RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit018p.rwl LOG FILE PROCESSED: brit018p.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: 572 1 Loch Maree LATEWOOD_PERCENT PISY - 572 2 Great Britain Scots pine, Scotch pine 100 5731-520 1756 1978 - 572 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 572012 MISSING VALUES FOUND: 43 IN 1 GAPS / 1902 1944 / -------------------------------------------------------------------- 3 572021 MISSING VALUES FOUND: 1 IN 1 GAPS / 1903 1903 / -------------------------------------------------------------------- 7 572041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1910 1910 / -------------------------------------------------------------------- 15 572091 MISSING VALUES FOUND: 1 IN 1 GAPS / 1934 1934 / -------------------------------------------------------------------- 16 572092 MISSING VALUES FOUND: 5 IN 2 GAPS / 1799 1801 / 1837 1838 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 3.339 0.965 0.087 2.711 0.282 0.304 2 572012 1808 1978 171 3.390 0.871 0.107 2.884 0.316 -0.124 3 572021 1885 1978 94 2.800 0.547 0.473 3.287 0.192 0.257 4 572022 1906 1978 73 2.591 0.622 0.265 5.318 0.257 0.193 5 572031 1871 1978 108 3.070 0.858 -0.363 3.824 0.306 0.166 6 572032 1845 1978 134 3.085 0.888 0.652 4.438 0.256 0.343 7 572041 1834 1978 145 3.394 0.690 0.242 3.229 0.197 0.247 8 572042 1855 1978 124 3.282 0.843 0.169 2.843 0.249 0.291 9 572051 1812 1978 167 3.808 0.944 1.301 10.150 0.211 0.128 10 572052 1853 1978 126 3.919 0.964 -0.181 5.342 0.289 0.049 11 572061 1765 1978 214 2.762 0.769 -0.132 3.522 0.297 0.197 12 572062 1795 1978 184 2.916 0.891 0.232 3.433 0.274 0.362 13 572071 1877 1978 102 3.921 0.983 0.462 3.475 0.217 0.412 14 572072 1822 1958 137 3.553 1.064 0.423 3.606 0.288 0.222 15 572091 1846 1978 133 3.531 1.025 0.314 5.657 0.288 0.304 16 572092 1756 1978 223 3.187 1.040 0.235 2.992 0.262 0.551 NUMBER OF SERIES READ IN: 16 FROM 1756 TO 1978 223 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 143 3.284 0.873 0.268 4.169 0.261 0.244 STANDARD DEVIATION 43 0.405 0.150 0.379 1.848 0.039 0.154 MEDIAN (50TH QUANTILE) 133 3.311 0.890 0.238 3.499 0.268 0.252 INTERQUARTILE RANGE 59 0.549 0.168 0.346 1.768 0.055 0.144 MINIMUM VALUE 73 2.591 0.547 -0.363 2.711 0.192 -0.124 LOWER HINGE (25TH QUANTILE) 116 2.993 0.806 0.097 3.110 0.233 0.180 UPPER HINGE (75TH QUANTILE) 175 3.542 0.974 0.443 4.878 0.289 0.324 MAXIMUM VALUE 218 3.921 1.064 1.301 10.150 0.316 0.551 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.282 0.185 0.017 -0.306 2.666 -0.214 0.674 MINIMUM CORRELATION: -0.214 SERIES 572062 AND 572071 102 YEARS MAXIMUM CORRELATION: 0.674 SERIES 572071 AND 572072 82 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.289 0.452 0.394 0.386 0.363 0.356 SDEV 0.256 0.108 0.176 0.184 0.200 0.203 SERR 0.148 0.034 0.033 0.023 0.020 0.020 EPS 0.673 0.869 0.880 0.898 0.899 0.898 NSS 5.1 8.1 11.3 14.0 15.6 16.0 |======================== 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 1756 1978 223 3.281 0.555 0.093 2.671 0.197 -0.046 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.208 0.135 0.270 47 176 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.16 0.43 1.01 1.07 1.51 4.06 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 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 136. 62. 73. 116. 178. 223. |----------- 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 -0.045 0.085 -0.104 0.033 -0.028 0.097 0.068 0.057 0.054 -0.044 PACF -0.045 0.083 -0.098 0.018 -0.010 0.083 0.083 0.046 0.066 -0.038 95% C.L. 0.134 0.134 0.135 0.137 0.137 0.137 0.138 0.139 0.139 0.139 |------------------ 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 0 0.000 |================== 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 572011 3 0.00000000 0.00000000 -0.00714246 4.08585835 2 572012 1 0.34280947 0.02847638 0.00000000 3.29868317 3 572021 3 0.00000000 0.00000000 -0.00227687 2.90825844 4 572022 3 0.00000000 0.00000000 0.00241978 2.50156403 5 572031 3 0.00000000 0.00000000 0.00018077 3.06024051 6 572032 3 0.00000000 0.00000000 0.00934575 2.45393777 7 572041 3 0.00000000 0.00000000 0.00433210 3.07781816 8 572042 1 0.78284156 0.01739063 0.00000000 2.96404433 9 572051 3 0.00000000 0.00000000 0.00571619 3.32786369 10 572052 3 0.00000000 0.00000000 0.00375241 3.68108702 11 572061 3 0.00000000 0.00000000 -0.00216409 2.99446225 12 572062 3 0.00000000 0.00000000 -0.00898006 3.74706888 13 572071 3 0.00000000 0.00000000 0.01238364 3.28322268 14 572072 3 0.00000000 0.00000000 0.00892429 2.93758154 15 572091 3 0.00000000 0.00000000 0.00164222 3.41733766 16 572092 3 0.00000000 0.00000000 -0.00592010 3.85361767 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.000 0.267 0.273 3.143 0.281 0.194 2 572012 1808 1978 171 1.000 0.255 0.185 2.982 0.298 -0.042 3 572021 1885 1978 94 1.000 0.192 0.423 3.294 0.188 0.238 4 572022 1906 1978 73 1.000 0.239 0.316 5.941 0.254 0.184 5 572031 1871 1978 108 1.000 0.279 -0.366 3.825 0.303 0.165 6 572032 1845 1978 134 0.999 0.257 0.489 4.013 0.254 0.219 7 572041 1834 1978 145 1.000 0.195 0.235 3.425 0.199 0.190 8 572042 1855 1978 124 1.000 0.253 0.264 2.956 0.247 0.259 9 572051 1812 1978 167 1.000 0.232 0.979 9.061 0.209 0.062 10 572052 1853 1978 126 1.000 0.243 -0.231 5.195 0.286 0.033 11 572061 1765 1978 214 1.000 0.277 -0.100 3.418 0.296 0.179 12 572062 1795 1978 184 1.000 0.264 0.133 3.983 0.272 0.155 13 572071 1877 1978 102 0.999 0.231 0.375 3.145 0.215 0.301 14 572072 1822 1958 137 1.000 0.276 0.065 3.253 0.286 0.158 15 572091 1846 1978 133 1.000 0.288 0.255 5.451 0.287 0.288 16 572092 1756 1978 223 0.999 0.306 0.286 3.184 0.263 0.455 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.254 0.224 4.142 0.259 0.190 STANDARD DEVIATION 44 0.000 0.031 0.307 1.604 0.037 0.115 MEDIAN (50TH QUANTILE) 135 1.000 0.256 0.259 3.421 0.268 0.187 INTERQUARTILE RANGE 61 0.000 0.041 0.247 1.440 0.055 0.092 MINIMUM VALUE 73 0.999 0.192 -0.366 2.956 0.188 -0.042 LOWER HINGE (25TH QUANTILE) 116 1.000 0.236 0.099 3.164 0.231 0.157 UPPER HINGE (75TH QUANTILE) 177 1.000 0.277 0.345 4.604 0.286 0.249 MAXIMUM VALUE 223 1.000 0.306 0.979 9.061 0.303 0.455 |------------------------ 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 572011 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 572012 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 572021 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 572022 -67 48 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 572031 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 572032 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 572041 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 572042 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 572051 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 572052 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 572061 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 572062 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 572071 -67 68 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 572072 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 572091 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 572092 -67 149 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 572011 1771 1978 208 0.999 0.257 0.214 3.162 0.281 0.137 2 572012 1808 1978 171 1.000 0.254 0.186 2.981 0.298 -0.043 3 572021 1885 1978 94 0.999 0.187 0.423 3.269 0.188 0.204 4 572022 1906 1978 73 0.998 0.218 0.312 5.602 0.253 0.001 5 572031 1871 1978 108 0.999 0.280 -0.155 4.168 0.303 0.140 6 572032 1845 1978 134 0.999 0.237 0.510 3.856 0.253 0.092 7 572041 1834 1978 145 1.000 0.190 0.199 3.558 0.199 0.149 8 572042 1855 1978 124 0.997 0.225 0.488 3.846 0.247 0.041 9 572051 1812 1978 167 0.999 0.222 1.005 10.314 0.209 -0.009 10 572052 1853 1978 126 0.998 0.232 -0.349 5.169 0.286 -0.076 11 572061 1765 1978 214 0.999 0.269 -0.102 3.501 0.296 0.111 12 572062 1795 1978 184 0.998 0.249 -0.061 3.905 0.272 0.073 13 572071 1877 1978 102 0.998 0.205 0.175 3.035 0.214 0.142 14 572072 1822 1958 137 0.997 0.256 -0.162 3.449 0.286 0.061 15 572091 1846 1978 133 0.998 0.275 0.168 5.088 0.287 0.202 16 572092 1756 1978 223 0.994 0.267 0.141 3.679 0.263 0.263 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 0.998 0.239 0.187 4.286 0.259 0.093 STANDARD DEVIATION 44 0.001 0.029 0.328 1.785 0.037 0.094 MEDIAN (50TH QUANTILE) 135 0.998 0.243 0.180 3.763 0.268 0.101 INTERQUARTILE RANGE 61 0.002 0.042 0.449 1.268 0.056 0.124 MINIMUM VALUE 73 0.994 0.187 -0.349 2.981 0.188 -0.076 LOWER HINGE (25TH QUANTILE) 116 0.998 0.220 -0.082 3.359 0.231 0.021 UPPER HINGE (75TH QUANTILE) 177 0.999 0.262 0.367 4.628 0.286 0.145 MAXIMUM VALUE 223 1.000 0.280 1.005 10.314 0.303 0.263 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.344 0.134 0.012 -0.455 3.075 -0.043 0.632 MINIMUM CORRELATION: -0.043 SERIES 572022 AND 572062 73 YEARS MAXIMUM CORRELATION: 0.632 SERIES 572011 AND 572012 171 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.301 0.463 0.423 0.405 0.405 0.380 SDEV 0.221 0.109 0.145 0.135 0.156 0.193 SERR 0.127 0.035 0.027 0.017 0.015 0.019 EPS 0.686 0.874 0.892 0.905 0.914 0.907 NSS 5.1 8.1 11.3 14.0 15.6 16.0 |======================== 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 1756 1978 223 1.000 0.163 0.141 2.892 0.193 -0.095 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.144 0.067 0.097 63 160 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.64 1.00 1.11 1.75 17.71 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.15 0.00 0.85 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 -0.094 0.004 -0.214 -0.002 -0.079 0.021 0.079 0.016 -0.029 -0.057 PACF -0.094 -0.005 -0.217 -0.045 -0.094 -0.047 0.065 -0.008 -0.034 -0.041 95% C.L. 0.134 0.135 0.135 0.141 0.141 0.142 0.142 0.143 0.143 0.143 |------------------ 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 0 0.000 |======================= 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 -0.070 0.081 -0.239 -0.071 -0.059 0.061 0.133 0.045 -0.118 -0.088 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 -0.070 2 -0.065 0.076 3 -0.047 0.061 -0.231 4 -0.073 0.068 -0.236 -0.110 5 -0.077 0.059 -0.234 -0.113 -0.039 6 -0.077 0.060 -0.231 -0.114 -0.038 0.013 7 -0.078 0.065 -0.218 -0.089 -0.045 0.021 0.110 8 -0.081 0.064 -0.217 -0.086 -0.038 0.019 0.112 0.030 9 -0.077 0.079 -0.214 -0.091 -0.050 -0.010 0.121 0.019 -0.132 10 -0.085 0.080 -0.207 -0.092 -0.053 -0.015 0.108 0.024 -0.136 -0.058 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) 1476.56 1477.46 1478.15 1467.91 1467.18 1468.84 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1470.80 1470.10 1471.90 1469.99 1471.24 SELECTED AUTOREGRESSION ORDER: 4 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 -0.073 0.068 -0.236 -0.110 R-SQUARED DUE TO POOLED AUTOREGRESSION: 7.50 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 108.11 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 4) PROCESS OUT TO ORDER 50: 1.0000 -0.073 0.073 -0.247 -0.070 -0.021 0.047 0.039 0.013 -0.007 -.0130 -0.007 0.000 0.003 0.003 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 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 572011 4 0.054 0.130 0.127 -0.059 0.111 2 572012 4 0.051 -0.062 -0.023 -0.185 -0.085 3 572021 4 0.119 0.170 0.226 -0.035 -0.198 4 572022 4 0.084 -0.004 0.026 -0.040 -0.162 5 572031 4 0.123 0.106 0.028 -0.269 -0.117 6 572032 4 0.031 0.083 0.007 -0.061 -0.127 7 572041 4 0.056 0.160 0.064 -0.177 0.055 8 572042 4 0.030 0.048 0.104 -0.075 0.036 9 572051 4 0.049 0.000 0.139 -0.117 -0.063 10 572052 4 0.077 -0.055 0.164 -0.136 -0.087 11 572061 4 0.036 0.085 0.103 0.058 0.077 12 572062 4 0.036 0.083 0.010 -0.078 0.154 13 572071 4 0.091 0.154 0.072 -0.144 0.075 14 572072 4 0.025 0.055 0.008 -0.109 -0.055 15 572091 4 0.125 0.161 0.289 -0.056 0.003 16 572092 4 0.108 0.208 0.158 0.028 0.063 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 4 0.068 0.083 0.094 -0.091 -0.020 STANDARD DEVIATION 0 0.036 0.081 0.087 0.081 0.105 MEDIAN 4 0.055 0.084 0.087 -0.077 -0.026 INTERQUARTILE RANGE 0 0.063 0.133 0.130 0.092 0.171 MINIMUM VALUE 4 0.025 -0.062 -0.023 -0.269 -0.198 LOWER HINGE 4 0.036 0.024 0.018 -0.140 -0.102 UPPER HINGE 4 0.099 0.157 0.148 -0.048 0.069 MAXIMUM VALUE 4 0.125 0.208 0.289 0.058 0.154 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.000 0.250 0.228 3.164 0.293 0.006 2 572012 1808 1978 171 1.000 0.249 0.245 3.154 0.283 -0.007 3 572021 1885 1978 94 1.000 0.176 0.385 3.338 0.197 0.008 4 572022 1906 1978 73 1.000 0.215 0.431 5.834 0.243 0.036 5 572031 1871 1978 108 1.000 0.263 -0.233 3.263 0.308 0.018 6 572032 1845 1978 134 1.000 0.234 0.426 3.534 0.261 0.005 7 572041 1834 1978 145 1.000 0.185 0.159 3.392 0.209 -0.004 8 572042 1855 1978 124 1.000 0.223 0.439 3.981 0.248 -0.003 9 572051 1812 1978 167 1.000 0.219 0.737 8.671 0.210 0.009 10 572052 1853 1978 126 1.000 0.225 -0.453 5.365 0.265 0.013 11 572061 1765 1978 214 1.000 0.264 -0.072 3.283 0.304 -0.002 12 572062 1795 1978 184 1.000 0.245 -0.025 3.855 0.278 -0.007 13 572071 1877 1978 102 1.000 0.200 0.134 2.901 0.224 0.015 14 572072 1822 1958 137 1.000 0.253 -0.075 3.414 0.290 -0.003 15 572091 1846 1978 133 1.000 0.258 0.661 5.953 0.278 0.000 16 572092 1756 1978 223 1.000 0.253 -0.022 3.830 0.290 -0.002 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.232 0.185 4.183 0.261 0.005 STANDARD DEVIATION 44 0.000 0.028 0.323 1.537 0.036 0.011 MEDIAN (50TH QUANTILE) 135 1.000 0.240 0.193 3.474 0.271 0.003 INTERQUARTILE RANGE 61 0.000 0.036 0.477 1.400 0.056 0.014 MINIMUM VALUE 73 1.000 0.176 -0.453 2.901 0.197 -0.007 LOWER HINGE (25TH QUANTILE) 116 1.000 0.217 -0.049 3.273 0.234 -0.003 UPPER HINGE (75TH QUANTILE) 177 1.000 0.253 0.428 4.673 0.290 0.011 MAXIMUM VALUE 223 1.000 0.264 0.737 8.671 0.308 0.036 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.344 0.125 0.011 -0.423 3.383 -0.067 0.647 MINIMUM CORRELATION: -0.067 SERIES 572022 AND 572062 73 YEARS MAXIMUM CORRELATION: 0.647 SERIES 572011 AND 572012 171 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.339 0.471 0.437 0.428 0.398 0.365 SDEV 0.185 0.116 0.137 0.123 0.153 0.182 SERR 0.107 0.037 0.026 0.015 0.015 0.018 EPS 0.723 0.877 0.897 0.913 0.912 0.902 NSS 5.1 8.1 11.3 14.0 15.6 16.0 |======================== 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 1756 1978 223 1.001 0.163 0.142 2.891 0.198 -0.151 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.143 0.062 0.098 61 162 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.33 0.57 1.00 1.12 1.69 8.19 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.14 0.00 0.86 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 -0.150 -0.069 -0.136 -0.015 -0.042 0.008 0.066 -0.001 -0.013 -0.077 PACF -0.150 -0.094 -0.167 -0.077 -0.093 -0.053 0.031 -0.008 -0.014 -0.076 95% C.L. 0.134 0.137 0.138 0.140 0.140 0.140 0.140 0.141 0.141 0.141 |------------------ 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 1 0.032 -0.151 |---------- 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 -0.007 -0.019 -0.015 -0.013 -0.091 -0.029 0.030 -0.023 -0.025 -0.085 PACF -0.007 -0.019 -0.015 -0.014 -0.092 -0.031 0.026 -0.027 -0.028 -0.096 95% C.L. 0.134 0.134 0.134 0.134 0.134 0.135 0.135 0.135 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 4 0.009 -0.008 -0.020 -0.015 -0.014 |========================= 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 1756 1978 223 1.002 0.165 0.184 3.150 0.194 -0.064 |------------ 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 -0.064 0.079 -0.256 -0.088 -0.097 0.038 0.092 0.023 -0.035 -0.094 PACF -0.064 0.076 -0.249 -0.128 -0.080 -0.027 0.052 -0.025 -0.065 -0.079 95% C.L. 0.134 0.134 0.135 0.144 0.145 0.146 0.146 0.147 0.147 0.147 |------------------- 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 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.16 MINUTES