RUN: aust FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: aust007x.rwl LOG FILE PROCESSED: aust007x.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 DENSITY_MAXIMUM 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 0.780 0.095 -0.506 4.074 0.117 0.239 2 249002 1775 1975 201 0.782 0.106 -0.456 3.569 0.120 0.385 3 249003 1795 1975 181 0.822 0.085 -1.055 4.630 0.100 0.213 4 249004 1784 1975 192 0.780 0.095 -0.700 3.615 0.106 0.345 5 249005 1800 1975 176 0.719 0.109 -0.497 3.428 0.148 0.246 6 250007 1782 1975 194 0.684 0.110 -0.379 2.965 0.151 0.321 7 250012 1824 1975 152 0.753 0.096 -0.326 3.015 0.090 0.537 8 250013 1782 1975 194 0.671 0.085 -0.572 3.760 0.135 0.079 9 250015 1824 1975 152 0.683 0.081 -0.559 4.125 0.130 0.061 10 250017 1850 1975 126 0.728 0.084 -0.449 3.207 0.117 0.192 11 250019 1806 1975 170 0.715 0.082 -0.649 4.179 0.084 0.532 12 250020 1745 1975 231 0.676 0.123 -0.244 2.496 0.158 0.465 13 250021 1899 1975 77 0.720 0.102 -0.629 3.510 0.178 -0.118 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 0.732 0.096 -0.540 3.583 0.126 0.269 STANDARD DEVIATION 38 0.048 0.013 0.202 0.583 0.028 0.192 MEDIAN (50TH QUANTILE) 180 0.720 0.095 -0.506 3.569 0.120 0.246 INTERQUARTILE RANGE 42 0.096 0.021 0.180 0.867 0.041 0.192 MINIMUM VALUE 77 0.671 0.081 -1.055 2.496 0.084 -0.118 LOWER HINGE (25TH QUANTILE) 152 0.684 0.085 -0.629 3.207 0.106 0.192 UPPER HINGE (75TH QUANTILE) 194 0.780 0.106 -0.449 4.074 0.148 0.385 MAXIMUM VALUE 231 0.822 0.123 -0.244 4.630 0.178 0.537 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.626 0.144 0.016 -0.905 3.534 0.190 0.818 MINIMUM CORRELATION: 0.190 SERIES 250012 AND 250020 152 YEARS MAXIMUM CORRELATION: 0.818 SERIES 249004 AND 250007 192 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 -0.235 0.509 0.534 0.657 0.790 0.777 0.675 SDEV 0.000 0.276 0.238 0.155 0.076 0.085 0.115 SERR 0.000 0.052 0.032 0.019 0.009 0.010 0.013 EPS 4.819 0.911 0.929 0.958 0.979 0.978 0.964 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 0.745 0.079 -0.759 4.300 0.101 0.266 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.118 -0.055 0.114 27 204 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.21 0.26 1.00 1.09 1.35 3.06 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.09 0.00 0.82 0.91 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 0.265 0.372 0.271 0.225 0.161 0.265 0.211 0.164 0.175 0.212 PACF 0.265 0.325 0.143 0.048 -0.010 0.156 0.094 -0.019 0.009 0.099 95% C.L. 0.132 0.141 0.157 0.165 0.170 0.172 0.179 0.184 0.186 0.189 |------------------ 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 0.188 0.132 0.301 0.143 |================== 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 0.16690955 0.02080408 0.00000000 0.73715717 2 249002 1 0.21127716 0.01382062 0.00000000 0.71155679 3 249003 3 0.00000000 0.00000000 0.00004446 0.81766665 4 249004 3 0.00000000 0.00000000 -0.00090814 0.86763579 5 249005 3 0.00000000 0.00000000 -0.00083280 0.79233897 6 250007 3 0.00000000 0.00000000 -0.00101348 0.78247422 7 250012 3 0.00000000 0.00000000 0.00057286 0.70959741 8 250013 1 0.12383536 0.01308268 0.00000000 0.62639332 9 250015 3 0.00000000 0.00000000 0.00017576 0.66951466 10 250017 3 0.00000000 0.00000000 -0.00071352 0.77300698 11 250019 3 0.00000000 0.00000000 -0.00073964 0.77782738 12 250020 3 0.00000000 0.00000000 -0.00117445 0.81199360 13 250021 3 0.00000000 0.00000000 -0.00009359 0.72365004 |-------------------- 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 0.110 -0.697 4.886 0.116 0.041 2 249002 1775 1975 201 1.000 0.119 -0.518 4.159 0.119 0.160 3 249003 1795 1975 181 1.000 0.103 -1.057 4.639 0.100 0.211 4 249004 1784 1975 192 1.000 0.105 -0.661 4.432 0.106 0.095 5 249005 1800 1975 176 1.000 0.140 -0.578 3.906 0.147 0.132 6 250007 1782 1975 194 1.000 0.140 -0.419 3.375 0.150 0.091 7 250012 1824 1975 152 1.000 0.122 -0.335 3.154 0.089 0.502 8 250013 1782 1975 194 1.000 0.118 -0.697 4.262 0.134 -0.060 9 250015 1824 1975 152 1.000 0.118 -0.592 4.173 0.129 0.053 10 250017 1850 1975 126 1.000 0.110 -0.409 3.158 0.117 0.105 11 250019 1806 1975 170 1.000 0.103 -0.782 4.718 0.084 0.387 12 250020 1745 1975 231 1.000 0.145 -0.232 3.256 0.157 0.090 13 250021 1899 1975 77 1.000 0.142 -0.621 3.501 0.176 -0.117 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.121 -0.584 3.971 0.125 0.130 STANDARD DEVIATION 38 0.000 0.016 0.213 0.622 0.027 0.165 MEDIAN (50TH QUANTILE) 180 1.000 0.118 -0.592 4.159 0.119 0.095 INTERQUARTILE RANGE 42 0.000 0.030 0.277 1.057 0.041 0.107 MINIMUM VALUE 77 1.000 0.103 -1.057 3.154 0.084 -0.117 LOWER HINGE (25TH QUANTILE) 152 1.000 0.110 -0.697 3.375 0.106 0.053 UPPER HINGE (75TH QUANTILE) 194 1.000 0.140 -0.419 4.432 0.147 0.160 MAXIMUM VALUE 231 1.000 0.145 -0.232 4.886 0.176 0.502 |------------------------ 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 1.000 0.108 -0.737 5.094 0.116 0.005 2 249002 1775 1975 201 1.000 0.114 -0.641 4.346 0.119 0.089 3 249003 1795 1975 181 1.000 0.100 -1.092 4.882 0.100 0.172 4 249004 1784 1975 192 1.000 0.103 -0.744 4.738 0.106 0.066 5 249005 1800 1975 176 1.000 0.137 -0.662 4.032 0.147 0.085 6 250007 1782 1975 194 1.000 0.139 -0.469 3.396 0.150 0.071 7 250012 1824 1975 152 0.999 0.101 -0.561 4.251 0.090 0.297 8 250013 1782 1975 194 1.000 0.117 -0.713 4.284 0.134 -0.067 9 250015 1824 1975 152 1.000 0.115 -0.556 4.177 0.129 -0.015 10 250017 1850 1975 126 1.000 0.110 -0.400 3.177 0.117 0.097 11 250019 1806 1975 170 0.999 0.092 -0.774 5.958 0.084 0.220 12 250020 1745 1975 231 1.000 0.141 -0.201 3.322 0.157 0.034 13 250021 1899 1975 77 1.000 0.134 -0.599 3.222 0.176 -0.292 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.116 -0.627 4.221 0.125 0.059 STANDARD DEVIATION 38 0.000 0.016 0.212 0.823 0.027 0.143 MEDIAN (50TH QUANTILE) 180 1.000 0.114 -0.641 4.251 0.119 0.071 INTERQUARTILE RANGE 42 0.000 0.031 0.181 1.342 0.041 0.092 MINIMUM VALUE 77 0.999 0.092 -1.092 3.177 0.084 -0.292 LOWER HINGE (25TH QUANTILE) 152 1.000 0.103 -0.737 3.396 0.106 0.005 UPPER HINGE (75TH QUANTILE) 194 1.000 0.134 -0.556 4.738 0.147 0.097 MAXIMUM VALUE 231 1.000 0.141 -0.201 5.958 0.176 0.297 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.680 0.096 0.011 -0.420 2.406 0.417 0.826 MINIMUM CORRELATION: 0.417 SERIES 250012 AND 250021 77 YEARS MAXIMUM CORRELATION: 0.826 SERIES 249002 AND 250015 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 -0.225 0.508 0.608 0.685 0.801 0.784 0.679 SDEV 0.000 0.283 0.187 0.102 0.072 0.086 0.126 SERR 0.000 0.053 0.025 0.013 0.009 0.010 0.014 EPS 5.537 0.911 0.947 0.963 0.981 0.979 0.965 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 0.095 -0.857 5.143 0.104 0.007 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.037 -0.013 0.072 56 175 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.49 0.83 1.00 1.10 1.92 5.36 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.12 0.00 0.81 0.93 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 0.007 0.186 0.008 -0.019 -0.125 0.021 -0.077 -0.108 -0.083 -0.017 PACF 0.007 0.186 0.006 -0.056 -0.133 0.038 -0.028 -0.122 -0.079 0.017 95% C.L. 0.132 0.132 0.136 0.136 0.136 0.138 0.138 0.139 0.140 0.141 |------------------ 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 0.035 0.006 0.187 |======================= 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 -0.029 0.186 0.022 -0.012 -0.115 0.042 -0.101 -0.111 -0.100 0.008 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 -0.029 2 -0.023 0.185 3 -0.029 0.186 0.033 4 -0.028 0.195 0.032 -0.047 5 -0.034 0.199 0.058 -0.051 -0.132 6 -0.028 0.201 0.055 -0.060 -0.131 0.047 7 -0.026 0.195 0.052 -0.057 -0.120 0.046 -0.052 8 -0.032 0.201 0.036 -0.065 -0.114 0.071 -0.055 -0.132 9 -0.045 0.195 0.043 -0.076 -0.120 0.075 -0.036 -0.135 -0.096 10 -0.040 0.202 0.044 -0.079 -0.114 0.078 -0.038 -0.144 -0.094 0.047 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) 1280.20 1282.01 1275.94 1277.68 1279.17 1277.09 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1278.58 1279.97 1277.93 1277.80 1279.29 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 -0.023 0.185 R-SQUARED DUE TO POOLED AUTOREGRESSION: 3.51 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 103.64 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 -0.023 0.186 -0.009 0.035 -0.002 0.006 -0.001 0.001 0.000 0.0002 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 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 0.066 0.004 0.256 2 249002 2 0.092 0.064 0.287 3 249003 2 0.064 0.141 0.187 4 249004 2 0.068 0.049 0.252 5 249005 2 0.059 0.066 0.227 6 250007 2 0.071 0.053 0.251 7 250012 2 0.171 0.210 0.296 8 250013 2 0.040 -0.054 0.186 9 250015 2 0.035 -0.012 0.185 10 250017 2 0.024 0.086 0.115 11 250019 2 0.135 0.163 0.264 12 250020 2 0.007 0.032 0.077 13 250021 2 0.107 -0.277 0.069 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.072 0.040 0.204 STANDARD DEVIATION 0 0.045 0.119 0.076 MEDIAN 2 0.066 0.053 0.227 INTERQUARTILE RANGE 0 0.052 0.082 0.071 MINIMUM VALUE 2 0.007 -0.277 0.069 LOWER HINGE 2 0.040 0.004 0.185 UPPER HINGE 2 0.092 0.086 0.256 MAXIMUM VALUE 2 0.171 0.210 0.296 |------------------- 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 0.104 -0.852 5.132 0.112 0.005 2 249002 1775 1975 201 1.000 0.109 -0.600 4.096 0.118 -0.016 3 249003 1795 1975 181 1.000 0.097 -1.012 4.860 0.105 -0.005 4 249004 1784 1975 192 1.000 0.099 -0.756 4.769 0.106 -0.002 5 249005 1800 1975 176 1.000 0.133 -0.666 4.008 0.150 -0.002 6 250007 1782 1975 194 1.000 0.134 -0.488 3.501 0.149 -0.014 7 250012 1824 1975 152 1.000 0.092 -0.764 4.996 0.098 -0.013 8 250013 1782 1975 194 1.000 0.115 -0.718 4.027 0.129 0.005 9 250015 1824 1975 152 1.000 0.113 -0.531 3.767 0.125 0.003 10 250017 1850 1975 126 1.000 0.109 -0.461 3.273 0.122 0.005 11 250019 1806 1975 170 1.000 0.086 -1.073 6.740 0.093 -0.041 12 250020 1745 1975 231 1.000 0.141 -0.184 3.288 0.159 0.000 13 250021 1899 1975 77 1.000 0.128 -0.611 3.280 0.150 -0.012 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 171 1.000 0.112 -0.670 4.287 0.124 -0.007 STANDARD DEVIATION 38 0.000 0.017 0.237 0.996 0.022 0.013 MEDIAN (50TH QUANTILE) 180 1.000 0.109 -0.666 4.027 0.122 -0.002 INTERQUARTILE RANGE 42 0.000 0.028 0.233 1.359 0.043 0.016 MINIMUM VALUE 77 1.000 0.086 -1.073 3.273 0.093 -0.041 LOWER HINGE (25TH QUANTILE) 152 1.000 0.099 -0.764 3.501 0.106 -0.013 UPPER HINGE (75TH QUANTILE) 194 1.000 0.128 -0.531 4.860 0.149 0.003 MAXIMUM VALUE 231 1.000 0.141 -0.184 6.740 0.159 0.005 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.705 0.087 0.010 -0.351 2.062 0.505 0.836 MINIMUM CORRELATION: 0.505 SERIES 250012 AND 250021 77 YEARS MAXIMUM CORRELATION: 0.836 SERIES 249002 AND 250015 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 -0.187 0.531 0.638 0.718 0.813 0.792 0.699 SDEV 0.000 0.268 0.176 0.095 0.058 0.078 0.104 SERR 0.000 0.051 0.024 0.012 0.007 0.009 0.012 EPS 22.413 0.918 0.953 0.968 0.982 0.980 0.968 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 1.001 0.093 -0.855 5.006 0.102 -0.046 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.048 -0.017 0.071 60 171 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 1.16 1.00 1.07 2.23 13.62 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.17 0.00 0.75 0.92 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 -0.046 -0.004 0.026 -0.064 -0.123 0.045 -0.040 -0.105 -0.076 0.008 PACF -0.046 -0.006 0.026 -0.061 -0.129 0.032 -0.034 -0.110 -0.108 -0.012 95% C.L. 0.132 0.132 0.132 0.132 0.132 0.134 0.135 0.135 0.136 0.137 |------------------ 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 0.000 0.001 0.022 -0.068 -0.124 0.036 -0.044 -0.111 -0.081 0.006 PACF 0.000 0.001 0.022 -0.068 -0.125 0.036 -0.041 -0.113 -0.103 -0.004 95% C.L. 0.132 0.132 0.132 0.132 0.132 0.134 0.134 0.135 0.136 0.137 |----------------- 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 0.001 0.000 0.001 |========================= 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 1.001 0.095 -0.895 5.341 0.104 -0.028 |------------ 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 -0.028 0.176 -0.011 -0.026 -0.132 0.016 -0.078 -0.098 -0.082 -0.004 PACF -0.028 0.175 -0.002 -0.059 -0.137 0.025 -0.030 -0.115 -0.086 0.016 95% C.L. 0.132 0.132 0.136 0.136 0.136 0.138 0.138 0.139 0.140 0.141 |------------------- 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 0.032 -0.023 0.176 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.20 MINUTES