RUN: 4DIG001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM052I.rwl.conv LOG FILE PROCESSED: GERM052I.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: 049 1 Seehalde (D), EU-Pr. DENSITY_EARLY PCAB - 049 2 Germany Norway spruce 1250 4751-802 1756 1995 - 049 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 049011 1791 1995 205 3.394 0.511 3.277 16.694 0.070 0.567 2 049013 1791 1995 205 3.338 0.324 3.444 22.798 0.055 0.538 3 049015 1791 1995 205 3.212 0.335 3.363 19.955 0.055 0.505 4 049017 1790 1995 206 3.388 0.402 3.973 27.674 0.050 0.648 5 049021 1782 1995 214 3.120 0.298 1.830 11.271 0.066 0.497 6 049023 1782 1995 214 3.207 0.347 1.281 6.581 0.063 0.675 7 049025 1782 1995 214 3.214 0.324 1.791 10.941 0.054 0.697 8 049027 1807 1995 189 3.214 0.237 -0.052 3.525 0.055 0.475 9 049031 1777 1995 219 3.159 0.483 3.551 21.003 0.057 0.778 10 049033 1777 1995 219 3.056 0.373 3.381 17.979 0.055 0.730 11 049035 1777 1995 219 3.018 0.437 3.097 17.116 0.057 0.749 12 049037 1780 1995 216 3.073 0.407 2.872 13.988 0.066 0.597 13 049041 1756 1995 240 3.436 0.372 3.871 28.902 0.049 0.516 14 049043 1758 1995 238 3.364 0.298 4.141 36.476 0.048 0.538 15 049045 1756 1995 240 3.246 0.371 4.304 33.308 0.050 0.675 16 049047 1757 1995 239 3.358 0.300 2.350 17.911 0.048 0.617 17 049051 1756 1995 240 3.141 0.417 4.219 29.964 0.058 0.558 18 049053 1756 1995 240 2.951 0.322 2.424 13.882 0.053 0.679 19 049055 1763 1995 233 2.919 0.218 1.401 6.756 0.052 0.553 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 2.815 0.355 3.775 24.104 0.058 0.566 NUMBER OF SERIES READ IN: 20 FROM 1756 TO 1995 240 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 3.181 0.357 2.915 19.042 0.056 0.608 STANDARD DEVIATION 15 0.173 0.073 1.168 9.118 0.006 0.090 MEDIAN (50TH QUANTILE) 219 3.210 0.351 3.320 17.945 0.055 0.582 INTERQUARTILE RANGE 29 0.284 0.094 1.733 13.313 0.007 0.139 MINIMUM VALUE 189 2.815 0.218 -0.052 3.525 0.048 0.475 LOWER HINGE (25TH QUANTILE) 210 3.065 0.311 2.090 12.577 0.051 0.538 UPPER HINGE (75TH QUANTILE) 239 3.348 0.405 3.823 25.889 0.058 0.677 MAXIMUM VALUE 240 3.436 0.511 4.304 36.476 0.070 0.778 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.408 0.198 0.014 -0.147 2.298 -0.027 0.852 MINIMUM CORRELATION: -0.027 SERIES 049013 AND 049043 205 YEARS MAXIMUM CORRELATION: 0.852 SERIES 049045 AND 049047 239 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.748 0.198 0.341 0.459 0.240 0.341 0.541 0.548 SDEV 0.099 0.269 0.243 0.182 0.210 0.240 0.149 0.140 SERR 0.031 0.026 0.018 0.013 0.015 0.017 0.011 0.010 EPS 0.974 0.825 0.912 0.944 0.863 0.912 0.959 0.960 NSS 12.7 19.1 20.0 20.0 20.0 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 1756 1995 240 3.205 0.319 4.761 39.767 0.041 0.627 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.395 0.157 -0.211 60 180 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.18 0.91 1.00 1.05 1.96 19.28 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.05 0.61 0.87 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 219. 30. 189. 210. 240. 240. |----------- 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 0.624 0.518 0.466 0.427 0.379 0.335 0.263 0.229 0.224 0.197 PACF 0.624 0.211 0.137 0.090 0.035 0.015 -0.055 -0.004 0.041 0.005 95% C.L. 0.129 0.172 0.196 0.214 0.228 0.238 0.246 0.251 0.254 0.257 |------------------ 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 0.625 0.558 0.168 0.122 |================== 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 049011 1 1.26579666 0.02330546 0.00000000 3.13444424 2 049013 1 2.91511965 0.27041093 0.00000000 3.29264212 3 049015 1 1.77875555 0.13318351 0.00000000 3.15153193 4 049017 1 3.87440109 0.27797127 0.00000000 3.32980323 5 049021 1 0.69095302 0.00635403 0.00000000 2.74375606 6 049023 1 0.73006040 0.01852675 0.00000000 3.02794766 7 049025 1 1.02310157 0.01813419 0.00000000 2.95822811 8 049027 3 0.00000000 0.00000000 -0.00230434 3.43314528 9 049031 1 4.04533625 0.20616619 0.00000000 3.07790685 10 049033 1 2.78437209 0.14277689 0.00000000 2.97318554 11 049035 1 2.85251474 0.11770762 0.00000000 2.91362834 12 049037 1 2.03909492 0.08940788 0.00000000 2.97230411 13 049041 3 0.00000000 0.00000000 -0.00240942 3.72591805 14 049043 3 0.00000000 0.00000000 -0.00063316 3.43940210 15 049045 3 0.00000000 0.00000000 -0.00283785 3.58846140 16 049047 1 0.81278181 0.01539579 0.00000000 3.14476037 17 049051 1 3.00056791 0.16560234 0.00000000 3.07183290 18 049053 3 0.00000000 0.00000000 -0.00196053 3.18724370 19 049055 3 0.00000000 0.00000000 -0.00123574 3.06380868 SERIES IDENT OPTION A B C D 20 049057 1 1.49352157 0.07015642 0.00000000 2.72912455 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.000 0.108 2.310 13.561 0.070 0.362 2 049013 1791 1995 205 1.000 0.065 0.629 3.463 0.054 0.395 3 049015 1791 1995 205 1.000 0.076 2.081 11.834 0.055 0.364 4 049017 1790 1995 206 1.000 0.076 1.131 5.132 0.049 0.609 5 049021 1782 1995 214 1.000 0.081 1.320 8.343 0.066 0.340 6 049023 1782 1995 214 1.000 0.089 0.517 4.874 0.062 0.532 7 049025 1782 1995 214 1.000 0.058 1.429 9.836 0.054 0.163 8 049027 1807 1995 189 1.000 0.063 0.443 4.077 0.055 0.274 9 049031 1777 1995 219 1.000 0.095 0.939 3.596 0.057 0.653 10 049033 1777 1995 219 1.000 0.064 0.346 2.791 0.055 0.359 11 049035 1777 1995 219 1.000 0.082 0.640 3.205 0.056 0.535 12 049037 1780 1995 216 1.000 0.085 0.723 4.097 0.066 0.298 13 049041 1756 1995 240 1.000 0.093 3.534 25.926 0.049 0.434 14 049043 1758 1995 238 1.000 0.087 3.743 32.613 0.048 0.536 15 049045 1756 1995 240 1.000 0.091 4.223 33.560 0.050 0.580 16 049047 1757 1995 239 1.000 0.062 1.652 12.491 0.048 0.373 17 049051 1756 1995 240 1.000 0.086 1.439 9.048 0.058 0.438 18 049053 1756 1995 240 1.000 0.095 1.771 10.373 0.053 0.627 19 049055 1763 1995 233 1.000 0.068 1.179 5.226 0.052 0.480 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.088 2.425 20.337 0.058 0.373 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.081 1.624 11.219 0.056 0.436 STANDARD DEVIATION 15 0.000 0.014 1.132 9.591 0.006 0.130 MEDIAN (50TH QUANTILE) 219 1.000 0.084 1.375 8.695 0.055 0.415 INTERQUARTILE RANGE 29 0.000 0.023 1.514 8.939 0.007 0.175 MINIMUM VALUE 189 1.000 0.058 0.346 2.791 0.048 0.163 LOWER HINGE (25TH QUANTILE) 210 1.000 0.067 0.681 4.087 0.051 0.361 UPPER HINGE (75TH QUANTILE) 239 1.000 0.090 2.196 13.026 0.058 0.535 MAXIMUM VALUE 240 1.000 0.108 4.223 33.560 0.070 0.653 |------------------------ 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 049011 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 049013 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 049015 -67 137 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 049017 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 049021 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 049023 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 049025 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 049027 -67 126 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 049031 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 049033 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 049035 -67 146 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 049037 -67 144 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 049041 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 049043 -67 159 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 049045 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 049047 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 049051 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 049053 -67 160 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 049055 -67 156 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 049057 -67 160 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 049011 1791 1995 205 1.000 0.106 2.509 14.629 0.070 0.342 2 049013 1791 1995 205 1.000 0.061 0.746 4.205 0.054 0.304 3 049015 1791 1995 205 1.000 0.070 2.257 14.673 0.054 0.235 4 049017 1790 1995 206 1.000 0.064 0.921 4.741 0.049 0.448 5 049021 1782 1995 214 1.000 0.080 1.497 9.404 0.066 0.314 6 049023 1782 1995 214 1.000 0.088 0.524 4.931 0.062 0.524 7 049025 1782 1995 214 1.000 0.058 1.546 10.434 0.054 0.146 8 049027 1807 1995 189 1.000 0.058 0.429 3.595 0.055 0.170 9 049031 1777 1995 219 1.000 0.081 0.919 3.920 0.057 0.524 10 049033 1777 1995 219 1.000 0.062 0.387 2.846 0.055 0.318 11 049035 1777 1995 219 1.000 0.073 0.912 4.365 0.056 0.404 12 049037 1780 1995 216 1.000 0.079 1.014 4.992 0.066 0.180 13 049041 1756 1995 240 1.000 0.080 3.734 29.077 0.049 0.315 14 049043 1758 1995 238 1.000 0.078 3.090 25.498 0.048 0.501 15 049045 1756 1995 240 1.000 0.081 3.267 24.999 0.050 0.540 16 049047 1757 1995 239 1.000 0.061 1.745 13.332 0.048 0.348 17 049051 1756 1995 240 1.000 0.080 1.744 11.466 0.058 0.365 18 049053 1756 1995 240 1.000 0.087 1.396 8.223 0.053 0.585 19 049055 1763 1995 233 1.000 0.063 0.749 4.015 0.052 0.408 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.083 2.872 25.410 0.058 0.284 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.075 1.613 11.238 0.056 0.363 STANDARD DEVIATION 15 0.000 0.013 1.019 8.599 0.006 0.128 MEDIAN (50TH QUANTILE) 219 1.000 0.079 1.447 8.813 0.055 0.345 INTERQUARTILE RANGE 29 0.000 0.019 1.552 10.366 0.007 0.181 MINIMUM VALUE 189 1.000 0.058 0.387 2.846 0.048 0.146 LOWER HINGE (25TH QUANTILE) 210 1.000 0.062 0.831 4.285 0.051 0.294 UPPER HINGE (75TH QUANTILE) 239 1.000 0.081 2.383 14.651 0.058 0.475 MAXIMUM VALUE 240 1.000 0.106 3.734 29.077 0.070 0.585 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.334 0.131 0.010 0.171 2.896 0.024 0.730 MINIMUM CORRELATION: 0.024 SERIES 049011 AND 049055 205 YEARS MAXIMUM CORRELATION: 0.730 SERIES 049045 AND 049047 239 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.380 0.254 0.352 0.417 0.245 0.375 0.548 0.557 SDEV 0.287 0.215 0.242 0.167 0.198 0.223 0.145 0.128 SERR 0.091 0.021 0.018 0.012 0.014 0.016 0.010 0.009 EPS 0.886 0.867 0.916 0.935 0.867 0.923 0.960 0.962 NSS 12.7 19.1 20.0 20.0 20.0 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 1756 1995 240 0.997 0.056 2.948 22.331 0.041 0.347 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.525 0.250 -0.196 98 142 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.99 1.00 1.09 2.08 21.85 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.66 0.87 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 0.346 0.251 0.214 0.223 0.123 0.095 0.050 -0.040 -0.038 -0.041 PACF 0.346 0.150 0.103 0.115 -0.020 -0.001 -0.030 -0.105 -0.026 -0.017 95% C.L. 0.129 0.144 0.151 0.156 0.161 0.163 0.164 0.164 0.164 0.164 |------------------ 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 4 0.218 0.286 0.135 0.088 0.120 |======================= 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 0.199 0.174 0.182 0.164 0.122 0.043 0.090 -0.083 -0.046 -0.068 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 0.199 2 0.171 0.140 3 0.152 0.118 0.132 4 0.140 0.106 0.117 0.097 5 0.135 0.101 0.112 0.091 0.044 6 0.137 0.105 0.117 0.095 0.049 -0.038 7 0.138 0.103 0.113 0.091 0.045 -0.044 0.037 8 0.144 0.096 0.120 0.104 0.062 -0.028 0.057 -0.150 9 0.136 0.099 0.118 0.107 0.068 -0.022 0.062 -0.142 -0.052 10 0.133 0.091 0.122 0.106 0.071 -0.016 0.069 -0.136 -0.044 -0.056 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) 1210.27 1202.60 1199.83 1197.63 1197.35 1198.89 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1200.53 1202.21 1198.78 1200.13 1201.38 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 0.140 0.106 0.117 0.097 R-SQUARED DUE TO POOLED AUTOREGRESSION: 8.35 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 109.11 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 4) PROCESS OUT TO ORDER 50: 1.0000 0.140 0.126 0.149 0.148 0.065 0.054 0.046 0.034 0.022 0.0175 0.013 0.010 0.007 0.005 0.004 0.003 0.002 0.002 0.001 0.0009 0.001 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 049011 4 0.208 0.330 0.086 -0.093 0.052 2 049013 4 0.129 0.243 0.081 0.126 0.056 3 049015 4 0.093 0.185 0.116 0.056 0.099 4 049017 4 0.239 0.360 0.070 0.108 0.085 5 049021 4 0.164 0.232 0.230 0.088 -0.082 6 049023 4 0.311 0.434 0.203 -0.039 0.002 7 049025 4 0.035 0.139 0.045 0.093 -0.046 8 049027 4 0.049 0.163 0.017 0.090 0.031 9 049031 4 0.344 0.354 0.232 0.138 -0.036 10 049033 4 0.137 0.261 0.146 0.090 -0.064 11 049035 4 0.223 0.294 0.184 0.148 -0.048 12 049037 4 0.080 0.169 0.023 0.202 -0.049 13 049041 4 0.131 0.349 -0.017 0.033 0.063 14 049043 4 0.368 0.522 0.088 0.021 0.038 15 049045 4 0.403 0.593 0.018 -0.013 0.094 16 049047 4 0.182 0.320 0.160 -0.002 0.056 17 049051 4 0.225 0.244 0.196 0.011 0.191 18 049053 4 0.435 0.507 0.043 0.059 0.153 19 049055 4 0.269 0.242 0.229 0.131 0.075 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 049057 4 0.087 0.300 -0.035 -0.044 0.029 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 4 0.206 0.312 0.106 0.060 0.035 STANDARD DEVIATION 0 0.119 0.124 0.087 0.075 0.073 MEDIAN 4 0.195 0.297 0.087 0.074 0.045 INTERQUARTILE RANGE 0 0.179 0.120 0.157 0.112 0.121 MINIMUM VALUE 4 0.035 0.139 -0.035 -0.093 -0.082 LOWER HINGE 4 0.111 0.237 0.033 0.005 -0.041 UPPER HINGE 4 0.290 0.357 0.190 0.117 0.080 MAXIMUM VALUE 4 0.435 0.593 0.232 0.202 0.191 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 049011 1791 1995 205 1.000 0.099 2.142 13.922 0.085 0.013 2 049013 1791 1995 205 1.000 0.057 0.962 4.675 0.060 0.000 3 049015 1791 1995 205 1.000 0.066 2.817 22.075 0.060 -0.008 4 049017 1790 1995 206 1.000 0.056 0.661 5.531 0.057 0.003 5 049021 1782 1995 214 1.000 0.073 1.534 9.354 0.073 -0.016 6 049023 1782 1995 214 1.000 0.074 1.480 10.213 0.076 -0.001 7 049025 1782 1995 214 1.000 0.057 1.586 10.378 0.057 0.002 8 049027 1807 1995 189 1.000 0.057 0.272 3.702 0.059 -0.001 9 049031 1777 1995 219 1.000 0.066 0.821 4.538 0.068 -0.003 10 049033 1777 1995 219 1.000 0.058 0.514 2.787 0.062 0.005 11 049035 1777 1995 219 1.000 0.064 1.010 4.548 0.065 0.003 12 049037 1780 1995 216 1.000 0.076 0.860 4.806 0.072 -0.003 13 049041 1756 1995 240 1.000 0.074 4.658 40.359 0.058 -0.038 14 049043 1758 1995 238 1.000 0.059 1.833 15.414 0.062 -0.106 15 049045 1756 1995 240 1.000 0.059 1.406 11.421 0.066 -0.095 16 049047 1757 1995 239 1.000 0.054 1.316 10.542 0.056 -0.045 17 049051 1756 1995 240 1.000 0.071 2.139 14.229 0.066 -0.004 18 049053 1756 1995 240 1.000 0.064 1.002 6.793 0.070 -0.059 19 049055 1763 1995 233 1.000 0.053 0.517 3.299 0.058 -0.018 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 049057 1756 1995 240 1.000 0.079 3.922 39.177 0.067 -0.002 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 222 1.000 0.066 1.573 11.888 0.065 -0.019 STANDARD DEVIATION 15 0.000 0.011 1.130 10.748 0.007 0.033 MEDIAN (50TH QUANTILE) 219 1.000 0.064 1.361 9.784 0.063 -0.003 INTERQUARTILE RANGE 29 0.000 0.016 1.145 9.464 0.010 0.029 MINIMUM VALUE 189 1.000 0.053 0.272 2.787 0.056 -0.106 LOWER HINGE (25TH QUANTILE) 210 1.000 0.057 0.841 4.612 0.059 -0.028 UPPER HINGE (75TH QUANTILE) 239 1.000 0.073 1.986 14.076 0.069 0.001 MAXIMUM VALUE 240 1.000 0.099 4.658 40.359 0.085 0.013 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.384 0.106 0.008 0.199 3.146 0.139 0.698 MINIMUM CORRELATION: 0.139 SERIES 049011 AND 049053 205 YEARS MAXIMUM CORRELATION: 0.698 SERIES 049025 AND 049027 189 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.65 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1781. 1810. 1835. 1860. 1885. 1910. 1935. 1960. CORR 10. 105. 190. 190. 190. 190. 190. 190. RBAR 0.398 0.283 0.396 0.460 0.339 0.420 0.598 0.616 SDEV 0.173 0.167 0.187 0.124 0.141 0.162 0.110 0.099 SERR 0.055 0.016 0.014 0.009 0.010 0.012 0.008 0.007 EPS 0.894 0.883 0.929 0.945 0.911 0.935 0.968 0.970 NSS 12.7 19.1 20.0 20.0 20.0 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 1756 1995 240 0.996 0.044 1.511 9.986 0.047 -0.114 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.340 0.139 -0.094 99 141 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.76 1.00 1.11 1.87 62.45 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.07 0.66 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 -0.113 0.011 0.020 0.072 0.028 0.053 0.063 -0.073 0.001 -0.002 PACF -0.113 -0.002 0.021 0.078 0.046 0.062 0.075 -0.067 -0.026 -0.020 95% C.L. 0.129 0.131 0.131 0.131 0.131 0.132 0.132 0.132 0.133 0.133 |------------------ 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 0.015 -0.124 |---------- 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 0.006 -0.007 -0.012 -0.003 0.061 0.066 0.060 -0.081 -0.010 -0.006 PACF 0.006 -0.007 -0.012 -0.003 0.061 0.066 0.061 -0.080 -0.007 -0.010 95% C.L. 0.129 0.129 0.129 0.129 0.129 0.130 0.130 0.131 0.131 0.131 |----------------- 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 0.005 0.006 -0.008 -0.013 -0.004 |========================= 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 1995 240 0.996 0.046 1.531 9.552 0.040 0.221 |------------ 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 0.220 0.187 0.190 0.173 0.139 0.128 0.106 -0.016 0.020 0.011 PACF 0.220 0.146 0.132 0.097 0.053 0.045 0.023 -0.104 -0.020 -0.017 95% C.L. 0.129 0.135 0.139 0.144 0.147 0.149 0.151 0.152 0.152 0.152 |------------------- 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 4 0.110 0.165 0.119 0.124 0.095 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.26 MINUTES