RUN: aust FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: aust007l.rwl LOG FILE PROCESSED: aust007l.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_LATE 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 0.133 0.074 2.458 11.104 0.302 0.723 2 249002 1775 1975 201 0.160 0.075 1.598 6.794 0.262 0.662 3 249003 1795 1975 181 0.232 0.121 1.415 4.745 0.256 0.751 4 249004 1784 1975 192 0.142 0.050 0.573 3.950 0.285 0.511 5 249005 1800 1975 176 0.214 0.170 3.672 25.094 0.442 0.524 6 250007 1782 1975 194 0.146 0.088 1.602 7.541 0.393 0.702 7 250012 1824 1975 152 0.161 0.061 0.561 2.827 0.255 0.606 8 250013 1782 1975 194 0.112 0.056 1.042 3.985 0.380 0.585 9 250015 1824 1975 152 0.130 0.071 1.797 6.782 0.368 0.567 10 250017 1850 1975 126 0.133 0.060 1.120 4.185 0.289 0.678 11 250019 1806 1975 170 0.123 0.062 2.263 13.123 0.324 0.589 12 250020 1745 1975 231 0.209 0.178 2.002 7.669 0.494 0.680 13 250021 1899 1975 77 0.222 0.097 0.949 5.260 0.452 0.073 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 0.163 0.090 1.619 7.928 0.346 0.589 STANDARD DEVIATION 38 0.042 0.042 0.856 5.939 0.081 0.172 MEDIAN (50TH QUANTILE) 180 0.146 0.074 1.598 6.782 0.324 0.606 INTERQUARTILE RANGE 42 0.075 0.036 0.960 3.484 0.107 0.114 MINIMUM VALUE 77 0.112 0.050 0.561 2.827 0.255 0.073 LOWER HINGE (25TH QUANTILE) 152 0.133 0.061 1.042 4.185 0.285 0.567 UPPER HINGE (75TH QUANTILE) 194 0.209 0.097 2.002 7.669 0.393 0.680 MAXIMUM VALUE 231 0.232 0.178 3.672 25.094 0.494 0.751 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.466 0.159 0.018 -0.327 2.344 0.114 0.736 MINIMUM CORRELATION: 0.114 SERIES 249001 AND 250021 77 YEARS MAXIMUM CORRELATION: 0.736 SERIES 249002 AND 250007 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 -0.345 0.325 0.426 0.363 0.447 0.383 0.342 SDEV 0.000 0.299 0.261 0.204 0.145 0.194 0.191 SERR 0.000 0.056 0.035 0.025 0.018 0.022 0.022 EPS 2.424 0.827 0.895 0.873 0.910 0.890 0.871 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 0.181 0.100 1.887 7.543 0.244 0.786 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.025 -0.010 0.052 103 128 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.46 3.55 1.00 1.26 4.81 30.61 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.23 0.00 0.71 0.95 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 0.783 0.758 0.707 0.668 0.620 0.565 0.517 0.479 0.477 0.422 PACF 0.783 0.376 0.127 0.058 -0.002 -0.050 -0.040 0.001 0.116 -0.043 95% C.L. 0.132 0.196 0.242 0.275 0.302 0.323 0.340 0.353 0.364 0.375 |------------------ 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 4 0.695 0.393 0.273 0.129 0.111 |================== 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 0.29328528 0.05260497 0.00000000 0.10328134 2 249002 1 0.24502951 0.02452693 0.00000000 0.11106215 3 249003 1 0.33135924 0.01862541 0.00000000 0.13812083 4 249004 1 0.12900771 0.01662465 0.00000000 0.10344225 5 249005 3 0.00000000 0.00000000 -0.00183217 0.37572661 6 250007 1 0.24387673 0.02487444 0.00000000 0.09600598 7 250012 1 0.12410641 0.07690443 0.00000000 0.15031275 8 250013 1 0.17339562 0.02612593 0.00000000 0.07840651 9 250015 1 0.19820161 0.04559656 0.00000000 0.10207722 10 250017 1 0.15693533 0.02392742 0.00000000 0.08450193 11 250019 1 0.18512402 0.00745031 0.00000000 0.01842292 12 250020 3 0.00000000 0.00000000 -0.00130139 0.35970563 13 250021 1 0.01827293 0.04126564 0.00000000 0.21642017 |-------------------- 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 0.320 0.661 5.377 0.300 0.254 2 249002 1775 1975 201 1.000 0.281 0.841 9.379 0.261 0.080 3 249003 1795 1975 181 1.000 0.347 0.651 3.335 0.256 0.498 4 249004 1784 1975 192 1.000 0.278 0.020 3.964 0.284 0.149 5 249005 1800 1975 176 1.020 0.562 3.109 22.675 0.440 0.312 6 250007 1782 1975 194 0.999 0.472 1.085 5.664 0.390 0.497 7 250012 1824 1975 152 1.000 0.361 0.642 3.324 0.253 0.586 8 250013 1782 1975 194 1.000 0.323 -0.426 3.241 0.378 0.099 9 250015 1824 1975 152 0.999 0.417 1.227 5.942 0.366 0.397 10 250017 1850 1975 126 1.000 0.335 0.858 4.894 0.286 0.470 11 250019 1806 1975 170 1.001 0.388 2.319 14.669 0.322 0.346 12 250020 1745 1975 231 1.004 0.733 2.191 9.158 0.492 0.561 13 250021 1899 1975 77 1.000 0.437 0.919 5.097 0.447 0.069 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.002 0.404 1.084 7.440 0.344 0.332 STANDARD DEVIATION 38 0.006 0.127 0.957 5.599 0.080 0.188 MEDIAN (50TH QUANTILE) 180 1.000 0.361 0.858 5.377 0.322 0.346 INTERQUARTILE RANGE 42 0.000 0.113 0.576 5.194 0.106 0.348 MINIMUM VALUE 77 0.999 0.278 -0.426 3.241 0.253 0.069 LOWER HINGE (25TH QUANTILE) 152 1.000 0.323 0.651 3.964 0.284 0.149 UPPER HINGE (75TH QUANTILE) 194 1.000 0.437 1.227 9.158 0.390 0.497 MAXIMUM VALUE 231 1.020 0.733 3.109 22.675 0.492 0.586 |------------------------ 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 0.298 0.343 5.179 0.301 0.187 2 249002 1775 1975 201 0.999 0.275 0.926 10.598 0.261 0.034 3 249003 1795 1975 181 0.998 0.338 0.547 3.065 0.256 0.473 4 249004 1784 1975 192 1.000 0.273 0.001 4.018 0.284 0.133 5 249005 1800 1975 176 0.994 0.508 3.065 23.917 0.440 0.254 6 250007 1782 1975 194 0.996 0.462 1.077 5.808 0.390 0.478 7 250012 1824 1975 152 0.997 0.336 0.559 3.347 0.253 0.539 8 250013 1782 1975 194 1.000 0.322 -0.435 3.274 0.378 0.090 9 250015 1824 1975 152 0.997 0.391 0.980 5.231 0.366 0.281 10 250017 1850 1975 126 0.999 0.332 0.849 4.961 0.286 0.460 11 250019 1806 1975 170 0.998 0.371 2.089 13.205 0.322 0.302 12 250020 1745 1975 231 0.978 0.642 1.907 7.685 0.492 0.488 13 250021 1899 1975 77 0.997 0.393 0.430 4.934 0.446 0.010 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 0.996 0.380 0.949 7.325 0.344 0.287 STANDARD DEVIATION 38 0.006 0.104 0.935 5.807 0.080 0.187 MEDIAN (50TH QUANTILE) 180 0.998 0.338 0.849 5.179 0.322 0.281 INTERQUARTILE RANGE 42 0.002 0.071 0.647 3.667 0.106 0.341 MINIMUM VALUE 77 0.978 0.273 -0.435 3.065 0.253 0.010 LOWER HINGE (25TH QUANTILE) 152 0.997 0.322 0.430 4.018 0.284 0.133 UPPER HINGE (75TH QUANTILE) 194 0.999 0.393 1.077 7.685 0.390 0.473 MAXIMUM VALUE 231 1.000 0.642 3.065 23.917 0.492 0.539 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.349 0.130 0.015 -0.276 2.509 0.029 0.625 MINIMUM CORRELATION: 0.029 SERIES 250007 AND 250012 152 YEARS MAXIMUM CORRELATION: 0.625 SERIES 249002 AND 250021 77 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 -0.251 0.366 0.375 0.314 0.453 0.401 0.366 SDEV 0.000 0.249 0.246 0.187 0.140 0.188 0.188 SERR 0.000 0.047 0.033 0.023 0.017 0.021 0.021 EPS 4.027 0.852 0.874 0.846 0.912 0.897 0.882 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 0.977 0.250 -0.183 4.497 0.257 0.250 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.129 0.068 0.157 83 148 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.74 2.02 1.02 1.17 3.19 219.14 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.16 0.00 0.76 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 0.249 0.227 0.050 -0.022 -0.084 -0.028 -0.079 -0.161 -0.143 -0.118 PACF 0.249 0.176 -0.044 -0.070 -0.072 0.028 -0.048 -0.151 -0.074 -0.021 95% C.L. 0.132 0.140 0.146 0.146 0.146 0.147 0.147 0.148 0.151 0.153 |------------------ 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 0.093 0.205 0.176 |======================= 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 0.180 0.240 -0.054 -0.048 -0.103 0.053 0.007 -0.064 -0.101 -0.052 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 0.180 2 0.142 0.215 3 0.171 0.234 -0.137 4 0.160 0.253 -0.124 -0.078 5 0.157 0.247 -0.114 -0.071 -0.042 6 0.162 0.255 -0.101 -0.099 -0.059 0.111 7 0.161 0.256 -0.100 -0.098 -0.062 0.109 0.010 8 0.162 0.271 -0.109 -0.111 -0.076 0.145 0.033 -0.140 9 0.150 0.274 -0.096 -0.118 -0.086 0.135 0.056 -0.126 -0.088 10 0.153 0.279 -0.098 -0.123 -0.082 0.140 0.060 -0.137 -0.094 0.039 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) 1690.52 1684.88 1675.97 1673.56 1674.15 1675.74 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1674.90 1676.88 1674.28 1674.49 1676.13 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 0.171 0.234 -0.137 R-SQUARED DUE TO POOLED AUTOREGRESSION: 9.46 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 110.45 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.171 0.264 -0.052 0.029 -0.043 0.007 -0.013 0.005 -0.003 0.0025 -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 3 0.101 0.160 0.260 -0.078 2 249002 3 0.045 0.045 0.187 -0.096 3 249003 3 0.267 0.370 0.213 0.011 4 249004 3 0.043 0.121 0.155 -0.052 5 249005 3 0.109 0.230 0.157 -0.080 6 250007 3 0.334 0.311 0.375 -0.023 7 250012 3 0.327 0.448 0.241 -0.087 8 250013 3 0.016 0.085 0.044 0.024 9 250015 3 0.130 0.258 0.175 -0.118 10 250017 3 0.244 0.406 0.197 -0.108 11 250019 3 0.113 0.251 0.144 0.033 12 250020 3 0.242 0.513 -0.041 -0.021 13 250021 3 0.075 0.010 0.002 -0.096 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.157 0.247 0.162 -0.053 STANDARD DEVIATION 0 0.111 0.159 0.111 0.052 MEDIAN 3 0.113 0.251 0.175 -0.078 INTERQUARTILE RANGE 0 0.168 0.249 0.069 0.075 MINIMUM VALUE 3 0.016 0.010 -0.041 -0.118 LOWER HINGE 3 0.075 0.121 0.144 -0.096 UPPER HINGE 3 0.244 0.370 0.213 -0.021 MAXIMUM VALUE 3 0.334 0.513 0.375 0.033 |------------------- 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 0.282 0.291 5.162 0.318 0.002 2 249002 1775 1975 201 1.000 0.269 0.717 10.524 0.272 0.003 3 249003 1795 1975 181 1.001 0.288 0.313 3.887 0.309 0.002 4 249004 1784 1975 192 1.000 0.267 0.063 4.290 0.299 0.002 5 249005 1800 1975 176 1.001 0.484 3.484 29.181 0.472 0.011 6 250007 1782 1975 194 1.000 0.377 0.842 4.866 0.403 0.001 7 250012 1824 1975 152 1.000 0.276 0.441 4.303 0.303 0.001 8 250013 1782 1975 194 1.000 0.320 -0.465 3.372 0.392 0.002 9 250015 1824 1975 152 1.000 0.368 0.784 4.963 0.403 -0.017 10 250017 1850 1975 126 1.000 0.289 0.321 4.194 0.344 -0.007 11 250019 1806 1975 170 1.000 0.349 2.013 14.176 0.361 0.000 12 250020 1745 1975 231 1.000 0.558 1.874 8.502 0.567 0.002 13 250021 1899 1975 77 1.000 0.391 0.452 4.894 0.449 -0.024 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.348 0.856 7.870 0.376 -0.002 STANDARD DEVIATION 38 0.000 0.089 1.037 7.131 0.084 0.009 MEDIAN (50TH QUANTILE) 180 1.000 0.320 0.452 4.894 0.361 0.002 INTERQUARTILE RANGE 42 0.000 0.095 0.528 4.212 0.095 0.003 MINIMUM VALUE 77 1.000 0.267 -0.465 3.372 0.272 -0.024 LOWER HINGE (25TH QUANTILE) 152 1.000 0.282 0.313 4.290 0.309 0.000 UPPER HINGE (75TH QUANTILE) 194 1.000 0.377 0.842 8.502 0.403 0.002 MAXIMUM VALUE 231 1.001 0.558 3.484 29.181 0.567 0.011 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.381 0.114 0.013 -0.160 2.316 0.105 0.632 MINIMUM CORRELATION: 0.105 SERIES 249002 AND 250020 201 YEARS MAXIMUM CORRELATION: 0.632 SERIES 249002 AND 250021 77 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 -0.201 0.362 0.407 0.351 0.452 0.414 0.399 SDEV 0.000 0.215 0.217 0.171 0.147 0.161 0.139 SERR 0.000 0.041 0.029 0.021 0.018 0.018 0.016 EPS 10.161 0.849 0.888 0.867 0.912 0.902 0.896 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 0.986 0.239 -0.102 4.735 0.281 -0.070 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.133 0.067 0.133 76 155 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.67 2.19 1.02 1.22 3.42 271.33 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.15 0.00 0.78 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 -0.070 0.021 0.057 -0.061 -0.091 0.022 -0.029 -0.110 -0.063 -0.039 PACF -0.070 0.016 0.060 -0.053 -0.103 0.008 -0.015 -0.108 -0.094 -0.052 95% C.L. 0.132 0.132 0.132 0.133 0.133 0.134 0.134 0.134 0.136 0.136 |------------------ 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 0.003 0.007 -0.002 -0.060 -0.091 0.018 -0.025 -0.111 -0.078 -0.042 PACF 0.003 0.007 -0.002 -0.060 -0.091 0.020 -0.024 -0.117 -0.091 -0.049 95% C.L. 0.132 0.132 0.132 0.132 0.132 0.133 0.133 0.133 0.135 0.136 |----------------- 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 0.004 0.003 0.007 -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 1745 1975 231 0.987 0.252 -0.130 4.458 0.263 0.186 |------------ 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 0.185 0.238 -0.083 -0.045 -0.141 -0.032 -0.092 -0.121 -0.125 -0.060 PACF 0.185 0.211 -0.170 -0.061 -0.071 0.017 -0.055 -0.138 -0.073 0.005 95% C.L. 0.132 0.136 0.143 0.144 0.144 0.147 0.147 0.148 0.149 0.151 |------------------- 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 0.108 0.182 0.237 -0.171 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.19 MINUTES