RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN018W.rwl LOG FILE PROCESSED: FRAN018W.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 20 10 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 260 1 Nizza, Foret dAillon WIDTH_RING PCAB - 260 2 France Norway spruce 1700 4353-720 1795 1975 - 260 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 260110 1842 1975 134 2.042 0.645 2.121 9.511 0.145 0.789 2 260120 1843 1975 133 1.826 0.624 1.075 3.947 0.178 0.737 3 260130 1890 1975 86 2.227 1.025 1.407 5.032 0.165 0.803 4 260140 1859 1975 117 2.013 1.124 0.767 3.201 0.159 0.906 5 260150 1828 1975 148 1.454 0.431 0.182 3.994 0.129 0.820 6 260160 1828 1975 148 1.387 0.371 1.761 8.064 0.150 0.703 7 260170 1795 1975 181 1.306 0.644 0.561 2.556 0.176 0.897 8 260180 1829 1975 147 1.437 0.404 0.342 3.807 0.159 0.748 9 260190 1852 1975 124 1.890 0.820 1.952 6.945 0.168 0.886 10 260200 1874 1975 102 1.526 0.651 0.734 2.700 0.157 0.869 NUMBER OF SERIES READ IN: 10 FROM 1795 TO 1975 181 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.711 0.674 1.090 4.976 0.159 0.816 STANDARD DEVIATION 26 0.326 0.253 0.687 2.394 0.015 0.072 MEDIAN (50TH QUANTILE) 133 1.676 0.645 0.921 3.970 0.159 0.811 INTERQUARTILE RANGE 31 0.576 0.388 1.201 3.744 0.018 0.138 MINIMUM VALUE 86 1.306 0.371 0.182 2.556 0.129 0.703 LOWER HINGE (25TH QUANTILE) 117 1.437 0.431 0.561 3.201 0.150 0.748 UPPER HINGE (75TH QUANTILE) 148 2.013 0.820 1.761 6.945 0.168 0.886 MAXIMUM VALUE 181 2.227 1.124 2.121 9.511 0.178 0.906 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.329 0.253 0.038 -0.152 2.930 -0.252 0.810 MINIMUM CORRELATION: -0.252 SERIES 260120 AND 260190 124 YEARS MAXIMUM CORRELATION: 0.810 SERIES 260130 AND 260140 86 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 64.32 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. 1920. 1930. CORR 6. 6. 15. 28. 28. 36. 45. 45. 45. 45. RBAR 0.347 0.017 0.197 0.272 0.421 0.470 0.319 0.206 0.318 0.665 SDEV 0.407 0.493 0.284 0.322 0.383 0.315 0.267 0.337 0.296 0.145 SERR 0.166 0.201 0.073 0.061 0.072 0.052 0.040 0.050 0.044 0.022 EPS 0.716 0.098 0.646 0.756 0.865 0.894 0.824 0.722 0.824 0.952 NSS 4.8 6.2 7.4 8.3 8.8 9.5 10.0 10.0 10.0 10.0 YEAR 1940. 1950. 1960. CORR 45. 45. 45. RBAR 0.734 0.458 0.358 SDEV 0.150 0.253 0.219 SERR 0.022 0.038 0.033 EPS 0.965 0.894 0.848 NSS 10.0 10.0 10.0 |======================== 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 1795 1975 181 1.512 0.457 0.069 4.116 0.131 0.806 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.704 0.460 -0.256 47 134 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.79 2.51 1.00 1.38 3.89 40.70 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.85 0.28 0.00 0.62 0.89 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 134. 31. 86. 117. 148. 181. |----------- 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 0.802 0.678 0.558 0.462 0.391 0.368 0.342 0.309 0.256 0.225 PACF 0.802 0.098 -0.030 -0.001 0.027 0.112 0.021 -0.020 -0.064 0.030 95% C.L. 0.149 0.225 0.266 0.291 0.307 0.317 0.327 0.334 0.341 0.345 |------------------ 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 1 0.650 0.804 |================== 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 260110 3 0.00000000 0.00000000 0.00497872 1.70572770 2 260120 3 0.00000000 0.00000000 0.00652610 1.38861585 3 260130 3 0.00000000 0.00000000 0.02686664 1.05862653 4 260140 3 0.00000000 0.00000000 0.01331483 1.22775865 5 260150 1 1.97077978 0.23291510 0.00000000 1.40287733 6 260160 1 1.92781913 0.11353309 0.00000000 1.27861786 7 260170 3 0.00000000 0.00000000 0.00498662 0.85257089 8 260180 3 0.00000000 0.00000000 0.00051206 1.39925075 9 260190 3 0.00000000 0.00000000 -0.01087172 2.56956339 10 260200 3 0.00000000 0.00000000 0.01331347 0.84043485 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 260110 1842 1975 134 1.000 0.290 1.684 7.688 0.144 0.757 2 260120 1843 1975 133 1.002 0.312 0.856 3.620 0.176 0.706 3 260130 1890 1975 86 1.010 0.341 1.168 4.536 0.165 0.683 4 260140 1859 1975 117 1.019 0.537 0.307 2.314 0.158 0.875 5 260150 1828 1975 148 1.000 0.269 -0.336 2.811 0.126 0.834 6 260160 1828 1975 148 1.000 0.167 -0.322 2.834 0.147 0.429 7 260170 1795 1975 181 1.004 0.454 0.522 3.171 0.176 0.873 8 260180 1829 1975 147 1.000 0.279 0.286 3.786 0.158 0.739 9 260190 1852 1975 124 0.999 0.344 1.558 5.987 0.166 0.820 10 260200 1874 1975 102 1.009 0.353 0.730 4.304 0.156 0.782 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.004 0.335 0.645 4.105 0.157 0.750 STANDARD DEVIATION 26 0.006 0.102 0.699 1.643 0.015 0.130 MEDIAN (50TH QUANTILE) 133 1.001 0.326 0.626 3.703 0.158 0.769 INTERQUARTILE RANGE 31 0.009 0.074 0.882 1.702 0.019 0.128 MINIMUM VALUE 86 0.999 0.167 -0.336 2.314 0.126 0.429 LOWER HINGE (25TH QUANTILE) 117 1.000 0.279 0.286 2.834 0.147 0.706 UPPER HINGE (75TH QUANTILE) 148 1.009 0.353 1.168 4.536 0.166 0.834 MAXIMUM VALUE 181 1.019 0.537 1.684 7.688 0.176 0.875 |------------------------ 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 260110 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 260120 -67 89 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 260130 -67 57 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 260140 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 260150 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 260160 -67 99 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 260170 -67 121 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 260180 -67 98 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 260190 -67 83 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 260200 -67 68 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 260110 1842 1975 134 0.997 0.264 1.398 6.540 0.144 0.720 2 260120 1843 1975 133 0.997 0.272 0.959 4.179 0.177 0.640 3 260130 1890 1975 86 0.991 0.248 0.887 4.603 0.165 0.550 4 260140 1859 1975 117 0.985 0.344 -0.201 2.910 0.157 0.819 5 260150 1828 1975 148 0.995 0.247 -0.283 3.094 0.126 0.807 6 260160 1828 1975 148 0.999 0.161 -0.370 3.012 0.147 0.390 7 260170 1795 1975 181 0.995 0.434 0.572 2.984 0.175 0.865 8 260180 1829 1975 147 0.997 0.264 0.271 3.664 0.157 0.711 9 260190 1852 1975 124 0.993 0.285 1.033 4.259 0.166 0.744 10 260200 1874 1975 102 0.995 0.308 0.532 2.692 0.156 0.769 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 0.995 0.283 0.480 3.794 0.157 0.702 STANDARD DEVIATION 26 0.004 0.071 0.612 1.171 0.015 0.142 MEDIAN (50TH QUANTILE) 133 0.995 0.268 0.552 3.379 0.157 0.732 INTERQUARTILE RANGE 31 0.004 0.060 1.160 1.275 0.019 0.167 MINIMUM VALUE 86 0.985 0.161 -0.370 2.692 0.126 0.390 LOWER HINGE (25TH QUANTILE) 117 0.993 0.248 -0.201 2.984 0.147 0.640 UPPER HINGE (75TH QUANTILE) 148 0.997 0.308 0.959 4.259 0.166 0.807 MAXIMUM VALUE 181 0.999 0.434 1.398 6.540 0.177 0.865 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.411 0.135 0.020 -0.061 2.254 0.167 0.696 MINIMUM CORRELATION: 0.167 SERIES 260120 AND 260190 124 YEARS MAXIMUM CORRELATION: 0.696 SERIES 260170 AND 260200 102 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 64.32 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. 1920. 1930. CORR 6. 6. 15. 28. 28. 36. 45. 45. 45. 45. RBAR 0.054 0.081 0.163 0.265 0.435 0.495 0.316 0.255 0.373 0.660 SDEV 0.368 0.431 0.290 0.296 0.388 0.299 0.272 0.286 0.241 0.174 SERR 0.150 0.176 0.075 0.056 0.073 0.050 0.041 0.043 0.036 0.026 EPS 0.214 0.354 0.593 0.750 0.871 0.903 0.822 0.774 0.856 0.951 NSS 4.8 6.2 7.4 8.3 8.8 9.5 10.0 10.0 10.0 10.0 YEAR 1940. 1950. 1960. CORR 45. 45. 45. RBAR 0.741 0.539 0.391 SDEV 0.148 0.192 0.198 SERR 0.022 0.029 0.030 EPS 0.966 0.921 0.865 NSS 10.0 10.0 10.0 |======================== 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 1795 1975 181 0.988 0.233 0.177 3.509 0.127 0.753 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.191 0.085 0.085 41 140 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 2.27 1.02 1.08 3.36 37.94 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.27 0.00 0.63 0.90 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 0.749 0.558 0.371 0.192 0.014 -0.102 -0.181 -0.228 -0.267 -0.285 PACF 0.749 -0.007 -0.102 -0.114 -0.148 -0.027 -0.036 -0.037 -0.084 -0.068 95% C.L. 0.149 0.217 0.246 0.258 0.262 0.262 0.262 0.265 0.269 0.275 |------------------ 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 0.572 0.756 |======================= 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 0.746 0.546 0.376 0.210 0.039 -0.091 -0.176 -0.214 -0.243 -0.270 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 0.746 2 0.766 -0.026 3 0.765 0.012 -0.050 4 0.760 0.013 0.031 -0.106 5 0.744 0.017 0.033 0.006 -0.147 6 0.734 0.018 0.035 0.007 -0.097 -0.068 7 0.731 0.014 0.036 0.009 -0.096 -0.039 -0.039 8 0.731 0.014 0.035 0.009 -0.096 -0.039 -0.037 -0.003 9 0.731 0.012 0.033 0.003 -0.096 -0.037 -0.036 0.038 -0.056 10 0.726 0.015 0.030 0.000 -0.104 -0.037 -0.033 0.039 0.009 -0.088 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) 1112.09 966.62 968.50 970.05 970.02 968.06 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 969.23 970.95 972.95 974.38 974.96 SELECTED AUTOREGRESSION ORDER: 1 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 0.746 R-SQUARED DUE TO POOLED AUTOREGRESSION: 55.72 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 225.85 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.746 0.557 0.416 0.311 0.232 0.173 0.129 0.096 0.072 0.0537 0.040 0.030 0.022 0.017 0.012 0.009 0.007 0.005 0.004 0.0029 0.002 0.002 0.001 0.001 0.001 0.000 0.000 0.000 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 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 260110 1 0.522 0.721 2 260120 1 0.438 0.645 3 260130 1 0.310 0.557 4 260140 1 0.695 0.824 5 260150 1 0.652 0.807 6 260160 1 0.153 0.391 7 260170 1 0.761 0.868 8 260180 1 0.522 0.722 9 260190 1 0.558 0.746 10 260200 1 0.604 0.771 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.522 0.705 STANDARD DEVIATION 0 0.182 0.142 MEDIAN 1 0.540 0.734 INTERQUARTILE RANGE 0 0.214 0.162 MINIMUM VALUE 1 0.153 0.391 LOWER HINGE 1 0.438 0.645 UPPER HINGE 1 0.652 0.807 MAXIMUM VALUE 1 0.761 0.868 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 260110 1842 1975 134 1.000 0.183 0.626 4.724 0.196 -0.048 2 260120 1843 1975 133 1.000 0.208 0.855 4.826 0.213 0.130 3 260130 1890 1975 86 1.000 0.205 1.365 6.536 0.198 0.014 4 260140 1859 1975 117 1.000 0.194 -0.146 4.558 0.186 0.180 5 260150 1828 1975 148 1.000 0.146 -0.234 3.823 0.161 0.042 6 260160 1828 1975 148 1.000 0.148 -0.130 3.260 0.169 0.008 7 260170 1795 1975 181 1.000 0.215 0.582 3.862 0.219 0.142 8 260180 1829 1975 147 1.000 0.182 0.195 3.297 0.209 0.036 9 260190 1852 1975 124 1.000 0.190 0.569 3.611 0.220 -0.038 10 260200 1874 1975 102 1.000 0.196 0.895 4.309 0.192 0.109 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.187 0.458 4.281 0.196 0.057 STANDARD DEVIATION 26 0.000 0.023 0.525 0.972 0.020 0.079 MEDIAN (50TH QUANTILE) 133 1.000 0.192 0.576 4.086 0.197 0.039 INTERQUARTILE RANGE 31 0.000 0.023 0.985 1.112 0.026 0.122 MINIMUM VALUE 86 1.000 0.146 -0.234 3.260 0.161 -0.048 LOWER HINGE (25TH QUANTILE) 117 1.000 0.182 -0.130 3.611 0.186 0.008 UPPER HINGE (75TH QUANTILE) 148 1.000 0.205 0.855 4.724 0.213 0.130 MAXIMUM VALUE 181 1.000 0.215 1.365 6.536 0.220 0.180 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.410 0.099 0.015 -0.143 2.431 0.217 0.582 MINIMUM CORRELATION: 0.217 SERIES 260160 AND 260170 148 YEARS MAXIMUM CORRELATION: 0.582 SERIES 260120 AND 260130 86 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 64.32 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. 1920. 1930. CORR 6. 6. 15. 28. 28. 36. 45. 45. 45. 45. RBAR 0.165 0.233 0.266 0.343 0.330 0.403 0.425 0.201 0.377 0.498 SDEV 0.313 0.214 0.155 0.188 0.238 0.204 0.153 0.223 0.193 0.132 SERR 0.128 0.087 0.040 0.036 0.045 0.034 0.023 0.033 0.029 0.020 EPS 0.483 0.653 0.730 0.813 0.812 0.865 0.881 0.715 0.858 0.908 NSS 4.8 6.2 7.4 8.3 8.8 9.5 10.0 10.0 10.0 10.0 YEAR 1940. 1950. 1960. CORR 45. 45. 45. RBAR 0.562 0.580 0.491 SDEV 0.172 0.119 0.176 SERR 0.026 0.018 0.026 EPS 0.928 0.932 0.906 NSS 10.0 10.0 10.0 |======================== 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 1795 1975 181 0.995 0.143 0.380 4.063 0.155 0.030 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.176 0.082 0.024 30 151 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.62 2.81 1.02 1.17 3.98 7.76 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.17 0.00 0.73 0.91 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.029 0.089 0.020 0.026 -0.090 -0.121 -0.097 -0.049 -0.072 -0.080 PACF 0.029 0.088 0.015 0.018 -0.095 -0.122 -0.079 -0.023 -0.047 -0.072 95% C.L. 0.149 0.149 0.150 0.150 0.150 0.151 0.153 0.155 0.155 0.156 |------------------ 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 -0.003 0.087 0.016 0.028 -0.087 -0.116 -0.092 -0.045 -0.068 -0.075 PACF -0.003 0.087 0.017 0.021 -0.091 -0.123 -0.082 -0.025 -0.046 -0.071 95% C.L. 0.149 0.149 0.150 0.150 0.150 0.151 0.153 0.154 0.155 0.155 |----------------- 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 1 0.008 -0.003 |========================= 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 1795 1975 181 0.997 0.213 0.501 3.823 0.117 0.745 |------------ 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 0.741 0.550 0.351 0.175 -0.006 -0.134 -0.203 -0.237 -0.263 -0.271 PACF 0.741 0.003 -0.125 -0.100 -0.152 -0.064 -0.004 -0.024 -0.076 -0.067 95% C.L. 0.149 0.215 0.244 0.255 0.258 0.258 0.259 0.263 0.268 0.273 |------------------- 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 1 0.550 0.742 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.08 MINUTES