RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM047X.rwl.conv LOG FILE PROCESSED: GERM047X.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 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: 028 1 Sirnitz SW (D), EU-Pr. DENSITY_MAXIMUM ABAL - 028 2 Germany silver fir, European fir 930 4748-745 1844 1995 - 028 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 6 028033 MISSING VALUES FOUND: 3 IN 1 GAPS / 1974 1976 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 0.918 0.076 -0.694 3.758 0.076 0.302 2 028023 1844 1995 152 0.924 0.067 -0.407 3.107 0.072 0.256 3 028025 1844 1995 152 0.911 0.071 -0.500 2.680 0.069 0.368 4 028027 1844 1995 152 0.904 0.076 -0.422 2.982 0.068 0.462 5 028031 1855 1995 141 0.830 0.080 -0.696 4.496 0.083 0.343 6 028033 1857 1995 139 0.828 0.082 -0.196 2.753 0.098 0.237 7 028035 1857 1995 139 0.852 0.075 -0.183 2.621 0.084 0.264 8 028037 1855 1995 141 0.840 0.079 -0.962 5.276 0.085 0.300 9 028051 1851 1995 145 0.848 0.092 -0.668 3.020 0.077 0.578 10 028053 1851 1995 145 0.836 0.069 -0.486 3.447 0.083 0.238 11 028055 1851 1995 145 0.851 0.067 -0.295 3.407 0.071 0.364 12 028057 1851 1995 145 0.888 0.068 -0.329 3.333 0.065 0.427 13 028071 1850 1995 146 0.865 0.068 -0.078 2.792 0.070 0.383 14 028073 1852 1995 144 0.886 0.066 -0.391 3.382 0.066 0.335 15 028075 1850 1995 146 0.875 0.073 -0.238 2.935 0.076 0.321 16 028077 1850 1995 146 0.896 0.077 -0.719 4.446 0.067 0.461 17 028091 1845 1995 151 0.862 0.076 -0.604 3.804 0.067 0.529 18 028093 1845 1995 151 0.871 0.071 -0.429 3.930 0.069 0.449 19 028095 1845 1995 151 0.870 0.074 -0.411 3.539 0.067 0.504 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 0.858 0.066 -0.229 3.248 0.068 0.358 NUMBER OF SERIES READ IN: 20 FROM 1844 TO 1995 152 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 0.871 0.074 -0.447 3.448 0.074 0.374 STANDARD DEVIATION 4 0.029 0.007 0.223 0.685 0.009 0.099 MEDIAN (50TH QUANTILE) 146 0.867 0.073 -0.417 3.358 0.070 0.361 INTERQUARTILE RANGE 6 0.043 0.009 0.369 0.822 0.012 0.154 MINIMUM VALUE 136 0.828 0.066 -0.962 2.621 0.065 0.237 LOWER HINGE (25TH QUANTILE) 144 0.850 0.068 -0.636 2.959 0.068 0.301 UPPER HINGE (75TH QUANTILE) 151 0.892 0.077 -0.267 3.781 0.080 0.455 MAXIMUM VALUE 152 0.924 0.092 -0.078 5.276 0.098 0.578 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.591 0.126 0.009 -0.152 2.500 0.299 0.849 MINIMUM CORRELATION: 0.299 SERIES 028033 AND 028055 139 YEARS MAXIMUM CORRELATION: 0.849 SERIES 028091 AND 028095 151 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.81 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1869. 1900. 1925. 1950. CORR 6. 190. 190. 190. RBAR 0.915 0.510 0.564 0.596 SDEV 0.017 0.182 0.177 0.147 SERR 0.007 0.013 0.013 0.011 EPS 0.995 0.954 0.963 0.967 NSS 17.9 20.0 20.0 20.0 |======================== 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 1844 1995 152 0.871 0.057 -0.247 3.100 0.056 0.414 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.227 -0.071 0.116 49 103 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.15 0.61 1.01 1.07 1.68 5.87 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.72 0.87 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 146. 6. 139. 144. 151. 152. |----------- 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 0.411 0.428 0.337 0.335 0.269 0.252 0.215 0.091 0.178 0.122 PACF 0.411 0.312 0.118 0.114 0.031 0.031 0.013 -0.133 0.083 0.018 95% C.L. 0.162 0.188 0.212 0.225 0.238 0.246 0.253 0.258 0.258 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 2 0.280 0.287 0.327 |================== 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 028021 3 0.00000000 0.00000000 -0.00017472 0.93178719 2 028023 3 0.00000000 0.00000000 -0.00046585 0.95938742 3 028025 3 0.00000000 0.00000000 -0.00007386 0.91663730 4 028027 3 0.00000000 0.00000000 -0.00036381 0.93197632 5 028031 1 0.28225160 0.00544326 0.00000000 0.63399100 6 028033 3 0.00000000 0.00000000 -0.00074495 0.88041651 7 028035 3 0.00000000 0.00000000 -0.00091112 0.91564906 8 028037 3 0.00000000 0.00000000 -0.00086070 0.90139312 9 028051 1 0.32424173 0.00590102 0.00000000 0.63104224 10 028053 3 0.00000000 0.00000000 -0.00032412 0.85945404 11 028055 1 0.06239552 0.00646095 0.00000000 0.81038857 12 028057 3 0.00000000 0.00000000 -0.00074736 0.94290233 13 028071 3 0.00000000 0.00000000 -0.00048968 0.90051204 14 028073 3 0.00000000 0.00000000 -0.00044856 0.91807598 15 028075 3 0.00000000 0.00000000 -0.00035923 0.90188289 16 028077 3 0.00000000 0.00000000 -0.00054178 0.93584788 17 028091 3 0.00000000 0.00000000 -0.00025493 0.88109666 18 028093 3 0.00000000 0.00000000 -0.00028940 0.89298809 19 028095 3 0.00000000 0.00000000 -0.00017180 0.88325560 SERIES IDENT OPTION A B C D 20 028097 3 0.00000000 0.00000000 -0.00011248 0.86616421 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 1.000 0.082 -0.784 3.930 0.076 0.289 2 028023 1844 1995 152 1.000 0.069 -0.556 3.126 0.072 0.182 3 028025 1844 1995 152 1.000 0.078 -0.516 2.718 0.069 0.364 4 028027 1844 1995 152 1.000 0.082 -0.572 3.412 0.068 0.438 5 028031 1855 1995 141 1.000 0.081 -0.953 5.264 0.082 0.089 6 028033 1857 1995 139 1.000 0.091 -0.492 3.205 0.096 0.114 7 028035 1857 1995 139 1.000 0.077 -0.495 3.033 0.084 0.042 8 028037 1855 1995 141 1.000 0.085 -1.048 5.360 0.085 0.154 9 028051 1851 1995 145 1.000 0.091 -0.407 3.823 0.077 0.384 10 028053 1851 1995 145 1.000 0.081 -0.450 3.259 0.082 0.203 11 028055 1851 1995 145 1.000 0.078 -0.211 3.355 0.070 0.346 12 028057 1851 1995 145 1.000 0.068 -0.124 2.935 0.065 0.266 13 028071 1850 1995 146 1.000 0.075 -0.069 2.825 0.069 0.324 14 028073 1852 1995 144 1.000 0.071 -0.550 3.505 0.065 0.269 15 028075 1850 1995 146 1.000 0.081 -0.249 2.818 0.076 0.287 16 028077 1850 1995 146 1.000 0.082 -0.812 4.714 0.067 0.412 17 028091 1845 1995 151 1.000 0.086 -0.678 4.172 0.066 0.516 18 028093 1845 1995 151 1.000 0.079 -0.698 4.516 0.068 0.424 19 028095 1845 1995 151 1.000 0.084 -0.488 3.876 0.067 0.495 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.077 -0.317 3.388 0.067 0.350 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.080 -0.523 3.662 0.074 0.297 STANDARD DEVIATION 4 0.000 0.006 0.259 0.789 0.008 0.134 MEDIAN (50TH QUANTILE) 146 1.000 0.081 -0.505 3.400 0.070 0.306 INTERQUARTILE RANGE 6 0.000 0.006 0.326 0.972 0.012 0.206 MINIMUM VALUE 139 1.000 0.068 -1.048 2.718 0.065 0.042 LOWER HINGE (25TH QUANTILE) 144 1.000 0.077 -0.688 3.080 0.067 0.192 UPPER HINGE (75TH QUANTILE) 151 1.000 0.083 -0.362 4.051 0.079 0.398 MAXIMUM VALUE 152 1.000 0.091 -0.069 5.360 0.096 0.516 |------------------------ 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 028021 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 028023 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 028025 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 028027 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 028031 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 028033 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 028035 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 028037 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 028051 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 028053 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 028055 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 028057 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 028071 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 028073 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 028075 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 028077 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 028091 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 028093 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 028095 -67 101 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 028097 -67 101 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 028021 1844 1995 152 1.000 0.075 -0.570 3.926 0.076 0.143 2 028023 1844 1995 152 1.000 0.066 -0.482 2.983 0.072 0.094 3 028025 1844 1995 152 1.000 0.072 -0.403 2.528 0.069 0.241 4 028027 1844 1995 152 1.000 0.073 -0.539 3.154 0.068 0.308 5 028031 1855 1995 141 1.000 0.081 -0.910 5.009 0.082 0.081 6 028033 1857 1995 139 1.000 0.090 -0.529 3.205 0.096 0.096 7 028035 1857 1995 139 1.000 0.076 -0.543 3.179 0.084 0.025 8 028037 1855 1995 141 1.000 0.083 -0.993 5.211 0.085 0.119 9 028051 1851 1995 145 1.000 0.081 -0.561 3.528 0.077 0.198 10 028053 1851 1995 145 1.000 0.075 -0.537 3.507 0.082 0.091 11 028055 1851 1995 145 1.000 0.077 -0.206 3.268 0.070 0.313 12 028057 1851 1995 145 1.000 0.063 -0.143 2.705 0.065 0.164 13 028071 1850 1995 146 1.000 0.068 0.044 2.826 0.069 0.191 14 028073 1852 1995 144 1.000 0.069 -0.384 3.116 0.066 0.234 15 028075 1850 1995 146 1.000 0.079 -0.210 2.700 0.076 0.252 16 028077 1850 1995 146 1.000 0.073 -0.776 4.340 0.067 0.264 17 028091 1845 1995 151 1.000 0.072 -0.203 3.536 0.066 0.299 18 028093 1845 1995 151 1.000 0.070 -0.344 3.839 0.068 0.259 19 028095 1845 1995 151 1.000 0.074 -0.137 3.410 0.067 0.359 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.068 -0.041 3.115 0.067 0.173 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.074 -0.423 3.454 0.074 0.195 STANDARD DEVIATION 4 0.000 0.006 0.277 0.717 0.008 0.093 MEDIAN (50TH QUANTILE) 146 1.000 0.074 -0.443 3.236 0.070 0.194 INTERQUARTILE RANGE 6 0.000 0.009 0.347 0.639 0.012 0.154 MINIMUM VALUE 139 1.000 0.063 -0.993 2.528 0.065 0.025 LOWER HINGE (25TH QUANTILE) 144 1.000 0.069 -0.552 3.049 0.067 0.107 UPPER HINGE (75TH QUANTILE) 151 1.000 0.078 -0.205 3.688 0.079 0.261 MAXIMUM VALUE 152 1.000 0.090 0.044 5.211 0.096 0.359 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.540 0.134 0.010 0.182 2.514 0.256 0.834 MINIMUM CORRELATION: 0.256 SERIES 028031 AND 028053 141 YEARS MAXIMUM CORRELATION: 0.834 SERIES 028025 AND 028027 152 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.81 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1869. 1900. 1925. 1950. CORR 6. 190. 190. 190. RBAR 0.900 0.517 0.592 0.591 SDEV 0.020 0.186 0.172 0.131 SERR 0.008 0.014 0.012 0.009 EPS 0.994 0.955 0.967 0.967 NSS 17.9 20.0 20.0 20.0 |======================== 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 1844 1995 152 1.000 0.056 -0.244 3.081 0.056 0.189 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.265 -0.092 0.140 51 101 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.94 1.01 1.12 2.06 6.55 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.73 0.86 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 0.188 0.228 0.098 0.101 0.013 0.023 -0.031 -0.178 -0.048 -0.116 PACF 0.188 0.200 0.028 0.040 -0.035 -0.005 -0.038 -0.188 0.019 -0.043 95% C.L. 0.162 0.168 0.176 0.177 0.179 0.179 0.179 0.179 0.184 0.184 |------------------ 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 0.078 0.154 0.205 |======================= 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 0.104 0.172 0.044 0.035 -0.056 -0.021 -0.046 -0.202 -0.048 -0.103 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 0.104 2 0.087 0.163 3 0.085 0.162 0.013 4 0.085 0.162 0.012 0.002 5 0.085 0.163 0.024 0.008 -0.071 6 0.083 0.163 0.024 0.011 -0.070 -0.018 7 0.083 0.161 0.025 0.011 -0.066 -0.016 -0.023 8 0.079 0.158 0.012 0.013 -0.061 0.016 -0.007 -0.194 9 0.078 0.158 0.012 0.013 -0.061 0.016 -0.007 -0.194 -0.001 10 0.078 0.151 0.012 0.014 -0.063 0.016 -0.006 -0.188 0.002 -0.039 LAST TERM IN EACH ROW ABOVE EQUALS THE PARTIAL AUTOCORRELATION COEFFICIENT AKAIKE INFORMATION CRITERION: AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) 785.20 785.56 783.45 785.43 787.43 788.66 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 790.61 792.53 788.67 790.67 792.44 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 0.087 0.163 R-SQUARED DUE TO POOLED AUTOREGRESSION: 3.71 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 103.86 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.087 0.171 0.029 0.030 0.007 0.006 0.002 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 028021 2 0.043 0.125 0.134 2 028023 2 0.041 0.078 0.179 3 028025 2 0.132 0.178 0.274 4 028027 2 0.139 0.252 0.200 5 028031 2 0.052 0.073 0.153 6 028033 2 0.024 0.086 0.118 7 028035 2 0.006 0.025 0.045 8 028037 2 0.027 0.114 0.103 9 028051 2 0.054 0.185 0.073 10 028053 2 0.034 0.080 0.137 11 028055 2 0.128 0.274 0.138 12 028057 2 0.035 0.157 0.074 13 028071 2 0.057 0.167 0.142 14 028073 2 0.096 0.197 0.195 15 028075 2 0.112 0.204 0.218 16 028077 2 0.090 0.250 0.109 17 028091 2 0.133 0.243 0.204 18 028093 2 0.109 0.210 0.204 19 028095 2 0.178 0.286 0.218 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 028097 2 0.080 0.138 0.223 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.078 0.166 0.157 STANDARD DEVIATION 0 0.048 0.075 0.060 MEDIAN 2 0.069 0.173 0.148 INTERQUARTILE RANGE 0 0.082 0.126 0.091 MINIMUM VALUE 2 0.006 0.025 0.045 LOWER HINGE 2 0.038 0.100 0.114 UPPER HINGE 2 0.120 0.227 0.204 MAXIMUM VALUE 2 0.178 0.286 0.274 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 028021 1844 1995 152 1.000 0.073 -0.713 4.363 0.081 -0.008 2 028023 1844 1995 152 1.000 0.064 -0.431 2.739 0.074 0.006 3 028025 1844 1995 152 1.000 0.067 -0.485 2.835 0.075 -0.011 4 028027 1844 1995 152 1.000 0.068 -0.439 2.847 0.077 -0.009 5 028031 1855 1995 141 1.000 0.080 -0.863 4.824 0.084 0.025 6 028033 1857 1995 139 1.000 0.089 -0.485 3.188 0.099 0.005 7 028035 1857 1995 139 1.000 0.076 -0.549 3.169 0.085 -0.003 8 028037 1855 1995 141 1.000 0.082 -1.060 5.404 0.089 0.011 9 028051 1851 1995 145 1.000 0.079 -0.636 4.019 0.085 -0.007 10 028053 1851 1995 145 1.000 0.074 -0.531 3.207 0.084 0.011 11 028055 1851 1995 145 1.000 0.072 -0.356 3.285 0.078 0.018 12 028057 1851 1995 145 1.000 0.062 -0.207 2.672 0.069 0.004 13 028071 1850 1995 146 1.000 0.066 0.014 2.826 0.076 0.003 14 028073 1852 1995 144 1.000 0.065 -0.392 3.011 0.071 0.003 15 028075 1850 1995 146 1.000 0.075 -0.279 2.756 0.083 0.006 16 028077 1850 1995 146 1.000 0.069 -0.849 4.563 0.076 0.014 17 028091 1845 1995 151 1.000 0.067 -0.140 3.130 0.074 -0.010 18 028093 1845 1995 151 1.000 0.066 -0.087 3.191 0.075 -0.002 19 028095 1845 1995 151 1.000 0.067 -0.059 3.381 0.076 -0.012 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 028097 1845 1995 151 1.000 0.065 -0.045 3.031 0.072 -0.007 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 147 1.000 0.071 -0.430 3.422 0.079 0.002 STANDARD DEVIATION 4 0.000 0.007 0.297 0.781 0.007 0.010 MEDIAN (50TH QUANTILE) 146 1.000 0.069 -0.435 3.179 0.077 0.003 INTERQUARTILE RANGE 6 0.000 0.010 0.419 0.859 0.009 0.016 MINIMUM VALUE 139 1.000 0.062 -1.060 2.672 0.069 -0.012 LOWER HINGE (25TH QUANTILE) 144 1.000 0.066 -0.593 2.841 0.074 -0.008 UPPER HINGE (75TH QUANTILE) 151 1.000 0.075 -0.173 3.700 0.084 0.009 MAXIMUM VALUE 152 1.000 0.089 0.014 5.404 0.099 0.025 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.554 0.116 0.008 0.389 2.873 0.288 0.834 MINIMUM CORRELATION: 0.288 SERIES 028031 AND 028053 141 YEARS MAXIMUM CORRELATION: 0.834 SERIES 028025 AND 028027 152 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.81 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1869. 1900. 1925. 1950. CORR 6. 190. 190. 190. RBAR 0.877 0.518 0.598 0.625 SDEV 0.022 0.178 0.163 0.111 SERR 0.009 0.013 0.012 0.008 EPS 0.992 0.956 0.967 0.971 NSS 17.9 20.0 20.0 20.0 |======================== 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 1844 1995 152 1.001 0.054 -0.381 3.272 0.061 -0.018 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.203 -0.069 0.114 51 101 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.36 1.03 1.01 1.14 2.18 8.41 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.75 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 -0.018 0.035 0.022 0.037 -0.022 0.034 -0.003 -0.176 -0.005 -0.082 PACF -0.018 0.034 0.023 0.037 -0.023 0.030 -0.002 -0.180 -0.011 -0.075 95% C.L. 0.162 0.162 0.162 0.163 0.163 0.163 0.163 0.163 0.168 0.168 |------------------ 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 -0.001 0.000 0.025 0.035 -0.023 0.037 -0.005 -0.175 -0.009 -0.077 PACF -0.001 0.000 0.025 0.035 -0.023 0.037 -0.006 -0.176 -0.010 -0.082 95% C.L. 0.162 0.162 0.162 0.162 0.163 0.163 0.163 0.163 0.168 0.168 |----------------- 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 -0.001 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 1844 1995 152 1.001 0.055 -0.347 3.254 0.058 0.100 |------------ 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 0.100 0.168 0.053 0.069 -0.002 0.022 -0.018 -0.180 -0.032 -0.103 PACF 0.100 0.160 0.024 0.037 -0.024 0.007 -0.020 -0.190 0.003 -0.048 95% C.L. 0.162 0.164 0.168 0.169 0.169 0.169 0.170 0.170 0.175 0.175 |------------------- 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 0.038 0.086 0.165 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES