RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM043I.rwl.conv LOG FILE PROCESSED: GERM043I.rwl.conv_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 20 10 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: 022 1 Kaiserstuhl (D), EU-Pr. DENSITY_EARLY ABAL - 022 2 Germany silver fir, European fir 440 4805-741 1926 1995 - 022 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 022011 1927 1995 69 3.516 0.346 0.038 3.113 0.093 0.285 2 022013 1928 1995 68 3.845 0.397 0.943 4.485 0.105 0.122 3 022015 1928 1995 68 3.677 0.349 0.085 3.918 0.101 0.183 4 022017 1928 1995 68 3.627 0.382 0.128 3.455 0.095 0.310 5 022021 1929 1995 67 3.437 0.452 0.972 4.205 0.109 0.488 6 022023 1935 1995 61 3.548 0.596 1.729 6.392 0.117 0.562 7 022025 1929 1995 67 3.311 0.345 -0.136 2.988 0.110 0.083 8 022027 1929 1995 67 3.188 0.352 0.342 4.152 0.111 0.140 9 022031 1927 1995 69 3.732 0.523 0.737 3.586 0.098 0.602 10 022033 1929 1995 67 3.110 0.370 0.644 3.440 0.118 0.248 11 022037 1926 1995 70 3.574 0.406 1.567 7.545 0.102 0.161 12 022043 1928 1995 68 3.739 0.328 0.654 3.652 0.097 0.090 13 022047 1928 1995 68 3.493 0.374 0.160 2.831 0.105 0.234 14 022053 1931 1995 65 3.618 0.368 0.122 3.058 0.106 0.250 15 022055 1929 1995 67 3.695 0.436 -0.068 2.906 0.114 0.344 16 022057 1928 1995 68 3.705 0.450 0.354 4.049 0.107 0.314 NUMBER OF SERIES READ IN: 16 FROM 1926 TO 1995 70 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 3.551 0.405 0.517 3.986 0.106 0.276 STANDARD DEVIATION 2 0.204 0.072 0.561 1.285 0.008 0.159 MEDIAN (50TH QUANTILE) 68 3.596 0.378 0.348 3.619 0.106 0.249 INTERQUARTILE RANGE 1 0.235 0.093 0.736 1.093 0.011 0.178 MINIMUM VALUE 61 3.110 0.328 -0.136 2.831 0.093 0.083 LOWER HINGE (25TH QUANTILE) 67 3.465 0.350 0.104 3.086 0.099 0.151 UPPER HINGE (75TH QUANTILE) 68 3.700 0.443 0.840 4.179 0.111 0.329 MAXIMUM VALUE 70 3.845 0.596 1.729 7.545 0.118 0.602 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.315 0.197 0.018 0.002 3.031 -0.242 0.785 MINIMUM CORRELATION: -0.242 SERIES 022031 AND 022047 68 YEARS MAXIMUM CORRELATION: 0.785 SERIES 022015 AND 022043 68 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.77 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1950. 1960. 1970. 1980. CORR 120. 120. 120. 120. RBAR 0.482 0.374 0.348 0.379 SDEV 0.223 0.211 0.265 0.274 SERR 0.020 0.019 0.024 0.025 EPS 0.937 0.905 0.895 0.907 NSS 16.0 16.0 16.0 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 1926 1995 70 3.575 0.318 2.494 14.681 0.077 0.150 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.111 -0.040 0.519 14 56 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.51 1.02 1.10 1.61 5.79 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.86 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 68. 1. 61. 67. 68. 70. |----------- 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 0.148 0.158 0.184 0.078 -0.002 -0.018 -0.105 0.046 0.003 0.067 PACF 0.148 0.139 0.150 0.018 -0.062 -0.054 -0.112 0.093 0.038 0.096 95% C.L. 0.239 0.244 0.250 0.258 0.259 0.259 0.259 0.261 0.262 0.262 |------------------ 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 0.108 0.116 0.155 0.200 |================== 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 022011 3 0.00000000 0.00000000 0.00359262 3.39063501 2 022013 1 2.10706210 0.53986168 0.00000000 3.80200362 3 022015 1 1.23063326 0.33449730 0.00000000 3.63120627 4 022017 3 0.00000000 0.00000000 -0.00592721 3.83140039 5 022021 3 0.00000000 0.00000000 0.00185170 3.37450480 6 022023 1 2.95444202 0.24288133 0.00000000 3.37153101 7 022025 1 0.31512004 0.12349440 0.00000000 3.27527285 8 022027 3 0.00000000 0.00000000 0.00051600 3.17066479 9 022031 3 0.00000000 0.00000000 -0.01686116 4.32231474 10 022033 1 2.23578644 0.00311637 0.00000000 1.09555089 11 022037 3 0.00000000 0.00000000 -0.00775838 3.84927964 12 022043 1 1.13779426 0.42421103 0.00000000 3.70715666 13 022047 3 0.00000000 0.00000000 0.00399321 3.35488153 14 022053 3 0.00000000 0.00000000 -0.00378584 3.74339414 15 022055 3 0.00000000 0.00000000 -0.00888858 3.99743557 16 022057 3 0.00000000 0.00000000 -0.01237222 4.13140011 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 022011 1927 1995 69 1.000 0.096 0.029 3.032 0.091 0.253 2 022013 1928 1995 68 1.000 0.093 0.837 4.856 0.102 0.011 3 022015 1928 1995 68 1.000 0.086 -0.387 3.685 0.100 0.016 4 022017 1928 1995 68 1.000 0.100 -0.067 3.160 0.094 0.243 5 022021 1929 1995 67 1.000 0.131 0.913 4.057 0.108 0.473 6 022023 1935 1995 61 1.000 0.111 0.567 4.407 0.113 0.174 7 022025 1929 1995 67 1.000 0.102 -0.223 2.822 0.108 0.076 8 022027 1929 1995 67 1.000 0.110 0.369 4.206 0.109 0.135 9 022031 1927 1995 69 1.000 0.104 0.427 3.383 0.097 0.331 10 022033 1929 1995 67 1.000 0.112 0.523 3.219 0.116 0.159 11 022037 1926 1995 70 1.000 0.103 1.035 5.133 0.100 0.084 12 022043 1928 1995 68 1.000 0.082 0.291 2.960 0.097 -0.053 13 022047 1928 1995 68 1.000 0.105 0.356 2.805 0.104 0.191 14 022053 1931 1995 65 1.000 0.099 -0.073 3.008 0.105 0.208 15 022055 1929 1995 67 1.000 0.108 -0.317 2.669 0.112 0.225 16 022057 1928 1995 68 1.000 0.100 0.163 3.264 0.105 0.044 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.103 0.278 3.542 0.104 0.161 STANDARD DEVIATION 2 0.000 0.011 0.435 0.766 0.007 0.133 MEDIAN (50TH QUANTILE) 68 1.000 0.103 0.324 3.241 0.104 0.166 INTERQUARTILE RANGE 1 0.000 0.011 0.615 1.147 0.011 0.174 MINIMUM VALUE 61 1.000 0.082 -0.387 2.669 0.091 -0.053 LOWER HINGE (25TH QUANTILE) 67 1.000 0.098 -0.070 2.984 0.098 0.060 UPPER HINGE (75TH QUANTILE) 68 1.000 0.109 0.545 4.131 0.109 0.234 MAXIMUM VALUE 70 1.000 0.131 1.035 5.133 0.116 0.473 |------------------------ 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 022011 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 022013 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 022015 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 022017 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 022021 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 022023 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 022025 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 022027 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 022031 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 022033 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 022037 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 022043 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 022047 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 022053 -67 43 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 022055 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 022057 -67 45 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 022011 1927 1995 69 1.000 0.092 -0.031 3.019 0.091 0.200 2 022013 1928 1995 68 1.000 0.090 0.775 5.001 0.102 -0.036 3 022015 1928 1995 68 1.000 0.081 -0.449 2.882 0.100 -0.127 4 022017 1928 1995 68 1.000 0.094 0.166 3.295 0.094 0.159 5 022021 1929 1995 67 0.999 0.112 0.211 3.389 0.107 0.283 6 022023 1935 1995 61 1.000 0.102 0.224 3.776 0.113 0.042 7 022025 1929 1995 67 1.000 0.100 -0.234 2.781 0.109 0.040 8 022027 1929 1995 67 1.000 0.099 0.207 3.513 0.110 -0.031 9 022031 1927 1995 69 0.999 0.096 0.712 4.198 0.097 0.191 10 022033 1929 1995 67 1.000 0.109 0.478 3.092 0.116 0.120 11 022037 1926 1995 70 1.000 0.096 0.815 3.804 0.100 0.001 12 022043 1928 1995 68 1.000 0.081 0.261 2.897 0.097 -0.065 13 022047 1928 1995 68 0.999 0.095 0.226 2.689 0.103 0.033 14 022053 1931 1995 65 1.000 0.091 -0.027 3.358 0.104 0.075 15 022055 1929 1995 67 1.000 0.103 -0.325 2.788 0.112 0.137 16 022057 1928 1995 68 1.000 0.095 0.175 3.789 0.105 -0.055 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.096 0.199 3.392 0.104 0.060 STANDARD DEVIATION 2 0.000 0.008 0.369 0.617 0.007 0.113 MEDIAN (50TH QUANTILE) 68 1.000 0.096 0.209 3.327 0.104 0.041 INTERQUARTILE RANGE 1 0.000 0.009 0.399 0.893 0.011 0.182 MINIMUM VALUE 61 0.999 0.081 -0.449 2.689 0.091 -0.127 LOWER HINGE (25TH QUANTILE) 67 1.000 0.092 -0.029 2.889 0.098 -0.034 UPPER HINGE (75TH QUANTILE) 68 1.000 0.101 0.370 3.782 0.109 0.148 MAXIMUM VALUE 70 1.000 0.112 0.815 5.001 0.116 0.283 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.366 0.158 0.014 0.460 3.179 0.037 0.798 MINIMUM CORRELATION: 0.037 SERIES 022031 AND 022047 68 YEARS MAXIMUM CORRELATION: 0.798 SERIES 022015 AND 022043 68 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.77 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1950. 1960. 1970. 1980. CORR 120. 120. 120. 120. RBAR 0.495 0.410 0.371 0.342 SDEV 0.208 0.192 0.258 0.286 SERR 0.019 0.018 0.024 0.026 EPS 0.940 0.918 0.904 0.892 NSS 16.0 16.0 16.0 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 1926 1995 70 1.003 0.071 -0.043 3.447 0.082 -0.049 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.118 0.045 0.025 19 51 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.58 1.01 1.06 1.64 4.02 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.00 0.86 0.91 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 -0.048 0.010 0.070 -0.002 -0.088 -0.055 -0.256 -0.098 -0.054 -0.035 PACF -0.048 0.007 0.071 0.005 -0.090 -0.069 -0.265 -0.127 -0.068 -0.020 95% C.L. 0.239 0.240 0.240 0.241 0.241 0.243 0.243 0.258 0.260 0.261 |------------------ 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 -0.064 0.037 0.000 -0.026 -0.031 0.053 -0.311 -0.135 -0.023 0.010 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 -0.064 2 -0.062 0.033 3 -0.062 0.034 0.004 4 -0.062 0.034 0.003 -0.027 5 -0.063 0.035 0.004 -0.030 -0.035 6 -0.061 0.036 0.004 -0.031 -0.032 0.051 7 -0.046 0.026 -0.006 -0.030 -0.021 0.032 -0.305 8 -0.104 0.033 -0.010 -0.036 -0.022 0.037 -0.314 -0.191 9 -0.110 0.022 -0.009 -0.037 -0.023 0.037 -0.313 -0.195 -0.033 10 -0.110 0.026 -0.003 -0.037 -0.022 0.038 -0.313 -0.195 -0.031 0.018 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) 290.98 292.69 294.62 296.61 298.56 300.48 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 302.29 297.46 296.85 298.77 300.75 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 022011 0 0.042 2 022013 0 0.001 3 022015 0 0.016 4 022017 0 0.026 5 022021 0 0.085 6 022023 0 0.002 7 022025 0 0.002 8 022027 0 0.001 9 022031 0 0.037 10 022033 0 0.015 11 022037 0 0.000 12 022043 0 0.004 13 022047 0 0.001 14 022053 0 0.006 15 022055 0 0.019 16 022057 0 0.003 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 0 0.016 STANDARD DEVIATION 0 0.023 MEDIAN 0 0.005 INTERQUARTILE RANGE 0 0.021 MINIMUM VALUE 0 0.000 LOWER HINGE 0 0.002 UPPER HINGE 0 0.023 MAXIMUM VALUE 0 0.085 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 022011 1927 1995 69 1.000 0.092 -0.031 3.019 0.091 0.200 2 022013 1928 1995 68 1.000 0.090 0.775 5.001 0.102 -0.036 3 022015 1928 1995 68 1.000 0.081 -0.449 2.882 0.100 -0.127 4 022017 1928 1995 68 1.000 0.094 0.166 3.295 0.093 0.159 5 022021 1929 1995 67 1.000 0.112 0.211 3.389 0.107 0.283 6 022023 1935 1995 61 1.000 0.102 0.224 3.776 0.113 0.042 7 022025 1929 1995 67 1.000 0.100 -0.234 2.781 0.108 0.040 8 022027 1929 1995 67 1.000 0.099 0.207 3.513 0.110 -0.031 9 022031 1927 1995 69 1.000 0.096 0.712 4.198 0.096 0.191 10 022033 1929 1995 67 1.000 0.109 0.478 3.092 0.116 0.120 11 022037 1926 1995 70 1.000 0.096 0.815 3.804 0.100 0.001 12 022043 1928 1995 68 1.000 0.081 0.261 2.897 0.097 -0.065 13 022047 1928 1995 68 1.000 0.095 0.226 2.689 0.103 0.033 14 022053 1931 1995 65 1.000 0.091 -0.028 3.358 0.104 0.075 15 022055 1929 1995 67 1.000 0.103 -0.325 2.788 0.112 0.137 16 022057 1928 1995 68 1.000 0.095 0.175 3.789 0.105 -0.055 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.096 0.199 3.392 0.104 0.060 STANDARD DEVIATION 2 0.000 0.008 0.369 0.617 0.007 0.113 MEDIAN (50TH QUANTILE) 68 1.000 0.096 0.209 3.327 0.104 0.041 INTERQUARTILE RANGE 1 0.000 0.009 0.399 0.893 0.011 0.182 MINIMUM VALUE 61 1.000 0.081 -0.449 2.689 0.091 -0.127 LOWER HINGE (25TH QUANTILE) 67 1.000 0.092 -0.029 2.889 0.098 -0.034 UPPER HINGE (75TH QUANTILE) 68 1.000 0.101 0.370 3.782 0.109 0.148 MAXIMUM VALUE 70 1.000 0.112 0.815 5.001 0.116 0.283 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.366 0.158 0.014 0.460 3.179 0.037 0.798 MINIMUM CORRELATION: 0.037 SERIES 022031 AND 022047 68 YEARS MAXIMUM CORRELATION: 0.798 SERIES 022015 AND 022043 68 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.77 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1950. 1960. 1970. 1980. CORR 120. 120. 120. 120. RBAR 0.495 0.410 0.371 0.342 SDEV 0.208 0.192 0.258 0.286 SERR 0.019 0.018 0.024 0.026 EPS 0.940 0.918 0.904 0.892 NSS 16.0 16.0 16.0 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 1926 1995 70 1.003 0.071 -0.045 3.445 0.082 -0.049 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.118 0.045 0.025 19 51 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.57 1.01 1.07 1.63 4.04 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.00 0.86 0.91 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 -0.048 0.009 0.069 -0.002 -0.088 -0.055 -0.256 -0.098 -0.054 -0.035 PACF -0.048 0.007 0.070 0.005 -0.090 -0.069 -0.265 -0.127 -0.068 -0.021 95% C.L. 0.239 0.240 0.240 0.241 0.241 0.243 0.243 0.258 0.260 0.261 |------------------ 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 1926 1995 70 1.003 0.071 -0.045 3.445 0.082 -0.049 |------------ 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 -0.048 0.009 0.069 -0.002 -0.088 -0.055 -0.256 -0.098 -0.054 -0.035 PACF -0.048 0.007 0.070 0.005 -0.090 -0.069 -0.265 -0.127 -0.068 -0.021 95% C.L. 0.239 0.240 0.240 0.241 0.241 0.243 0.243 0.258 0.260 0.261 |------------------- 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: 0.09 MINUTES