALUE 231 1.001 0.354 1.299 6.013 0.192 0.775 |------------------------ 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 249001 -67 120 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 249002 -67 134 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 249003 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 249004 -67 128 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 249005 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 250007 -67 129 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 250012 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 250013 -67 129 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 250015 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 250017 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 250019 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 250020 -67 154 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 250021 -67 51 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 249001 1796 1975 180 0.999 0.201 0.550 3.262 0.155 0.536 2 249002 1775 1975 201 0.999 0.208 0.089 3.275 0.186 0.413 3 249003 1795 1975 181 0.999 0.192 0.598 3.817 0.155 0.437 4 249004 1784 1975 192 1.000 0.179 0.536 3.310 0.140 0.498 5 249005 1800 1975 176 0.999 0.212 0.448 3.927 0.161 0.515 6 250007 1782 1975 194 1.000 0.235 0.913 4.656 0.152 0.643 7 250012 1824 1975 152 0.997 0.260 0.046 2.583 0.192 0.564 8 250013 1782 1975 194 0.999 0.191 0.136 3.263 0.169 0.388 9 250015 1824 1975 152 0.996 0.227 0.498 3.859 0.172 0.551 10 250017 1850 1975 126 0.999 0.217 0.720 3.628 0.154 0.641 11 250019 1806 1975 170 1.000 0.193 0.474 4.541 0.149 0.462 12 250020 1745 1975 231 0.992 0.286 0.574 3.800 0.185 0.659 13 250021 1899 1975 77 0.998 0.159 1.143 6.388 0.149 0.273 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.998 0.212 0.517 3.870 0.163 0.506 STANDARD DEVIATION 38 0.002 0.034 0.311 0.937 0.016 0.112 MEDIAN (50TH QUANTILE) 180 0.999 0.208 0.536 3.800 0.155 0.515 INTERQUARTILE RANGE 42 0.002 0.035 0.150 0.651 0.020 0.128 MINIMUM VALUE 77 0.992 0.159 0.046 2.583 0.140 0.273 LOWER HINGE (25TH QUANTILE) 152 0.998 0.192 0.448 3.275 0.152 0.437 UPPER HINGE (75TH QUANTILE) 194 0.999 0.227 0.598 3.927 0.172 0.564 MAXIMUM VALUE 231 1.000 0.286 1.143 6.388 0.192 0.659 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.399 0.125 0.014 -0.169 2.811 0.075 0.652 MINIMUM CORRELATION: 0.075 SERIES 250007 AND 250019 170 YEARS MAXIMUM CORRELATION: 0.652 SERIES 249005 AND 250007 176 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.01 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 1. 28. 55. 66. 66. 78. 78. RBAR -0.185 0.392 0.362 0.407 0.576 0.497 0.340 SDEV 0.000 0.228 0.235 0.156 0.145 0.184 0.193 SERR 0.000 0.043 0.032 0.019 0.018 0.021 0.022 EPS 26.946 0.865 0.867 0.892 0.944 0.928 0.870 NSS 6.6 9.9 11.5 12.0 12.5 13.0 13.0 |======================== 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 1745 1975 231 1.000 0.184 0.791 5.071 0.143 0.503 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.097 -0.046 0.190 54 177 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.40 1.46 1.02 1.12 2.58 19.66 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.12 0.00 0.80 0.92 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 0.362 0.185 0.163 0.080 0.145 0.075 -0.045 -0.141 -0.104 PACF 0.501 0.149 -0.060 0.068 -0.032 0.118 -0.041 -0.165 -0.102 0.040 95% C.L. 0.132 0.161 0.175 0.178 0.181 0.181 0.183 0.184 0.184 0.186 |------------------ 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 0.270 0.426 0.149 |======================= 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 0.378 0.253 0.110 0.107 -0.033 0.071 0.008 -0.088 -0.209 -0.145 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 0.378 2 0.330 0.129 3 0.333 0.137 -0.027 4 0.335 0.130 -0.045 0.055 5 0.341 0.125 -0.031 0.092 -0.110 6 0.353 0.115 -0.027 0.078 -0.148 0.110 7 0.356 0.111 -0.025 0.077 -0.144 0.120 -0.028 8 0.352 0.127 -0.045 0.088 -0.148 0.135 0.020 -0.137 9 0.331 0.130 -0.024 0.065 -0.134 0.128 0.040 -0.082 -0.156 10 0.328 0.129 -0.023 0.067 -0.136 0.129 0.040 -0.080 -0.151 -0.014 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) 1442.10 1408.44 1406.59 1408.42 1409.73 1408.91 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1408.11 1409.93 1407.57 1403.88 1405.83 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 0.330 0.129 R-SQUARED DUE TO POOLED AUTOREGRESSION: 15.72 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 118.65 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.330 0.237 0.121 0.070 0.039 0.022 0.012 0.007 0.004 0.0021 0.001 0.001 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 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 249001 2 0.294 0.530 0.014 2 249002 2 0.213 0.330 0.204 3 249003 2 0.266 0.307 0.300 4 249004 2 0.255 0.464 0.072 5 249005 2 0.280 0.450 0.128 6 250007 2 0.422 0.580 0.101 7 250012 2 0.340 0.473 0.165 8 250013 2 0.174 0.327 0.161 9 250015 2 0.315 0.490 0.114 10 250017 2 0.428 0.551 0.145 11 250019 2 0.229 0.403 0.128 12 250020 2 0.436 0.634 0.039 13 250021 2 0.092 0.308 -0.122 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.288 0.450 0.111 STANDARD DEVIATION 0 0.102 0.109 0.101 MEDIAN 2 0.280 0.464 0.128 INTERQUARTILE RANGE 0 0.110 0.201 0.089 MINIMUM VALUE 2 0.092 0.307 -0.122 LOWER HINGE 2 0.229 0.330 0.072 UPPER HINGE 2 0.340 0.530 0.161 MAXIMUM VALUE 2 0.436 0.634 0.300 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 249001 1796 1975 180 1.000 0.169 0.441 3.339 0.190 -0.002 2 249002 1775 1975 201 1.000 0.185 0.130 3.479 0.207 0.020 3 249003 1795 1975 181 1.000 0.164 0.533 3.543 0.180 0.000 4 249004 1784 1975 192 1.000 0.154 0.537 3.876 0.168 0.000 5 249005 1800 1975 176 1.000 0.180 0.563 4.579 0.190 0.007 6 250007 1782 1975 194 1.000 0.179 0.732 5.128 0.196 -0.002 7 250012 1824 1975 152 1.000 0.211 -0.039 3.495 0.239 0.002 8 250013 1782 1975 194 1.000 0.174 0.254 3.745 0.193 0.000 9 250015 1824 1975 152 1.000 0.188 0.306 3.927 0.212 0.000 10 250017 1850 1975 126 1.000 0.164 0.403 3.026 0.187 -0.003 11 250019 1806 1975 170 1.000 0.169 0.425 4.301 0.175 -0.008 12 250020 1745 1975 231 1.000 0.215 0.392 4.315 0.234 0.001 13 250021 1899 1975 77 1.000 0.151 1.015 5.718 0.164 -0.008 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.177 0.438 4.036 0.195 0.000 STANDARD DEVIATION 38 0.000 0.019 0.263 0.760 0.023 0.007 MEDIAN (50TH QUANTILE) 180 1.000 0.174 0.425 3.876 0.190 0.000 INTERQUARTILE RANGE 42 0.000 0.021 0.230 0.819 0.028 0.004 MINIMUM VALUE 77 1.000 0.151 -0.039 3.026 0.164 -0.008 LOWER HINGE (25TH QUANTILE) 152 1.000 0.164 0.306 3.495 0.180 -0.002 UPPER HINGE (75TH QUANTILE) 194 1.000 0.185 0.537 4.315 0.207 0.001 MAXIMUM VALUE 231 1.000 0.215 1.015 5.718 0.239 0.020 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.497 0.093 0.010 -0.611 3.196 0.238 0.649 MINIMUM CORRELATION: 0.238 SERIES 249002 AND 250020 201 YEARS MAXIMUM CORRELATION: 0.649 SERIES 249003 AND 250012 152 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 65.01 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1800. 1825. 1850. 1875. 1900. 1925. 1950. CORR 1. 28. 55. 66. 66. 78. 78. RBAR -0.112 0.379 0.466 0.521 0.614 0.601 0.503 SDEV 0.000 0.185 0.183 0.096 0.107 0.129 0.125 SERR 0.000 0.035 0.025 0.012 0.013 0.015 0.014 EPS -2.031 0.858 0.909 0.929 0.952 0.951 0.929 NSS 6.6 9.9 11.5 12.0 12.5 13.0 13.0 |======================== 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 1745 1975 231 0.999 0.153 0.342 5.164 0.170 -0.089 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.070 0.031 0.079 43 188 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.71 1.01 1.14 1.85 6.68 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.12 0.00 0.81 0.93 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 -0.089 0.056 -0.087 0.050 -0.096 0.138 0.066 -0.038 -0.162 0.002 PACF -0.089 0.048 -0.079 0.034 -0.083 0.116 0.102 -0.053 -0.158 -0.024 95% C.L. 0.132 0.133 0.133 0.134 0.134 0.136 0.138 0.138 0.139 0.142 |------------------ 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 0.004 -0.009 -0.072 0.026 -0.081 0.138 0.088 -0.053 -0.171 -0.004 PACF 0.004 -0.009 -0.072 0.027 -0.083 0.136 0.090 -0.066 -0.151 -0.006 95% C.L. 0.132 0.132 0.132 0.132 0.132 0.133 0.136 0.137 0.137 0.141 |----------------- 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 0.004 -0.009 |========================= 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 1745 1975 231 0.999 0.165 0.614 4.957 0.142 0.367 |------------ 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 0.365 0.227 0.064 0.077 0.005 0.124 0.063 -0.067 -0.177 -0.099 PACF 0.365 0.108 -0.057 0.056 -0.038 0.137 -0.012 -0.153 -0.134 0.029 95% C.L. 0.132 0.148 0.154 0.154 0.155 0.155 0.157 0.157 0.158 0.161 |------------------- 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 0.146 0.326 0.108 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.20 MINUTES