RUN: SPAI001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SPAI004E.rwl.conv LOG FILE PROCESSED: SPAI004E.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: 488 1 Las Blancas, Jaca WIDTH_EARLY PIMU - 488 2 Spain krummholz pine 1760 4241-34 1808 1977 - 488 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 11 488071 MISSING VALUES FOUND: 19 IN 1 GAPS / 1935 1953 / -------------------------------------------------------------------- 13 488081 MISSING VALUES FOUND: 1 IN 1 GAPS / 1942 1942 / -------------------------------------------------------------------- 14 488082 MISSING VALUES FOUND: 3 IN 1 GAPS / 1957 1959 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 488021 1834 1977 144 1.133 0.956 2.066 6.828 0.222 0.905 2 488022 1831 1977 147 1.136 0.902 1.838 5.727 0.252 0.907 3 488031 1814 1977 164 0.951 1.036 2.212 6.515 0.212 0.951 4 488032 1817 1942 126 1.003 1.149 2.232 6.990 0.270 0.927 5 488041 1819 1977 159 0.997 0.782 1.609 4.536 0.197 0.923 6 488042 1825 1977 153 0.957 0.796 1.830 6.181 0.195 0.871 7 488051 1842 1977 136 1.064 0.246 0.397 3.433 0.185 0.413 8 488052 1846 1977 132 0.903 0.287 -0.070 2.891 0.174 0.800 9 488061 1857 1977 121 0.890 0.199 0.140 3.134 0.220 0.254 10 488062 1853 1977 125 1.146 0.529 0.512 2.800 0.210 0.819 11 488071 1822 1977 156 1.044 0.723 1.584 5.186 0.206 0.899 12 488072 1823 1977 155 1.120 0.832 1.543 4.831 0.169 0.912 13 488081 1809 1977 169 1.055 0.974 1.425 3.881 0.279 0.944 14 488082 1808 1977 170 0.925 1.032 1.496 4.119 0.362 0.940 15 488101 1846 1977 132 1.042 0.628 1.207 4.009 0.205 0.855 16 488102 1853 1977 125 1.183 0.914 1.726 5.016 0.196 0.925 17 488111 1844 1977 134 1.294 0.666 0.989 3.082 0.178 0.896 18 488112 1850 1977 128 1.336 0.585 0.816 3.172 0.195 0.842 19 488121 1841 1977 137 1.413 0.501 1.043 6.146 0.145 0.801 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 488122 1824 1977 154 1.080 0.591 1.909 7.393 0.169 0.895 NUMBER OF SERIES READ IN: 20 FROM 1808 TO 1977 170 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 1.084 0.716 1.325 4.793 0.212 0.834 STANDARD DEVIATION 15 0.142 0.272 0.679 1.509 0.049 0.179 MEDIAN (50TH QUANTILE) 137 1.060 0.752 1.520 4.683 0.201 0.897 INTERQUARTILE RANGE 24 0.164 0.378 0.931 2.861 0.039 0.093 MINIMUM VALUE 121 0.890 0.199 -0.070 2.800 0.145 0.254 LOWER HINGE (25TH QUANTILE) 130 0.977 0.557 0.903 3.303 0.182 0.831 UPPER HINGE (75TH QUANTILE) 154 1.141 0.935 1.834 6.163 0.221 0.924 MAXIMUM VALUE 168 1.413 1.149 2.232 7.393 0.362 0.951 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.600 0.271 0.020 -0.425 1.822 -0.011 0.953 MINIMUM CORRELATION: -0.011 SERIES 488032 AND 488052 97 YEARS MAXIMUM CORRELATION: 0.953 SERIES 488081 AND 488082 169 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 77.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1860. 1885. 1910. 1935. CORR 55. 190. 190. 171. RBAR 0.853 0.263 0.309 0.126 SDEV 0.044 0.322 0.237 0.265 SERR 0.006 0.023 0.017 0.020 EPS 0.990 0.877 0.899 0.739 NSS 17.7 20.0 20.0 19.7 |======================== 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 1808 1977 170 1.310 0.937 1.460 3.918 0.120 0.950 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.483 0.099 0.309 57 113 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.39 1.00 1.08 1.47 8.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.86 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 140. 26. 121. 130. 156. 170. |----------- 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 0.945 0.916 0.892 0.860 0.841 0.814 0.796 0.779 0.768 0.749 PACF 0.945 0.215 0.099 -0.057 0.087 -0.047 0.070 0.022 0.091 -0.070 95% C.L. 0.153 0.256 0.324 0.377 0.421 0.459 0.492 0.521 0.548 0.573 |------------------ 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 0.960 0.454 0.339 0.195 |================== 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 488021 1 4.26107550 0.05509290 0.00000000 0.61045736 2 488022 1 3.64153409 0.04110456 0.00000000 0.54710591 3 488031 1 4.44023752 0.04532158 0.00000000 0.36731890 4 488032 1 5.33929253 0.06342985 0.00000000 0.35566625 5 488041 1 3.02508616 0.03142177 0.00000000 0.40523344 6 488042 1 3.20755076 0.03638904 0.00000000 0.39381191 7 488051 3 0.00000000 0.00000000 -0.00180378 1.18738234 8 488052 3 0.00000000 0.00000000 -0.00297976 1.10088134 9 488061 1 0.21332918 0.02621206 0.00000000 0.82673299 10 488062 3 0.00000000 0.00000000 -0.01100596 1.83913553 11 488071 1 2.76237440 0.03318558 0.00000000 0.43528304 12 488072 1 3.16511631 0.02935004 0.00000000 0.44143021 13 488081 1 3.81207180 0.02678924 0.00000000 0.22863568 14 488082 1 3.99302340 0.02693271 0.00000000 0.05962266 15 488101 1 2.29843450 0.02184142 0.00000000 0.29747912 16 488102 1 3.73216462 0.04414028 0.00000000 0.52401674 17 488111 1 2.33447099 0.01901812 0.00000000 0.45714095 18 488112 3 0.00000000 0.00000000 -0.01156539 2.08182693 19 488121 3 0.00000000 0.00000000 -0.00894585 2.03003764 SERIES IDENT OPTION A B C D 20 488122 1 2.09738755 0.02886205 0.00000000 0.62029308 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 488021 1834 1977 144 1.001 0.395 1.400 6.239 0.220 0.723 2 488022 1831 1977 147 1.001 0.331 0.380 3.262 0.250 0.587 3 488031 1814 1977 164 1.025 0.387 0.532 2.955 0.209 0.755 4 488032 1817 1942 126 1.007 0.363 1.248 6.758 0.267 0.435 5 488041 1819 1977 159 1.007 0.299 0.916 4.974 0.194 0.646 6 488042 1825 1977 153 1.002 0.284 0.822 4.092 0.194 0.556 7 488051 1842 1977 136 1.000 0.221 0.393 3.242 0.184 0.399 8 488052 1846 1977 132 0.998 0.302 0.210 2.859 0.173 0.780 9 488061 1857 1977 121 1.000 0.218 0.181 3.009 0.218 0.221 10 488062 1853 1977 125 0.999 0.328 0.746 3.438 0.208 0.632 11 488071 1822 1977 156 0.998 0.346 1.142 5.222 0.199 0.716 12 488072 1823 1977 155 0.999 0.294 0.970 4.264 0.167 0.670 13 488081 1809 1977 169 1.013 0.358 1.375 6.568 0.284 0.346 14 488082 1808 1977 170 1.057 0.475 1.397 6.514 0.358 0.440 15 488101 1846 1977 132 1.000 0.223 0.322 2.977 0.204 0.377 16 488102 1853 1977 125 1.001 0.238 1.424 7.981 0.195 0.473 17 488111 1844 1977 134 1.001 0.263 0.931 4.394 0.177 0.564 18 488112 1850 1977 128 1.008 0.337 1.880 8.899 0.193 0.670 19 488121 1841 1977 137 1.002 0.264 1.272 5.139 0.144 0.697 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 488122 1824 1977 154 1.000 0.246 1.141 6.183 0.168 0.592 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 143 1.006 0.309 0.934 4.949 0.210 0.564 STANDARD DEVIATION 15 0.014 0.068 0.478 1.806 0.049 0.154 MEDIAN (50TH QUANTILE) 140 1.001 0.300 0.951 4.684 0.197 0.590 INTERQUARTILE RANGE 25 0.007 0.098 0.861 3.124 0.038 0.246 MINIMUM VALUE 121 0.998 0.218 0.181 2.859 0.144 0.221 LOWER HINGE (25TH QUANTILE) 130 1.000 0.255 0.463 3.252 0.181 0.438 UPPER HINGE (75TH QUANTILE) 155 1.007 0.352 1.323 6.377 0.219 0.683 MAXIMUM VALUE 170 1.057 0.475 1.880 8.899 0.358 0.780 |------------------------ 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 488021 -67 96 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 488022 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 488031 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 488032 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 488041 -67 106 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 488042 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 488051 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 488052 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 488061 -67 81 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 488062 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 488071 -67 104 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 488072 -67 103 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 488081 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 488082 -67 113 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 488101 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 488102 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 488111 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 488112 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 19 488121 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH SERIES IDENT OPTION A B C D 20 488122 -67 103 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 488021 1834 1977 144 0.986 0.275 0.331 3.407 0.221 0.524 2 488022 1831 1977 147 0.997 0.321 0.367 3.337 0.250 0.567 3 488031 1814 1977 164 0.988 0.311 0.077 2.737 0.209 0.660 4 488032 1817 1942 126 0.997 0.336 1.045 5.768 0.267 0.397 5 488041 1819 1977 159 0.998 0.273 0.464 3.815 0.194 0.606 6 488042 1825 1977 153 0.999 0.268 0.568 3.400 0.194 0.533 7 488051 1842 1977 136 0.999 0.214 0.551 3.789 0.184 0.325 8 488052 1846 1977 132 0.997 0.254 0.276 3.645 0.172 0.647 9 488061 1857 1977 121 0.998 0.207 0.114 2.946 0.218 0.144 10 488062 1853 1977 125 0.995 0.300 0.584 3.231 0.209 0.571 11 488071 1822 1977 156 0.992 0.307 0.924 4.509 0.198 0.657 12 488072 1823 1977 155 0.997 0.273 0.675 3.407 0.167 0.644 13 488081 1809 1977 169 0.999 0.321 0.739 4.797 0.284 0.304 14 488082 1808 1977 170 0.996 0.386 0.669 4.500 0.358 0.375 15 488101 1846 1977 132 0.999 0.219 0.287 2.993 0.204 0.359 16 488102 1853 1977 125 1.000 0.232 1.205 6.940 0.195 0.448 17 488111 1844 1977 134 0.999 0.251 0.698 3.963 0.178 0.544 18 488112 1850 1977 128 0.997 0.299 1.633 8.640 0.193 0.626 19 488121 1841 1977 137 0.994 0.224 0.877 3.781 0.143 0.624 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 488122 1824 1977 154 0.998 0.238 1.158 6.315 0.167 0.569 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 143 0.996 0.276 0.662 4.296 0.210 0.506 STANDARD DEVIATION 15 0.004 0.047 0.394 1.524 0.049 0.144 MEDIAN (50TH QUANTILE) 140 0.997 0.273 0.626 3.785 0.197 0.556 INTERQUARTILE RANGE 25 0.003 0.074 0.551 1.284 0.039 0.239 MINIMUM VALUE 121 0.986 0.207 0.077 2.737 0.143 0.144 LOWER HINGE (25TH QUANTILE) 130 0.996 0.235 0.349 3.368 0.181 0.386 UPPER HINGE (75TH QUANTILE) 155 0.999 0.309 0.901 4.653 0.219 0.625 MAXIMUM VALUE 170 1.000 0.386 1.633 8.640 0.358 0.660 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.179 0.154 0.011 0.169 2.623 -0.146 0.553 MINIMUM CORRELATION: -0.146 SERIES 488052 AND 488112 128 YEARS MAXIMUM CORRELATION: 0.553 SERIES 488111 AND 488112 128 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 77.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1860. 1885. 1910. 1935. CORR 55. 190. 190. 171. RBAR 0.253 0.184 0.151 0.134 SDEV 0.189 0.213 0.212 0.248 SERR 0.025 0.015 0.015 0.019 EPS 0.857 0.818 0.780 0.753 NSS 17.7 20.0 20.0 19.7 |======================== 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 1808 1977 170 0.983 0.130 0.026 3.489 0.126 0.334 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.235 0.157 0.070 58 112 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.62 1.01 1.07 1.68 15.64 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.09 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 0.332 0.310 0.185 0.114 0.081 0.022 0.132 -0.013 -0.087 -0.144 PACF 0.332 0.224 0.037 -0.012 0.005 -0.032 0.133 -0.090 -0.145 -0.108 95% C.L. 0.153 0.169 0.182 0.187 0.188 0.189 0.189 0.191 0.191 0.192 |------------------ 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 0.159 0.255 0.230 |======================= 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 0.320 0.315 0.149 0.079 0.071 0.023 0.164 -0.006 -0.096 -0.120 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 0.320 2 0.244 0.237 3 0.245 0.238 -0.004 4 0.245 0.246 0.005 -0.037 5 0.246 0.246 -0.003 -0.044 0.030 6 0.247 0.246 -0.003 -0.041 0.033 -0.011 7 0.248 0.240 0.004 -0.041 -0.008 -0.052 0.166 8 0.266 0.235 0.003 -0.045 -0.008 -0.027 0.192 -0.103 9 0.246 0.271 -0.002 -0.047 -0.016 -0.027 0.236 -0.054 -0.188 10 0.235 0.268 0.013 -0.048 -0.017 -0.030 0.236 -0.037 -0.172 -0.062 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) 1165.10 1148.73 1140.93 1142.92 1144.69 1146.54 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1148.52 1145.78 1145.95 1141.86 1143.22 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 0.244 0.237 R-SQUARED DUE TO POOLED AUTOREGRESSION: 15.27 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 118.02 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.244 0.296 0.130 0.102 0.056 0.038 0.022 0.014 0.009 0.0056 0.003 0.002 0.001 0.001 0.001 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 488021 2 0.312 0.424 0.202 2 488022 2 0.351 0.471 0.171 3 488031 2 0.466 0.567 0.146 4 488032 2 0.188 0.322 0.189 5 488041 2 0.456 0.385 0.366 6 488042 2 0.387 0.339 0.367 7 488051 2 0.196 0.245 0.288 8 488052 2 0.483 0.470 0.288 9 488061 2 0.061 0.123 0.172 10 488062 2 0.341 0.524 0.092 11 488071 2 0.455 0.538 0.184 12 488072 2 0.438 0.578 0.115 13 488081 2 0.181 0.231 0.242 14 488082 2 0.186 0.291 0.224 15 488101 2 0.151 0.340 0.069 16 488102 2 0.217 0.444 0.011 17 488111 2 0.314 0.496 0.100 18 488112 2 0.409 0.636 -0.013 19 488121 2 0.428 0.584 0.101 SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 20 488122 2 0.346 0.623 -0.074 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.318 0.432 0.162 STANDARD DEVIATION 0 0.126 0.143 0.117 MEDIAN 2 0.344 0.457 0.172 INTERQUARTILE RANGE 0 0.241 0.222 0.137 MINIMUM VALUE 2 0.061 0.123 -0.074 LOWER HINGE 2 0.192 0.331 0.096 UPPER HINGE 2 0.433 0.553 0.233 MAXIMUM VALUE 2 0.483 0.636 0.367 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 488021 1834 1977 144 1.000 0.228 0.129 3.687 0.265 0.006 2 488022 1831 1977 147 1.000 0.260 0.343 3.034 0.292 0.015 3 488031 1814 1977 164 1.000 0.230 0.298 3.884 0.251 -0.021 4 488032 1817 1942 126 1.000 0.303 1.472 9.048 0.312 0.003 5 488041 1819 1977 159 1.000 0.201 0.090 3.238 0.230 -0.041 6 488042 1825 1977 153 1.000 0.211 0.869 3.946 0.217 0.024 7 488051 1842 1977 136 1.000 0.191 0.591 3.594 0.200 0.008 8 488052 1846 1977 132 1.000 0.182 0.058 3.081 0.203 -0.020 9 488061 1857 1977 121 1.000 0.202 0.197 2.853 0.233 -0.017 10 488062 1853 1977 125 1.000 0.244 0.233 3.903 0.268 -0.003 11 488071 1822 1977 156 1.000 0.227 0.283 4.761 0.250 0.003 12 488072 1823 1977 155 1.000 0.206 0.581 5.155 0.206 0.001 13 488081 1809 1977 169 1.000 0.297 0.600 5.071 0.319 -0.049 14 488082 1808 1977 170 1.000 0.349 0.605 4.725 0.394 -0.011 15 488101 1846 1977 132 1.000 0.203 0.057 3.104 0.237 0.008 16 488102 1853 1977 125 1.000 0.208 0.468 4.777 0.236 0.003 17 488111 1844 1977 134 1.000 0.208 0.384 3.817 0.224 0.015 18 488112 1850 1977 128 1.000 0.233 1.355 7.784 0.247 0.000 19 488121 1841 1977 137 1.000 0.168 0.652 3.532 0.180 -0.006 SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 20 488122 1824 1977 154 1.000 0.193 0.810 4.377 0.211 -0.003 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 143 1.000 0.227 0.504 4.368 0.249 -0.004 STANDARD DEVIATION 15 0.000 0.045 0.394 1.563 0.050 0.018 MEDIAN (50TH QUANTILE) 140 1.000 0.209 0.426 3.893 0.237 0.000 INTERQUARTILE RANGE 25 0.000 0.037 0.414 1.384 0.053 0.021 MINIMUM VALUE 121 1.000 0.168 0.057 2.853 0.180 -0.049 LOWER HINGE (25TH QUANTILE) 130 1.000 0.201 0.215 3.385 0.214 -0.014 UPPER HINGE (75TH QUANTILE) 155 1.000 0.238 0.629 4.769 0.267 0.007 MAXIMUM VALUE 170 1.000 0.349 1.472 9.048 0.394 0.024 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 190 0.243 0.116 0.008 0.338 4.501 -0.159 0.626 MINIMUM CORRELATION: -0.159 SERIES 488061 AND 488082 121 YEARS MAXIMUM CORRELATION: 0.626 SERIES 488111 AND 488112 128 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 77.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1860. 1885. 1910. 1935. CORR 55. 190. 190. 171. RBAR 0.356 0.240 0.219 0.210 SDEV 0.119 0.151 0.151 0.158 SERR 0.016 0.011 0.011 0.012 EPS 0.907 0.863 0.848 0.840 NSS 17.7 20.0 20.0 19.7 |======================== 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 1808 1977 170 0.992 0.118 -0.012 3.005 0.149 -0.201 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.268 0.135 0.043 68 102 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 0.59 1.00 1.08 1.67 11.54 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.08 0.00 0.86 0.95 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 -0.200 -0.001 0.007 -0.021 0.006 -0.109 0.177 -0.012 -0.011 -0.007 PACF -0.200 -0.042 -0.002 -0.021 -0.002 -0.114 0.139 0.048 0.004 -0.015 95% C.L. 0.153 0.159 0.159 0.159 0.159 0.159 0.161 0.166 0.166 0.166 |------------------ 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 0.042 -0.202 |---------- 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 -0.002 0.000 0.000 -0.024 -0.012 -0.082 0.164 0.018 -0.008 -0.026 PACF -0.002 0.000 0.000 -0.024 -0.012 -0.082 0.165 0.017 -0.008 -0.032 95% C.L. 0.153 0.153 0.153 0.153 0.153 0.154 0.155 0.159 0.159 0.159 |----------------- 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 0.000 -0.002 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 1808 1977 170 0.991 0.125 -0.135 3.632 0.122 0.317 |------------ 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 0.315 0.297 0.135 0.075 0.053 -0.010 0.127 0.006 -0.039 -0.106 PACF 0.315 0.220 -0.008 -0.025 0.014 -0.041 0.148 -0.054 -0.107 -0.090 95% C.L. 0.153 0.168 0.180 0.182 0.183 0.183 0.183 0.185 0.185 0.186 |------------------- 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 0.144 0.245 0.223 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.20 MINUTES