RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit016p.rwl LOG FILE PROCESSED: brit016p.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: 571 1 Shieldaig LATEWOOD_PERCENT PISY - 571 2 Great Britain Scots pine, Scotch pine 12 5730-537 1847 1978 - 571 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 571031 MISSING VALUES FOUND: 1 IN 1 GAPS / 1924 1924 / -------------------------------------------------------------------- 7 571041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1959 1959 / -------------------------------------------------------------------- 18 571092 MISSING VALUES FOUND: 1 IN 1 GAPS / 1889 1889 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 2.647 0.703 0.411 3.039 0.322 -0.052 2 571012 1899 1978 80 2.604 0.703 0.626 3.713 0.262 0.251 3 571021 1868 1978 111 3.196 0.781 0.554 4.417 0.228 0.318 4 571022 1860 1978 119 3.225 0.898 1.314 7.282 0.230 0.351 5 571031 1873 1978 106 3.805 0.840 0.115 3.138 0.213 0.348 6 571032 1847 1978 132 2.765 0.999 -0.037 2.994 0.347 0.414 7 571041 1866 1978 113 4.244 0.862 -0.406 4.236 0.222 0.184 8 571042 1864 1966 103 4.073 1.106 0.452 2.789 0.213 0.600 9 571051 1859 1978 120 2.769 0.738 0.617 3.902 0.270 0.182 10 571052 1899 1978 80 3.248 0.903 0.830 3.703 0.245 0.305 11 571061 1891 1978 88 4.804 0.781 0.017 2.669 0.168 0.225 12 571062 1883 1978 96 4.197 0.908 0.199 2.878 0.217 0.236 13 571071 1873 1967 95 2.977 0.767 0.533 3.086 0.238 0.321 14 571072 1876 1965 90 2.951 0.935 0.894 3.508 0.267 0.377 15 571081 1874 1978 105 3.335 0.727 -0.003 2.699 0.248 0.062 16 571082 1853 1978 126 3.544 1.048 -0.532 3.726 0.262 0.434 17 571091 1866 1978 113 3.267 0.703 -0.698 4.559 0.214 0.274 18 571092 1868 1978 111 3.211 0.680 -0.559 3.813 0.210 0.220 19 571101 1877 1976 100 3.701 0.999 1.380 7.923 0.271 0.002 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 3.129 0.709 0.029 3.174 0.252 0.011 21 571111 1856 1978 123 3.665 1.003 0.083 3.368 0.250 0.383 NUMBER OF SERIES READ IN: 21 FROM 1847 TO 1978 132 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 3.398 0.847 0.277 3.839 0.245 0.259 STANDARD DEVIATION 16 0.580 0.131 0.572 1.369 0.039 0.159 MEDIAN (50TH QUANTILE) 105 3.248 0.840 0.199 3.508 0.245 0.274 INTERQUARTILE RANGE 23 0.725 0.208 0.620 0.863 0.045 0.167 MINIMUM VALUE 70 2.604 0.680 -0.698 2.669 0.168 -0.052 LOWER HINGE (25TH QUANTILE) 90 2.977 0.727 -0.003 3.039 0.217 0.184 UPPER HINGE (75TH QUANTILE) 113 3.701 0.935 0.617 3.902 0.262 0.351 MAXIMUM VALUE 132 4.804 1.106 1.380 7.923 0.347 0.600 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.356 0.144 0.010 -0.170 2.715 -0.009 0.713 MINIMUM CORRELATION: -0.009 SERIES 571051 AND 571111 120 YEARS MAXIMUM CORRELATION: 0.713 SERIES 571042 AND 571072 90 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.370 0.426 0.369 SDEV 0.134 0.129 0.155 SERR 0.015 0.009 0.013 EPS 0.917 0.939 0.922 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 3.212 0.719 -0.916 5.775 0.171 0.498 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.555 0.231 0.064 33 99 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.73 1.00 1.08 1.81 5.70 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.09 0.00 0.86 0.95 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 105. 23. 70. 90. 113. 132. |----------- 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 0.495 0.494 0.428 0.352 0.409 0.323 0.330 0.260 0.175 0.220 PACF 0.495 0.330 0.150 0.029 0.169 0.012 0.045 -0.040 -0.102 0.047 95% C.L. 0.174 0.212 0.245 0.266 0.280 0.298 0.308 0.319 0.325 0.328 |------------------ 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 0.418 0.223 0.315 0.237 |================== 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 571011 3 0.00000000 0.00000000 0.00963958 2.30479503 2 571012 3 0.00000000 0.00000000 0.00963994 2.21308231 3 571021 3 0.00000000 0.00000000 0.01241400 2.50130224 4 571022 3 0.00000000 0.00000000 0.00506559 2.92068648 5 571031 3 0.00000000 0.00000000 0.01376160 3.06535244 6 571032 3 0.00000000 0.00000000 -0.00172515 2.87987399 7 571041 3 0.00000000 0.00000000 0.00480749 3.98203230 8 571042 3 0.00000000 0.00000000 0.02410952 2.81892633 9 571051 3 0.00000000 0.00000000 -0.00570238 3.11357713 10 571052 3 0.00000000 0.00000000 0.01126911 2.79160118 11 571061 3 0.00000000 0.00000000 0.00581513 4.54474926 12 571062 3 0.00000000 0.00000000 0.00034177 4.18019533 13 571071 3 0.00000000 0.00000000 0.01383315 2.31253529 14 571072 3 0.00000000 0.00000000 0.02470338 1.82744074 15 571081 3 0.00000000 0.00000000 0.00522517 3.05839920 16 571082 3 0.00000000 0.00000000 0.01746220 2.43480134 17 571091 3 0.00000000 0.00000000 0.00734339 2.84841824 18 571092 3 0.00000000 0.00000000 -0.00100223 3.26348972 19 571101 3 0.00000000 0.00000000 0.01236382 3.07692719 SERIES IDENT OPTION A B C D 20 571102 3 0.00000000 0.00000000 0.00527417 2.90477610 21 571111 3 0.00000000 0.00000000 0.01839077 2.52465010 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 1.000 0.258 0.641 3.510 0.317 -0.115 2 571012 1899 1978 80 0.999 0.254 0.668 3.895 0.258 0.146 3 571021 1868 1978 111 1.000 0.211 0.490 3.766 0.225 0.065 4 571022 1860 1978 119 1.000 0.271 1.292 7.336 0.228 0.315 5 571031 1873 1978 106 1.000 0.190 0.113 3.195 0.208 0.103 6 571032 1847 1978 132 1.000 0.361 -0.025 3.069 0.345 0.407 7 571041 1866 1978 113 1.000 0.201 -0.433 4.203 0.221 0.139 8 571042 1864 1966 103 1.003 0.219 0.549 4.021 0.211 0.241 9 571051 1859 1978 120 1.000 0.260 0.920 4.962 0.267 0.142 10 571052 1899 1978 80 1.000 0.263 0.844 4.084 0.242 0.232 11 571061 1891 1978 88 1.000 0.160 0.016 2.900 0.166 0.189 12 571062 1883 1978 96 1.000 0.216 0.192 2.867 0.214 0.234 13 571071 1873 1967 95 0.999 0.218 0.336 2.980 0.236 0.090 14 571072 1876 1965 90 1.002 0.227 0.891 4.949 0.263 -0.129 15 571081 1874 1978 105 1.000 0.212 -0.066 2.995 0.246 0.000 16 571082 1853 1978 126 0.998 0.262 -0.048 5.476 0.260 0.165 17 571091 1866 1978 113 1.000 0.212 -0.218 4.632 0.212 0.151 18 571092 1868 1978 111 1.000 0.212 -0.519 3.789 0.207 0.217 19 571101 1877 1976 100 1.000 0.244 0.900 5.775 0.269 -0.131 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.223 -0.005 3.180 0.249 -0.025 21 571111 1856 1978 123 1.001 0.210 -0.459 4.705 0.247 -0.103 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.233 0.289 4.109 0.243 0.111 STANDARD DEVIATION 16 0.001 0.041 0.518 1.141 0.039 0.150 MEDIAN (50TH QUANTILE) 105 1.000 0.219 0.192 3.895 0.242 0.142 INTERQUARTILE RANGE 23 0.000 0.047 0.716 1.525 0.046 0.217 MINIMUM VALUE 70 0.998 0.160 -0.519 2.867 0.166 -0.131 LOWER HINGE (25TH QUANTILE) 90 1.000 0.212 -0.048 3.180 0.214 0.000 UPPER HINGE (75TH QUANTILE) 113 1.000 0.258 0.668 4.705 0.260 0.217 MAXIMUM VALUE 132 1.003 0.361 1.292 7.336 0.345 0.407 |------------------------ 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 571011 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 571012 -67 53 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 571021 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 571022 -67 79 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 571031 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 571032 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 571041 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 571042 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 571051 -67 80 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 571052 -67 53 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 571061 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 571062 -67 64 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 571071 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 571072 -67 60 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 571081 -67 70 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 571082 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 571091 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 571092 -67 74 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 571101 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 571102 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 21 571111 -67 82 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 571011 1909 1978 70 0.999 0.249 0.491 3.447 0.316 -0.158 2 571012 1899 1978 80 0.999 0.231 0.380 3.098 0.258 -0.005 3 571021 1868 1978 111 0.999 0.206 0.412 3.382 0.225 0.027 4 571022 1860 1978 119 0.999 0.234 1.026 5.577 0.228 0.127 5 571031 1873 1978 106 0.999 0.180 -0.054 3.243 0.208 0.011 6 571032 1847 1978 132 0.994 0.345 0.159 3.442 0.344 0.354 7 571041 1866 1978 113 0.999 0.188 -0.539 4.198 0.221 -0.009 8 571042 1864 1966 103 0.998 0.184 0.131 3.348 0.210 0.020 9 571051 1859 1978 120 0.999 0.236 0.586 3.823 0.268 -0.018 10 571052 1899 1978 80 0.998 0.231 0.467 3.749 0.242 0.068 11 571061 1891 1978 88 1.000 0.156 0.003 2.876 0.166 0.151 12 571062 1883 1978 96 0.998 0.197 0.258 3.159 0.214 0.080 13 571071 1873 1967 95 0.999 0.207 0.321 3.198 0.236 -0.008 14 571072 1876 1965 90 0.999 0.219 0.760 3.624 0.264 -0.201 15 571081 1874 1978 105 1.000 0.209 -0.108 3.058 0.246 -0.025 16 571082 1853 1978 126 0.998 0.252 0.007 5.490 0.260 0.076 17 571091 1866 1978 113 0.999 0.202 0.254 5.991 0.212 -0.088 18 571092 1868 1978 111 0.999 0.204 -0.471 3.610 0.207 0.156 19 571101 1877 1976 100 1.000 0.244 0.964 6.094 0.269 -0.140 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 0.999 0.213 0.275 3.352 0.249 -0.160 21 571111 1856 1978 123 0.999 0.204 -0.588 4.849 0.247 -0.161 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 0.999 0.219 0.226 3.934 0.242 0.005 STANDARD DEVIATION 16 0.001 0.038 0.438 1.021 0.039 0.133 MEDIAN (50TH QUANTILE) 105 0.999 0.209 0.258 3.447 0.242 -0.005 INTERQUARTILE RANGE 23 0.001 0.032 0.464 0.956 0.046 0.164 MINIMUM VALUE 70 0.994 0.156 -0.588 2.876 0.166 -0.201 LOWER HINGE (25TH QUANTILE) 90 0.999 0.202 0.003 3.243 0.214 -0.088 UPPER HINGE (75TH QUANTILE) 113 0.999 0.234 0.467 4.198 0.260 0.076 MAXIMUM VALUE 132 1.000 0.345 1.026 6.094 0.344 0.354 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.348 0.114 0.008 -0.212 2.897 0.036 0.667 MINIMUM CORRELATION: 0.036 SERIES 571061 AND 571111 88 YEARS MAXIMUM CORRELATION: 0.667 SERIES 571081 AND 571082 105 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.410 0.389 0.395 SDEV 0.127 0.130 0.154 SERR 0.014 0.009 0.013 EPS 0.929 0.930 0.930 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.985 0.179 0.254 4.256 0.186 0.065 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.220 0.079 0.082 46 86 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.79 1.00 1.06 1.85 4.32 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.87 0.95 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 0.065 0.123 0.027 0.019 0.075 0.008 0.094 -0.022 -0.127 -0.050 PACF 0.065 0.119 0.013 0.002 0.070 -0.003 0.078 -0.035 -0.150 -0.037 95% C.L. 0.174 0.175 0.177 0.178 0.178 0.179 0.179 0.180 0.180 0.183 |------------------ 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 -0.076 0.070 -0.039 -0.098 0.091 -0.047 0.116 -0.034 -0.085 0.013 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 -0.076 2 -0.071 0.064 3 -0.069 0.062 -0.030 4 -0.072 0.069 -0.037 -0.108 5 -0.063 0.072 -0.043 -0.102 0.083 6 -0.061 0.070 -0.044 -0.100 0.082 -0.023 7 -0.059 0.062 -0.035 -0.096 0.075 -0.018 0.094 8 -0.057 0.062 -0.033 -0.098 0.075 -0.016 0.093 -0.020 9 -0.059 0.070 -0.035 -0.091 0.066 -0.019 0.098 -0.025 -0.091 10 -0.059 0.070 -0.035 -0.091 0.066 -0.019 0.098 -0.025 -0.091 0.001 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) 872.79 874.03 875.49 877.37 877.82 878.90 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 880.83 881.66 883.61 884.51 886.51 SELECTED AUTOREGRESSION ORDER: 0 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 571011 0 0.026 2 571012 0 0.000 3 571021 0 0.001 4 571022 0 0.016 5 571031 0 0.000 6 571032 0 0.129 7 571041 0 0.000 8 571042 0 0.000 9 571051 0 0.000 10 571052 0 0.005 11 571061 0 0.023 12 571062 0 0.006 13 571071 0 0.000 14 571072 0 0.041 15 571081 0 0.001 16 571082 0 0.006 17 571091 0 0.008 18 571092 0 0.026 19 571101 0 0.020 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 571102 0 0.027 21 571111 0 0.027 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.017 STANDARD DEVIATION 0 0.028 MEDIAN 0 0.006 INTERQUARTILE RANGE 0 0.025 MINIMUM VALUE 0 0.000 LOWER HINGE 0 0.000 UPPER HINGE 0 0.026 MAXIMUM VALUE 0 0.129 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 571011 1909 1978 70 1.000 0.249 0.491 3.447 0.316 -0.158 2 571012 1899 1978 80 1.000 0.231 0.380 3.098 0.258 -0.005 3 571021 1868 1978 111 1.000 0.206 0.412 3.382 0.225 0.027 4 571022 1860 1978 119 1.000 0.234 1.026 5.577 0.228 0.127 5 571031 1873 1978 106 1.000 0.180 -0.054 3.243 0.208 0.011 6 571032 1847 1978 132 1.000 0.345 0.159 3.442 0.342 0.354 7 571041 1866 1978 113 1.000 0.188 -0.539 4.198 0.221 -0.009 8 571042 1864 1966 103 1.000 0.184 0.131 3.348 0.210 0.020 9 571051 1859 1978 120 1.000 0.236 0.586 3.823 0.267 -0.018 10 571052 1899 1978 80 1.000 0.231 0.467 3.749 0.242 0.068 11 571061 1891 1978 88 1.000 0.156 0.003 2.876 0.166 0.151 12 571062 1883 1978 96 1.000 0.197 0.258 3.159 0.214 0.080 13 571071 1873 1967 95 1.000 0.207 0.321 3.198 0.236 -0.008 14 571072 1876 1965 90 1.000 0.219 0.760 3.624 0.264 -0.201 15 571081 1874 1978 105 1.000 0.209 -0.108 3.058 0.246 -0.025 16 571082 1853 1978 126 1.000 0.252 0.007 5.490 0.260 0.076 17 571091 1866 1978 113 1.000 0.202 0.254 5.991 0.212 -0.088 18 571092 1868 1978 111 1.000 0.204 -0.471 3.610 0.207 0.156 19 571101 1877 1976 100 1.000 0.244 0.964 6.094 0.268 -0.140 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 571102 1877 1960 84 1.000 0.213 0.275 3.352 0.249 -0.160 21 571111 1856 1978 123 1.000 0.204 -0.588 4.849 0.247 -0.161 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 103 1.000 0.219 0.226 3.934 0.242 0.005 STANDARD DEVIATION 16 0.000 0.038 0.438 1.021 0.039 0.133 MEDIAN (50TH QUANTILE) 105 1.000 0.209 0.258 3.447 0.242 -0.005 INTERQUARTILE RANGE 23 0.000 0.032 0.464 0.956 0.046 0.164 MINIMUM VALUE 70 1.000 0.156 -0.588 2.876 0.166 -0.201 LOWER HINGE (25TH QUANTILE) 90 1.000 0.202 0.003 3.243 0.214 -0.088 UPPER HINGE (75TH QUANTILE) 113 1.000 0.234 0.467 4.198 0.260 0.076 MAXIMUM VALUE 132 1.000 0.345 1.026 6.094 0.342 0.354 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 210 0.348 0.114 0.008 -0.212 2.897 0.036 0.667 MINIMUM CORRELATION: 0.036 SERIES 571061 AND 571111 88 YEARS MAXIMUM CORRELATION: 0.667 SERIES 571081 AND 571082 105 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 69.52 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1900. 1925. 1950. CORR 78. 190. 136. RBAR 0.410 0.389 0.395 SDEV 0.127 0.130 0.154 SERR 0.014 0.009 0.013 EPS 0.929 0.930 0.930 NSS 18.8 20.8 20.2 |======================== 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 1847 1978 132 0.987 0.178 0.262 4.243 0.185 0.063 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.222 0.081 0.081 46 86 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.83 1.00 1.06 1.90 4.59 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.87 0.94 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 0.063 0.120 0.026 0.018 0.073 0.008 0.094 -0.022 -0.127 -0.050 PACF 0.063 0.117 0.013 0.002 0.069 -0.003 0.079 -0.035 -0.149 -0.037 95% C.L. 0.174 0.175 0.177 0.177 0.177 0.178 0.178 0.180 0.180 0.183 |------------------ 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 |========================= 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 1847 1978 132 0.987 0.178 0.262 4.243 0.185 0.063 |------------ 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 0.063 0.120 0.026 0.018 0.073 0.008 0.094 -0.022 -0.127 -0.050 PACF 0.063 0.117 0.013 0.002 0.069 -0.003 0.079 -0.035 -0.149 -0.037 95% C.L. 0.174 0.175 0.177 0.177 0.177 0.178 0.178 0.180 0.180 0.183 |------------------- 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: 0.12 MINUTES