RUN: brit FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: brit018n.rwl LOG FILE PROCESSED: brit018n.rwl_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 50 25 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 572 1 Loch Maree DENSITY_MINIMUM PISY - 572 2 Great Britain Scots pine, Scotch pine 100 5731-520 1756 1978 - 572 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 2 572012 MISSING VALUES FOUND: 43 IN 1 GAPS / 1902 1944 / -------------------------------------------------------------------- 3 572021 MISSING VALUES FOUND: 1 IN 1 GAPS / 1903 1903 / -------------------------------------------------------------------- 7 572041 MISSING VALUES FOUND: 1 IN 1 GAPS / 1910 1910 / -------------------------------------------------------------------- 15 572091 MISSING VALUES FOUND: 1 IN 1 GAPS / 1934 1934 / -------------------------------------------------------------------- 16 572092 MISSING VALUES FOUND: 5 IN 2 GAPS / 1799 1801 / 1837 1838 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 0.356 0.026 0.647 3.252 0.053 0.545 2 572012 1808 1978 171 0.361 0.024 0.041 3.135 0.057 0.464 3 572021 1885 1978 94 0.383 0.027 1.161 5.893 0.051 0.544 4 572022 1906 1978 73 0.355 0.025 -0.024 2.967 0.047 0.608 5 572031 1871 1978 108 0.330 0.022 0.449 3.795 0.056 0.407 6 572032 1845 1978 134 0.353 0.025 0.283 2.973 0.053 0.585 7 572041 1834 1978 145 0.394 0.026 -0.068 3.186 0.057 0.430 8 572042 1855 1978 124 0.360 0.036 -0.270 3.453 0.060 0.733 9 572051 1812 1978 167 0.410 0.034 0.260 4.669 0.053 0.614 10 572052 1853 1978 126 0.392 0.028 0.508 3.346 0.053 0.543 11 572061 1765 1978 214 0.362 0.026 0.416 2.832 0.046 0.649 12 572062 1795 1978 184 0.388 0.037 0.168 2.891 0.046 0.791 13 572071 1877 1978 102 0.396 0.033 -0.434 3.568 0.065 0.513 14 572072 1822 1958 137 0.402 0.047 0.121 2.967 0.067 0.732 15 572091 1846 1978 133 0.373 0.029 0.508 5.360 0.062 0.410 16 572092 1756 1978 223 0.376 0.033 0.817 3.747 0.052 0.699 NUMBER OF SERIES READ IN: 16 FROM 1756 TO 1978 223 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 143 0.374 0.030 0.287 3.627 0.055 0.579 STANDARD DEVIATION 43 0.022 0.006 0.406 0.910 0.006 0.120 MEDIAN (50TH QUANTILE) 133 0.374 0.027 0.272 3.299 0.053 0.565 INTERQUARTILE RANGE 59 0.035 0.008 0.499 0.801 0.007 0.186 MINIMUM VALUE 73 0.330 0.022 -0.434 2.832 0.046 0.407 LOWER HINGE (25TH QUANTILE) 116 0.358 0.025 0.009 2.970 0.051 0.489 UPPER HINGE (75TH QUANTILE) 175 0.393 0.033 0.508 3.771 0.059 0.674 MAXIMUM VALUE 218 0.410 0.047 1.161 5.893 0.067 0.791 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.149 0.212 0.019 -0.011 2.401 -0.361 0.625 MINIMUM CORRELATION: -0.361 SERIES 572051 AND 572062 167 YEARS MAXIMUM CORRELATION: 0.625 SERIES 572062 AND 572092 184 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.178 0.242 0.130 0.191 0.158 0.213 SDEV 0.377 0.169 0.277 0.220 0.278 0.220 SERR 0.217 0.053 0.052 0.027 0.027 0.021 EPS 0.523 0.720 0.627 0.768 0.745 0.812 NSS 5.1 8.1 11.3 14.0 15.6 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 1756 1978 223 0.375 0.016 0.110 2.921 0.037 0.424 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.090 -0.086 0.062 33 190 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 0.55 1.02 1.11 1.67 12.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.15 0.00 0.84 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 136. 62. 73. 116. 178. 223. |----------- 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 0.422 0.349 0.306 0.300 0.256 0.209 0.162 0.225 0.258 0.209 PACF 0.422 0.208 0.129 0.121 0.054 0.011 -0.017 0.107 0.119 0.017 95% C.L. 0.134 0.156 0.169 0.179 0.188 0.194 0.198 0.200 0.205 0.211 |------------------ 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 4 0.241 0.294 0.144 0.091 0.121 |================== 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 572011 1 0.05064024 0.02109218 0.00000000 0.34492296 2 572012 3 0.00000000 0.00000000 -0.00012808 0.36844903 3 572021 3 0.00000000 0.00000000 -0.00021876 0.39343336 4 572022 3 0.00000000 0.00000000 -0.00012434 0.35966894 5 572031 1 0.03847643 0.04184539 0.00000000 0.32129115 6 572032 3 0.00000000 0.00000000 -0.00002938 0.35466951 7 572041 3 0.00000000 0.00000000 0.00013420 0.38462210 8 572042 1 0.05817871 0.01395314 0.00000000 0.33252832 9 572051 3 0.00000000 0.00000000 0.00031288 0.38347882 10 572052 1 0.06481825 0.01275907 0.00000000 0.36026627 11 572061 1 0.06394628 0.01657466 0.00000000 0.34427217 12 572062 3 0.00000000 0.00000000 -0.00047703 0.43238595 13 572071 3 0.00000000 0.00000000 0.00007328 0.39230439 14 572072 3 0.00000000 0.00000000 0.00069805 0.35344031 15 572091 3 0.00000000 0.00000000 -0.00034999 0.39622352 16 572092 3 0.00000000 0.00000000 -0.00014166 0.39193329 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.000 0.063 0.315 3.136 0.053 0.386 2 572012 1808 1978 171 1.000 0.063 0.354 3.152 0.055 0.413 3 572021 1885 1978 94 1.000 0.068 0.812 5.085 0.050 0.503 4 572022 1906 1978 73 1.000 0.071 0.095 3.167 0.046 0.591 5 572031 1871 1978 108 1.000 0.061 0.307 3.790 0.056 0.262 6 572032 1845 1978 134 1.000 0.071 0.268 2.986 0.052 0.581 7 572041 1834 1978 145 1.000 0.064 0.050 3.290 0.057 0.402 8 572042 1855 1978 124 1.000 0.094 -0.317 3.258 0.060 0.682 9 572051 1812 1978 167 1.000 0.074 0.619 4.749 0.053 0.508 10 572052 1853 1978 126 1.000 0.059 -0.016 3.246 0.052 0.352 11 572061 1765 1978 214 1.000 0.055 0.502 4.010 0.045 0.420 12 572062 1795 1978 184 1.000 0.068 0.538 3.681 0.046 0.567 13 572071 1877 1978 102 1.000 0.084 -0.472 3.662 0.064 0.504 14 572072 1822 1958 137 1.000 0.095 0.158 2.999 0.067 0.613 15 572091 1846 1978 133 1.000 0.068 0.478 5.896 0.062 0.232 16 572092 1756 1978 223 1.000 0.083 0.850 3.958 0.051 0.677 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.071 0.284 3.754 0.054 0.481 STANDARD DEVIATION 44 0.000 0.012 0.365 0.834 0.006 0.136 MEDIAN (50TH QUANTILE) 135 1.000 0.068 0.311 3.476 0.053 0.504 INTERQUARTILE RANGE 61 0.000 0.015 0.447 0.824 0.007 0.192 MINIMUM VALUE 73 1.000 0.055 -0.472 2.986 0.045 0.232 LOWER HINGE (25TH QUANTILE) 116 1.000 0.063 0.072 3.160 0.051 0.394 UPPER HINGE (75TH QUANTILE) 177 1.000 0.078 0.520 3.984 0.058 0.586 MAXIMUM VALUE 223 1.000 0.095 0.850 5.896 0.067 0.682 |------------------------ 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 572011 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 572012 -67 114 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 572021 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 572022 -67 48 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 572031 -67 72 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 572032 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 572041 -67 97 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 572042 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 572051 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 572052 -67 84 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 572061 -67 143 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 572062 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 572071 -67 68 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 572072 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 572091 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 572092 -67 149 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 572011 1771 1978 208 1.000 0.061 0.277 3.282 0.053 0.348 2 572012 1808 1978 171 1.000 0.059 0.411 3.351 0.055 0.325 3 572021 1885 1978 94 1.000 0.063 1.479 8.790 0.050 0.418 4 572022 1906 1978 73 1.000 0.047 0.030 3.660 0.046 0.126 5 572031 1871 1978 108 1.000 0.060 0.288 3.741 0.056 0.257 6 572032 1845 1978 134 1.000 0.063 0.227 2.873 0.052 0.456 7 572041 1834 1978 145 1.000 0.060 -0.114 3.033 0.057 0.318 8 572042 1855 1978 124 0.999 0.072 -0.456 3.827 0.060 0.458 9 572051 1812 1978 167 1.000 0.069 0.774 5.179 0.053 0.443 10 572052 1853 1978 126 1.000 0.056 -0.212 3.495 0.053 0.258 11 572061 1765 1978 214 1.000 0.055 0.425 3.862 0.046 0.407 12 572062 1795 1978 184 1.000 0.054 0.215 3.973 0.046 0.326 13 572071 1877 1978 102 1.000 0.079 -0.739 4.090 0.064 0.455 14 572072 1822 1958 137 0.999 0.079 -0.039 3.550 0.067 0.443 15 572091 1846 1978 133 1.000 0.066 0.518 6.583 0.062 0.175 16 572092 1756 1978 223 0.999 0.065 0.427 4.001 0.051 0.474 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.063 0.219 4.206 0.054 0.355 STANDARD DEVIATION 44 0.000 0.009 0.509 1.509 0.006 0.108 MEDIAN (50TH QUANTILE) 135 1.000 0.062 0.252 3.784 0.053 0.377 INTERQUARTILE RANGE 61 0.000 0.010 0.502 0.623 0.008 0.161 MINIMUM VALUE 73 0.999 0.047 -0.739 2.873 0.046 0.126 LOWER HINGE (25TH QUANTILE) 116 1.000 0.057 -0.076 3.423 0.051 0.288 UPPER HINGE (75TH QUANTILE) 177 1.000 0.068 0.426 4.046 0.058 0.449 MAXIMUM VALUE 223 1.000 0.079 1.479 8.790 0.067 0.474 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.182 0.144 0.013 0.100 3.677 -0.246 0.616 MINIMUM CORRELATION: -0.246 SERIES 572021 AND 572091 94 YEARS MAXIMUM CORRELATION: 0.616 SERIES 572071 AND 572072 82 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.266 0.255 0.165 0.187 0.174 0.220 SDEV 0.158 0.160 0.201 0.168 0.226 0.191 SERR 0.091 0.051 0.038 0.021 0.022 0.019 EPS 0.648 0.734 0.690 0.763 0.767 0.819 NSS 5.1 8.1 11.3 14.0 15.6 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 1756 1978 223 0.998 0.034 -0.034 3.424 0.035 0.159 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.012 0.008 0.040 59 164 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.21 0.83 1.00 1.10 1.93 19.91 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.15 0.00 0.85 1.00 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 0.158 0.107 0.030 0.017 -0.070 -0.056 -0.013 0.024 0.048 0.039 PACF 0.158 0.084 0.002 0.004 -0.078 -0.038 0.014 0.037 0.045 0.017 95% C.L. 0.134 0.137 0.139 0.139 0.139 0.140 0.140 0.140 0.140 0.140 |------------------ 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 1 0.032 0.159 |======================= 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 0.072 0.124 0.007 0.019 -0.087 -0.015 -0.029 0.051 0.023 0.043 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 0.072 2 0.064 0.119 3 0.065 0.120 -0.010 4 0.065 0.120 -0.010 0.004 5 0.065 0.119 0.000 0.010 -0.090 6 0.065 0.119 0.000 0.011 -0.090 -0.006 7 0.065 0.118 0.000 0.011 -0.089 -0.006 -0.007 8 0.065 0.118 0.006 0.010 -0.089 -0.013 -0.011 0.058 9 0.064 0.119 0.006 0.012 -0.089 -0.013 -0.013 0.056 0.024 10 0.063 0.118 0.006 0.013 -0.087 -0.013 -0.014 0.054 0.023 0.020 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) 753.03 753.86 752.65 754.63 756.62 756.81 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 758.80 760.79 762.03 763.90 765.82 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 0.064 0.119 R-SQUARED DUE TO POOLED AUTOREGRESSION: 1.94 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 101.98 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.064 0.124 0.015 0.016 0.003 0.002 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 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 572011 2 0.189 0.260 0.267 2 572012 2 0.168 0.240 0.263 3 572021 2 0.193 0.465 -0.111 4 572022 2 0.043 0.132 -0.040 5 572031 2 0.079 0.231 0.109 6 572032 2 0.251 0.362 0.216 7 572041 2 0.122 0.276 0.134 8 572042 2 0.237 0.394 0.144 9 572051 2 0.219 0.385 0.142 10 572052 2 0.078 0.236 0.099 11 572061 2 0.181 0.360 0.115 12 572062 2 0.133 0.283 0.141 13 572071 2 0.277 0.325 0.291 14 572072 2 0.205 0.418 0.059 15 572091 2 0.052 0.164 0.077 16 572092 2 0.267 0.374 0.213 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.168 0.307 0.133 STANDARD DEVIATION 0 0.076 0.094 0.108 MEDIAN 2 0.185 0.304 0.138 INTERQUARTILE RANGE 0 0.127 0.142 0.126 MINIMUM VALUE 2 0.043 0.132 -0.111 LOWER HINGE 2 0.100 0.238 0.088 UPPER HINGE 2 0.228 0.380 0.215 MAXIMUM VALUE 2 0.277 0.465 0.291 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 572011 1771 1978 208 1.000 0.055 0.124 3.775 0.060 -0.015 2 572012 1808 1978 171 1.000 0.054 0.361 3.090 0.062 -0.005 3 572021 1885 1978 94 1.000 0.057 1.067 5.796 0.060 0.012 4 572022 1906 1978 73 1.000 0.047 -0.077 3.826 0.049 0.006 5 572031 1871 1978 108 1.000 0.058 0.122 3.864 0.063 0.001 6 572032 1845 1978 134 1.000 0.054 0.048 3.025 0.063 -0.012 7 572041 1834 1978 145 1.000 0.056 -0.035 2.820 0.066 0.008 8 572042 1855 1978 124 1.000 0.063 -0.384 3.830 0.071 0.013 9 572051 1812 1978 167 1.000 0.061 0.838 5.924 0.064 0.001 10 572052 1853 1978 126 1.000 0.053 -0.255 3.396 0.060 -0.006 11 572061 1765 1978 214 1.000 0.050 0.032 3.476 0.055 -0.009 12 572062 1795 1978 184 1.000 0.051 0.335 4.665 0.053 -0.007 13 572071 1877 1978 102 1.000 0.068 -0.428 3.864 0.075 -0.001 14 572072 1822 1958 137 1.000 0.070 0.223 3.320 0.077 0.003 15 572091 1846 1978 133 1.000 0.065 0.652 6.568 0.067 0.007 16 572092 1756 1978 223 1.000 0.056 0.323 3.522 0.063 -0.018 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 146 1.000 0.057 0.184 4.048 0.063 -0.001 STANDARD DEVIATION 44 0.000 0.007 0.413 1.113 0.007 0.009 MEDIAN (50TH QUANTILE) 135 1.000 0.056 0.123 3.801 0.063 0.000 INTERQUARTILE RANGE 61 0.000 0.008 0.404 0.907 0.007 0.014 MINIMUM VALUE 73 1.000 0.047 -0.428 2.820 0.049 -0.018 LOWER HINGE (25TH QUANTILE) 116 1.000 0.053 -0.056 3.358 0.060 -0.008 UPPER HINGE (75TH QUANTILE) 177 1.000 0.062 0.348 4.265 0.066 0.006 MAXIMUM VALUE 223 1.000 0.070 1.067 6.568 0.077 0.013 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.244 0.115 0.010 -0.266 4.470 -0.181 0.585 MINIMUM CORRELATION: -0.181 SERIES 572021 AND 572091 94 YEARS MAXIMUM CORRELATION: 0.585 SERIES 572071 AND 572072 82 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 53.38 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1810. 1835. 1860. 1885. 1910. 1935. CORR 3. 10. 28. 66. 105. 105. RBAR 0.308 0.245 0.236 0.251 0.225 0.274 SDEV 0.037 0.132 0.125 0.131 0.199 0.172 SERR 0.021 0.042 0.024 0.016 0.019 0.017 EPS 0.694 0.723 0.776 0.825 0.819 0.858 NSS 5.1 8.1 11.3 14.0 15.6 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 1756 1978 223 0.999 0.034 0.114 3.270 0.041 -0.140 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.032 0.018 0.025 60 163 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.28 0.66 1.00 1.07 1.74 6.83 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.14 0.00 0.86 1.00 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 -0.139 -0.068 -0.050 0.039 -0.083 -0.071 0.009 0.021 0.057 0.037 PACF -0.139 -0.089 -0.075 0.015 -0.088 -0.100 -0.031 -0.010 0.052 0.053 95% C.L. 0.134 0.136 0.137 0.137 0.138 0.139 0.139 0.139 0.139 0.140 |------------------ 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 0.027 -0.139 |---------- 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 -0.009 -0.078 0.006 -0.097 -0.082 -0.001 0.030 0.072 0.052 PACF -0.006 -0.009 -0.078 0.005 -0.099 -0.090 -0.005 0.012 0.061 0.046 95% C.L. 0.134 0.134 0.134 0.135 0.135 0.136 0.137 0.137 0.137 0.138 |----------------- 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 0.006 -0.006 -0.009 |========================= 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 1978 223 0.999 0.033 0.114 3.121 0.036 0.052 |------------ 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 0.052 0.107 -0.076 -0.001 -0.109 -0.082 -0.008 0.030 0.078 0.059 PACF 0.052 0.104 -0.088 -0.004 -0.093 -0.079 0.022 0.032 0.064 0.040 95% C.L. 0.134 0.134 0.136 0.137 0.137 0.138 0.139 0.139 0.139 0.140 |------------------- 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: 0.24 MINUTES