RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN016L.rwl LOG FILE PROCESSED: FRAN016L.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: 257 1 Col dAllos WIDTH_LATE PCAB - 257 2 France Norway spruce 1900 4416-634 1792 1975 - 257 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 257150 MISSING VALUES FOUND: 5 IN 1 GAPS / 1933 1937 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 0.304 0.163 4.213 28.450 0.243 0.588 2 257070 1823 1975 153 0.173 0.060 1.169 4.253 0.193 0.668 3 257090 1835 1975 141 0.222 0.084 1.746 8.388 0.228 0.592 4 257120 1881 1975 95 0.336 0.175 4.409 29.600 0.321 0.288 5 257150 1792 1975 184 0.240 0.078 1.134 4.865 0.212 0.637 6 257160 1803 1975 173 0.212 0.059 1.674 7.445 0.197 0.412 7 257220 1847 1975 129 0.400 0.103 0.644 3.213 0.220 0.405 8 257230 1826 1975 150 0.332 0.097 1.203 5.972 0.230 0.411 9 257260 1850 1975 126 0.420 0.144 0.904 4.393 0.238 0.610 NUMBER OF SERIES READ IN: 9 FROM 1792 TO 1975 184 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 0.293 0.107 1.900 10.731 0.231 0.512 STANDARD DEVIATION 25 0.086 0.044 1.410 10.500 0.038 0.134 MEDIAN (50TH QUANTILE) 141 0.304 0.097 1.203 5.972 0.228 0.588 INTERQUARTILE RANGE 24 0.113 0.066 0.612 3.995 0.026 0.199 MINIMUM VALUE 95 0.173 0.059 0.644 3.213 0.193 0.288 LOWER HINGE (25TH QUANTILE) 129 0.222 0.078 1.134 4.393 0.212 0.411 UPPER HINGE (75TH QUANTILE) 153 0.336 0.144 1.746 8.388 0.238 0.610 MAXIMUM VALUE 179 0.420 0.175 4.409 29.600 0.321 0.668 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.201 0.162 0.027 -0.097 2.820 -0.152 0.526 MINIMUM CORRELATION: -0.152 SERIES 257090 AND 257230 141 YEARS MAXIMUM CORRELATION: 0.526 SERIES 257070 AND 257220 129 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 68.75 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. CORR 1. 1. 6. 10. 28. 28. 28. 28. 36. 36. RBAR 0.056 0.528 0.612 0.192 0.290 0.244 0.147 0.123 0.177 0.071 SDEV 0.000 0.000 0.155 0.205 0.240 0.241 0.215 0.295 0.254 0.350 SERR 0.000 0.000 0.063 0.065 0.045 0.046 0.041 0.056 0.042 0.058 EPS 0.132 0.809 0.888 0.618 0.765 0.720 0.592 0.556 0.660 0.407 NSS 2.5 3.8 5.1 6.8 8.0 8.0 8.4 8.9 9.0 9.0 YEAR 1920. 1930. 1940. 1950. 1960. CORR 36. 36. 36. 36. 36. RBAR 0.184 0.094 0.139 0.446 0.535 SDEV 0.287 0.268 0.271 0.171 0.153 SERR 0.048 0.045 0.045 0.029 0.025 EPS 0.669 0.482 0.592 0.879 0.912 NSS 9.0 9.0 9.0 9.0 9.0 |======================== 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 1792 1975 184 0.267 0.057 0.255 3.214 0.179 0.446 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.508 0.484 -0.030 33 151 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.37 6.57 1.07 1.27 7.84 168.64 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.19 0.00 0.81 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 141. 24. 95. 129. 153. 184. |----------- 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 0.444 0.277 0.229 0.137 0.031 -0.018 -0.083 0.058 0.123 0.078 PACF 0.444 0.100 0.093 -0.014 -0.074 -0.044 -0.079 0.174 0.114 -0.009 95% C.L. 0.147 0.174 0.183 0.189 0.192 0.192 0.192 0.193 0.193 0.195 |------------------ 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 0.206 0.445 |================== 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 257030 1 0.62073433 0.12826717 0.00000000 0.26856112 2 257070 1 0.08362948 0.05804252 0.00000000 0.16359998 3 257090 3 0.00000000 0.00000000 0.00083377 0.16321377 4 257120 3 0.00000000 0.00000000 -0.00073026 0.37094736 5 257150 1 0.11400071 0.01000888 0.00000000 0.18831074 6 257160 1 0.08577663 0.06731495 0.00000000 0.20530739 7 257220 3 0.00000000 0.00000000 0.00044471 0.37086120 8 257230 3 0.00000000 0.00000000 -0.00013247 0.34153467 9 257260 3 0.00000000 0.00000000 0.00199148 0.29377905 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 1.000 0.368 1.424 5.673 0.244 0.519 2 257070 1823 1975 153 1.000 0.336 1.436 5.398 0.192 0.642 3 257090 1835 1975 141 1.005 0.341 1.008 4.662 0.227 0.560 4 257120 1881 1975 95 1.000 0.524 4.475 29.725 0.317 0.278 5 257150 1792 1975 184 1.000 0.313 1.837 9.104 0.214 0.582 6 257160 1803 1975 173 1.000 0.258 1.199 6.256 0.197 0.392 7 257220 1847 1975 129 1.000 0.254 0.582 3.220 0.218 0.382 8 257230 1826 1975 150 1.000 0.295 1.291 6.173 0.228 0.407 9 257260 1850 1975 126 1.000 0.290 0.741 4.214 0.237 0.485 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 1.000 0.331 1.555 8.269 0.230 0.472 STANDARD DEVIATION 26 0.002 0.082 1.159 8.212 0.037 0.116 MEDIAN (50TH QUANTILE) 141 1.000 0.313 1.291 5.673 0.227 0.485 INTERQUARTILE RANGE 24 0.000 0.051 0.428 1.594 0.022 0.168 MINIMUM VALUE 95 1.000 0.254 0.582 3.220 0.192 0.278 LOWER HINGE (25TH QUANTILE) 129 1.000 0.290 1.008 4.662 0.214 0.392 UPPER HINGE (75TH QUANTILE) 153 1.000 0.341 1.436 6.256 0.237 0.560 MAXIMUM VALUE 184 1.005 0.524 4.475 29.725 0.317 0.642 |------------------------ 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 257030 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 257070 -67 102 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 257090 -67 94 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 257120 -67 63 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 257150 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 257160 -67 115 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 257220 -67 86 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 257230 -67 100 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 257260 -67 84 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 257030 1847 1975 129 0.994 0.299 1.184 6.211 0.244 0.335 2 257070 1823 1975 153 0.995 0.282 1.157 5.029 0.192 0.540 3 257090 1835 1975 141 0.996 0.236 1.039 5.946 0.226 0.193 4 257120 1881 1975 95 0.993 0.463 3.779 23.753 0.318 0.226 5 257150 1792 1975 184 0.997 0.293 1.593 8.167 0.215 0.535 6 257160 1803 1975 173 0.999 0.245 1.154 6.480 0.197 0.348 7 257220 1847 1975 129 0.998 0.241 0.558 3.586 0.218 0.329 8 257230 1826 1975 150 0.998 0.258 0.858 5.330 0.229 0.272 9 257260 1850 1975 126 0.998 0.277 0.654 3.946 0.237 0.438 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 0.996 0.288 1.331 7.605 0.231 0.357 STANDARD DEVIATION 26 0.002 0.070 0.969 6.209 0.037 0.125 MEDIAN (50TH QUANTILE) 141 0.997 0.277 1.154 5.946 0.226 0.335 INTERQUARTILE RANGE 24 0.003 0.048 0.327 1.451 0.022 0.166 MINIMUM VALUE 95 0.993 0.236 0.558 3.586 0.192 0.193 LOWER HINGE (25TH QUANTILE) 129 0.995 0.245 0.858 5.029 0.215 0.272 UPPER HINGE (75TH QUANTILE) 153 0.998 0.293 1.184 6.480 0.237 0.438 MAXIMUM VALUE 184 0.999 0.463 3.779 23.753 0.318 0.540 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.191 0.122 0.020 -0.076 2.774 -0.052 0.439 MINIMUM CORRELATION: -0.052 SERIES 257070 AND 257230 150 YEARS MAXIMUM CORRELATION: 0.439 SERIES 257070 AND 257220 129 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 68.75 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. CORR 1. 1. 6. 10. 28. 28. 28. 28. 36. 36. RBAR -0.029 0.491 0.598 0.197 0.238 0.292 0.144 0.130 0.168 0.087 SDEV 0.000 0.000 0.185 0.196 0.241 0.213 0.206 0.280 0.252 0.342 SERR 0.000 0.000 0.076 0.062 0.045 0.040 0.039 0.053 0.042 0.057 EPS -0.077 0.785 0.882 0.626 0.714 0.768 0.587 0.572 0.646 0.461 NSS 2.5 3.8 5.1 6.8 8.0 8.0 8.4 8.9 9.0 9.0 YEAR 1920. 1930. 1940. 1950. 1960. CORR 36. 36. 36. 36. 36. RBAR 0.147 0.089 0.145 0.452 0.555 SDEV 0.267 0.248 0.267 0.177 0.145 SERR 0.045 0.041 0.044 0.030 0.024 EPS 0.607 0.469 0.604 0.881 0.918 NSS 9.0 9.0 9.0 9.0 9.0 |======================== 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 1792 1975 184 0.977 0.171 0.206 3.478 0.163 0.300 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.330 0.234 -0.032 38 146 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.48 1.89 1.00 1.07 2.96 70.38 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.17 0.00 0.83 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 0.298 0.203 0.114 0.072 -0.052 -0.165 -0.205 -0.117 0.009 -0.063 PACF 0.298 0.125 0.026 0.012 -0.103 -0.159 -0.125 0.017 0.129 -0.045 95% C.L. 0.147 0.160 0.166 0.167 0.168 0.168 0.172 0.177 0.179 0.179 |------------------ 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 0.105 0.261 0.127 |======================= 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 0.307 0.213 0.126 0.115 -0.079 -0.149 -0.207 -0.127 -0.003 -0.113 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 0.307 2 0.267 0.131 3 0.263 0.122 0.032 4 0.261 0.116 0.019 0.052 5 0.270 0.119 0.037 0.094 -0.162 6 0.248 0.131 0.042 0.110 -0.126 -0.135 7 0.230 0.115 0.057 0.116 -0.109 -0.102 -0.130 8 0.231 0.116 0.057 0.115 -0.109 -0.103 -0.132 0.006 9 0.230 0.135 0.072 0.131 -0.125 -0.111 -0.148 -0.027 0.143 10 0.244 0.132 0.058 0.120 -0.137 -0.099 -0.142 -0.014 0.165 -0.094 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) 1010.79 994.54 993.36 995.17 996.67 993.77 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 992.41 991.25 993.24 991.43 991.79 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 0.267 0.131 R-SQUARED DUE TO POOLED AUTOREGRESSION: 10.99 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 112.35 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.267 0.202 0.089 0.050 0.025 0.013 0.007 0.004 0.002 0.0010 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 257030 2 0.120 0.357 -0.055 2 257070 2 0.339 0.409 0.248 3 257090 2 0.048 0.174 0.102 4 257120 2 0.057 0.238 -0.055 5 257150 2 0.297 0.505 0.058 6 257160 2 0.126 0.333 0.046 7 257220 2 0.144 0.282 0.145 8 257230 2 0.084 0.266 0.024 9 257260 2 0.304 0.276 0.371 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.169 0.316 0.098 STANDARD DEVIATION 0 0.113 0.099 0.140 MEDIAN 2 0.126 0.282 0.058 INTERQUARTILE RANGE 0 0.213 0.090 0.121 MINIMUM VALUE 2 0.048 0.174 -0.055 LOWER HINGE 2 0.084 0.266 0.024 UPPER HINGE 2 0.297 0.357 0.145 MAXIMUM VALUE 2 0.339 0.505 0.371 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 257030 1847 1975 129 1.000 0.281 0.843 5.508 0.279 -0.006 2 257070 1823 1975 153 1.000 0.229 0.860 4.683 0.235 -0.003 3 257090 1835 1975 141 1.000 0.231 1.072 6.179 0.242 -0.002 4 257120 1881 1975 95 1.000 0.451 4.365 28.979 0.341 0.003 5 257150 1792 1975 184 1.000 0.247 0.843 5.759 0.274 0.005 6 257160 1803 1975 173 1.000 0.229 0.812 6.049 0.238 0.001 7 257220 1847 1975 129 1.000 0.225 0.516 3.618 0.252 -0.020 8 257230 1826 1975 150 1.000 0.248 0.686 4.903 0.257 0.002 9 257260 1850 1975 126 1.000 0.231 0.409 3.238 0.262 -0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 142 1.000 0.263 1.156 7.657 0.264 -0.003 STANDARD DEVIATION 26 0.000 0.072 1.219 8.061 0.032 0.008 MEDIAN (50TH QUANTILE) 141 1.000 0.231 0.843 5.508 0.257 -0.002 INTERQUARTILE RANGE 24 0.000 0.018 0.174 1.366 0.032 0.008 MINIMUM VALUE 95 1.000 0.225 0.409 3.238 0.235 -0.020 LOWER HINGE (25TH QUANTILE) 129 1.000 0.229 0.686 4.683 0.242 -0.006 UPPER HINGE (75TH QUANTILE) 153 1.000 0.248 0.860 6.049 0.274 0.002 MAXIMUM VALUE 184 1.000 0.451 4.365 28.979 0.341 0.005 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 36 0.214 0.099 0.016 0.315 3.313 0.007 0.470 MINIMUM CORRELATION: 0.007 SERIES 257030 AND 257120 95 YEARS MAXIMUM CORRELATION: 0.470 SERIES 257090 AND 257220 129 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 68.75 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1820. 1830. 1840. 1850. 1860. 1870. 1880. 1890. 1900. 1910. CORR 1. 1. 6. 10. 28. 28. 28. 28. 36. 36. RBAR -0.021 0.512 0.478 0.295 0.233 0.321 0.173 0.191 0.227 0.208 SDEV 0.000 0.000 0.224 0.191 0.227 0.174 0.200 0.240 0.225 0.225 SERR 0.000 0.000 0.092 0.060 0.043 0.033 0.038 0.045 0.037 0.038 EPS -0.055 0.799 0.822 0.740 0.709 0.791 0.638 0.679 0.726 0.702 NSS 2.5 3.8 5.1 6.8 8.0 8.0 8.4 8.9 9.0 9.0 YEAR 1920. 1930. 1940. 1950. 1960. CORR 36. 36. 36. 36. 36. RBAR 0.195 0.120 0.157 0.389 0.531 SDEV 0.223 0.217 0.234 0.178 0.131 SERR 0.037 0.036 0.039 0.030 0.022 EPS 0.685 0.552 0.627 0.851 0.911 NSS 9.0 9.0 9.0 9.0 9.0 |======================== 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 1792 1975 184 0.990 0.155 0.323 3.482 0.176 -0.038 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.200 0.145 0.032 40 144 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.55 2.79 1.01 1.09 3.89 15.08 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.17 0.00 0.83 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 -0.038 0.006 0.019 0.060 -0.071 -0.124 -0.142 -0.072 0.060 -0.075 PACF -0.038 0.004 0.020 0.061 -0.067 -0.131 -0.158 -0.090 0.070 -0.050 95% C.L. 0.147 0.148 0.148 0.148 0.148 0.149 0.151 0.154 0.155 0.155 |------------------ 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 0.000 0.001 0.022 0.059 -0.073 -0.132 -0.150 -0.074 0.055 -0.072 PACF 0.000 0.001 0.022 0.059 -0.073 -0.134 -0.157 -0.082 0.070 -0.051 95% C.L. 0.147 0.147 0.147 0.148 0.148 0.149 0.151 0.155 0.155 0.156 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 2 0.001 0.000 0.001 |========================= 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 1792 1975 184 0.990 0.164 0.342 3.505 0.155 0.309 |------------ 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 0.307 0.214 0.100 0.051 -0.100 -0.183 -0.208 -0.142 -0.030 -0.091 PACF 0.307 0.131 0.003 -0.004 -0.142 -0.148 -0.104 -0.004 0.095 -0.071 95% C.L. 0.147 0.161 0.167 0.168 0.168 0.170 0.174 0.179 0.182 0.182 |------------------- 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 0.111 0.267 0.133 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.09 MINUTES