RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN017W.rwl LOG FILE PROCESSED: FRAN017W.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: 259 1 Nizza, Foret dAillon WIDTH_RING ABAL - 259 2 France silver fir, European fir 1700 4353-720 1838 1975 - 259 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 259010 1935 1975 41 4.293 1.197 0.320 3.706 0.151 0.752 2 259020 1876 1975 100 2.985 0.652 0.156 2.470 0.122 0.744 3 259030 1895 1975 81 3.533 1.630 0.428 2.374 0.161 0.917 4 259040 1849 1975 127 1.714 0.457 0.648 2.947 0.129 0.772 5 259050 1848 1975 128 1.867 0.849 0.952 3.064 0.135 0.924 6 259060 1844 1975 132 1.786 0.641 2.120 7.640 0.126 0.904 7 259070 1860 1975 116 2.144 0.974 0.104 2.197 0.141 0.927 8 259080 1861 1975 115 1.648 0.454 0.569 3.179 0.159 0.705 9 259090 1908 1975 68 1.681 1.005 0.948 3.284 0.169 0.946 10 259100 1838 1975 138 1.740 0.828 1.110 4.033 0.184 0.885 NUMBER OF SERIES READ IN: 10 FROM 1838 TO 1975 138 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 2.339 0.869 0.735 3.490 0.148 0.848 STANDARD DEVIATION 31 0.936 0.359 0.595 1.568 0.020 0.093 MEDIAN (50TH QUANTILE) 115 1.827 0.839 0.608 3.122 0.146 0.894 INTERQUARTILE RANGE 47 1.270 0.364 0.632 1.236 0.031 0.172 MINIMUM VALUE 41 1.648 0.454 0.104 2.197 0.122 0.705 LOWER HINGE (25TH QUANTILE) 81 1.714 0.641 0.320 2.470 0.129 0.752 UPPER HINGE (75TH QUANTILE) 128 2.985 1.005 0.952 3.706 0.161 0.924 MAXIMUM VALUE 138 4.293 1.630 2.120 7.640 0.184 0.946 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.403 0.244 0.036 -0.026 2.266 -0.076 0.890 MINIMUM CORRELATION: -0.076 SERIES 259070 AND 259080 115 YEARS MAXIMUM CORRELATION: 0.890 SERIES 259030 AND 259090 68 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 62.61 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1860. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 6. 10. 15. 21. 21. 28. 36. 36. 36. 45. RBAR 0.248 0.131 0.188 0.128 0.198 0.174 0.361 0.531 0.652 0.189 SDEV 0.363 0.237 0.296 0.375 0.387 0.365 0.343 0.324 0.261 0.316 SERR 0.148 0.075 0.076 0.082 0.084 0.069 0.057 0.054 0.044 0.047 EPS 0.620 0.482 0.607 0.516 0.660 0.645 0.836 0.913 0.948 0.700 NSS 4.9 6.2 6.7 7.2 7.8 8.6 9.0 9.2 9.8 10.0 YEAR 1960. CORR 45. RBAR 0.399 SDEV 0.437 SERR 0.065 EPS 0.869 NSS 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 1838 1975 138 2.104 0.716 1.177 3.658 0.133 0.891 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.264 0.172 0.415 50 88 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.83 3.53 1.03 1.34 4.87 87.03 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.12 0.00 0.79 0.91 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 116. 47. 41. 81. 128. 138. |----------- 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 0.885 0.830 0.754 0.662 0.587 0.501 0.471 0.399 0.346 0.277 PACF 0.885 0.218 -0.064 -0.157 -0.013 -0.055 0.206 -0.120 -0.057 -0.141 95% C.L. 0.170 0.273 0.338 0.384 0.416 0.439 0.455 0.469 0.479 0.486 |------------------ 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 2 0.835 0.569 0.367 |================== 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 259010 3 0.00000000 0.00000000 -0.01029094 4.50903654 2 259020 3 0.00000000 0.00000000 0.00179964 2.89401817 3 259030 3 0.00000000 0.00000000 0.00002033 3.53188276 4 259040 3 0.00000000 0.00000000 0.00419795 1.44574058 5 259050 1 2.85942173 0.12735528 0.00000000 1.70240021 6 259060 1 2.40598536 0.06057038 0.00000000 1.49456787 7 259070 3 0.00000000 0.00000000 0.00244739 2.00131035 8 259080 3 0.00000000 0.00000000 0.00111102 1.58338666 9 259090 3 0.00000000 0.00000000 0.01595946 1.13086915 10 259100 1 2.73243093 0.03816217 0.00000000 1.23399568 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 259010 1935 1975 41 1.000 0.272 0.185 4.009 0.147 0.720 2 259020 1876 1975 100 1.000 0.217 0.130 2.427 0.121 0.735 3 259030 1895 1975 81 1.000 0.461 0.427 2.373 0.159 0.905 4 259040 1849 1975 127 1.000 0.246 0.296 2.221 0.128 0.751 5 259050 1848 1975 128 1.000 0.422 1.345 4.491 0.134 0.912 6 259060 1844 1975 132 1.000 0.198 0.333 2.840 0.125 0.700 7 259070 1860 1975 116 1.000 0.444 0.003 2.187 0.140 0.916 8 259080 1861 1975 115 1.000 0.273 0.498 3.006 0.157 0.703 9 259090 1908 1975 68 0.998 0.540 0.556 2.659 0.167 0.917 10 259100 1838 1975 138 1.000 0.329 0.993 4.641 0.183 0.737 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.340 0.477 3.085 0.146 0.800 STANDARD DEVIATION 31 0.001 0.118 0.410 0.942 0.020 0.098 MEDIAN (50TH QUANTILE) 115 1.000 0.301 0.380 2.749 0.144 0.744 INTERQUARTILE RANGE 47 0.000 0.198 0.370 1.636 0.030 0.193 MINIMUM VALUE 41 0.998 0.198 0.003 2.187 0.121 0.700 LOWER HINGE (25TH QUANTILE) 81 1.000 0.246 0.185 2.373 0.128 0.720 UPPER HINGE (75TH QUANTILE) 128 1.000 0.444 0.556 4.009 0.159 0.912 MAXIMUM VALUE 138 1.000 0.540 1.345 4.641 0.183 0.917 |------------------------ 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 259010 -67 27 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 259020 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 259030 -67 54 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 259040 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 259050 -67 85 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 259060 -67 88 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 259070 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 259080 -67 77 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 259090 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 259100 -67 92 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 259010 1935 1975 41 0.991 0.155 -0.113 3.515 0.137 0.398 2 259020 1876 1975 100 0.997 0.200 0.131 2.543 0.120 0.696 3 259030 1895 1975 81 0.961 0.261 -0.489 2.707 0.156 0.775 4 259040 1849 1975 127 0.996 0.223 0.119 2.352 0.128 0.684 5 259050 1848 1975 128 0.983 0.301 0.530 3.802 0.134 0.856 6 259060 1844 1975 132 0.999 0.185 0.230 2.734 0.125 0.648 7 259070 1860 1975 116 0.976 0.287 0.177 3.185 0.140 0.837 8 259080 1861 1975 115 0.997 0.231 0.362 3.490 0.157 0.648 9 259090 1908 1975 68 0.943 0.283 -0.129 2.592 0.161 0.770 10 259100 1838 1975 138 0.997 0.311 0.920 4.469 0.183 0.713 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 0.984 0.244 0.174 3.139 0.144 0.703 STANDARD DEVIATION 31 0.019 0.053 0.386 0.675 0.020 0.129 MEDIAN (50TH QUANTILE) 115 0.994 0.246 0.154 2.960 0.138 0.705 INTERQUARTILE RANGE 47 0.021 0.087 0.475 0.923 0.029 0.127 MINIMUM VALUE 41 0.943 0.155 -0.489 2.352 0.120 0.398 LOWER HINGE (25TH QUANTILE) 81 0.976 0.200 -0.113 2.592 0.128 0.648 UPPER HINGE (75TH QUANTILE) 128 0.997 0.287 0.362 3.515 0.157 0.775 MAXIMUM VALUE 138 0.999 0.311 0.920 4.469 0.183 0.856 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.384 0.193 0.029 0.080 2.507 0.069 0.789 MINIMUM CORRELATION: 0.069 SERIES 259020 AND 259080 100 YEARS MAXIMUM CORRELATION: 0.789 SERIES 259030 AND 259070 81 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 62.61 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1860. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 6. 10. 15. 21. 21. 28. 36. 36. 36. 45. RBAR 0.298 0.155 0.241 0.182 0.258 0.216 0.388 0.553 0.612 0.209 SDEV 0.373 0.428 0.225 0.268 0.282 0.286 0.348 0.291 0.279 0.266 SERR 0.152 0.135 0.058 0.059 0.062 0.054 0.058 0.048 0.046 0.040 EPS 0.677 0.529 0.680 0.617 0.732 0.704 0.851 0.920 0.939 0.726 NSS 4.9 6.2 6.7 7.2 7.8 8.6 9.0 9.2 9.8 10.0 YEAR 1960. CORR 45. RBAR 0.305 SDEV 0.420 SERR 0.063 EPS 0.815 NSS 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 1838 1975 138 0.989 0.157 -0.258 3.389 0.113 0.690 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.064 0.033 0.150 25 113 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.30 2.32 1.01 1.09 3.41 17.39 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.10 0.00 0.83 0.93 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.685 0.581 0.476 0.329 0.269 0.182 0.190 0.075 0.009 -0.064 PACF 0.685 0.210 0.035 -0.118 0.028 -0.039 0.124 -0.174 -0.073 -0.100 95% C.L. 0.170 0.237 0.275 0.298 0.308 0.315 0.318 0.321 0.322 0.322 |------------------ 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 0.494 0.539 0.212 |======================= 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 0.742 0.654 0.573 0.402 0.340 0.251 0.215 0.109 0.028 -0.084 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 0.742 2 0.570 0.232 3 0.555 0.194 0.066 4 0.569 0.236 0.187 -0.218 5 0.577 0.229 0.178 -0.238 0.037 6 0.578 0.223 0.183 -0.232 0.052 -0.027 7 0.581 0.218 0.205 -0.250 0.030 -0.083 0.098 8 0.599 0.202 0.211 -0.297 0.069 -0.042 0.207 -0.188 9 0.583 0.219 0.208 -0.292 0.044 -0.025 0.224 -0.138 -0.083 10 0.567 0.191 0.253 -0.297 0.053 -0.084 0.266 -0.093 0.036 -0.203 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) 770.52 662.23 656.62 658.01 653.32 655.14 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 657.04 657.71 654.77 655.81 652.01 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 0.570 0.232 R-SQUARED DUE TO POOLED AUTOREGRESSION: 57.44 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 234.99 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.570 0.557 0.449 0.385 0.324 0.274 0.231 0.195 0.165 0.1390 0.117 0.099 0.084 0.071 0.060 0.050 0.043 0.036 0.030 0.0256 0.022 0.018 0.015 0.013 0.011 0.009 0.008 0.007 0.006 0.0047 0.004 0.003 0.003 0.002 0.002 0.002 0.001 0.001 0.001 0.0009 0.001 0.001 0.001 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 259010 2 0.195 0.479 -0.147 2 259020 2 0.504 0.645 0.083 3 259030 2 0.654 0.520 0.334 4 259040 2 0.539 0.574 0.196 5 259050 2 0.740 0.784 0.088 6 259060 2 0.452 0.634 0.039 7 259070 2 0.720 0.820 0.032 8 259080 2 0.445 0.688 -0.033 9 259090 2 0.638 0.567 0.270 10 259100 2 0.509 0.727 -0.020 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.540 0.644 0.084 STANDARD DEVIATION 0 0.161 0.112 0.146 MEDIAN 2 0.524 0.639 0.061 INTERQUARTILE RANGE 0 0.202 0.160 0.216 MINIMUM VALUE 2 0.195 0.479 -0.147 LOWER HINGE 2 0.452 0.567 -0.020 UPPER HINGE 2 0.654 0.727 0.196 MAXIMUM VALUE 2 0.740 0.820 0.334 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 259010 1935 1975 41 1.000 0.138 -0.354 3.390 0.155 -0.028 2 259020 1876 1975 100 1.000 0.141 0.010 3.704 0.153 0.005 3 259030 1895 1975 81 1.000 0.153 0.452 3.275 0.180 -0.016 4 259040 1849 1975 127 1.000 0.152 0.779 5.862 0.159 0.013 5 259050 1848 1975 128 1.000 0.153 0.334 3.662 0.174 0.000 6 259060 1844 1975 132 1.000 0.138 0.219 2.983 0.158 0.003 7 259070 1860 1975 116 1.000 0.152 -0.053 3.620 0.172 -0.001 8 259080 1861 1975 115 1.000 0.172 -0.263 3.302 0.196 0.014 9 259090 1908 1975 68 1.000 0.172 0.340 3.079 0.188 0.037 10 259100 1838 1975 138 1.000 0.218 -0.119 4.015 0.247 0.000 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.159 0.135 3.689 0.178 0.003 STANDARD DEVIATION 31 0.000 0.024 0.352 0.824 0.028 0.017 MEDIAN (50TH QUANTILE) 115 1.000 0.152 0.115 3.505 0.173 0.002 INTERQUARTILE RANGE 47 0.000 0.030 0.459 0.429 0.030 0.014 MINIMUM VALUE 41 1.000 0.138 -0.354 2.983 0.153 -0.028 LOWER HINGE (25TH QUANTILE) 81 1.000 0.141 -0.119 3.275 0.158 -0.001 UPPER HINGE (75TH QUANTILE) 128 1.000 0.172 0.340 3.704 0.188 0.013 MAXIMUM VALUE 138 1.000 0.218 0.779 5.862 0.247 0.037 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.409 0.098 0.015 -0.139 3.121 0.167 0.648 MINIMUM CORRELATION: 0.167 SERIES 259090 AND 259100 68 YEARS MAXIMUM CORRELATION: 0.648 SERIES 259030 AND 259050 81 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 62.61 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1860. 1870. 1880. 1890. 1900. 1910. 1920. 1930. 1940. 1950. CORR 6. 10. 15. 21. 21. 28. 36. 36. 36. 45. RBAR 0.463 0.371 0.493 0.495 0.365 0.354 0.523 0.561 0.447 0.378 SDEV 0.146 0.161 0.139 0.152 0.216 0.187 0.152 0.171 0.198 0.180 SERR 0.059 0.051 0.036 0.033 0.047 0.035 0.025 0.028 0.033 0.027 EPS 0.810 0.784 0.867 0.877 0.819 0.825 0.908 0.922 0.887 0.859 NSS 4.9 6.2 6.7 7.2 7.8 8.6 9.0 9.2 9.8 10.0 YEAR 1960. CORR 45. RBAR 0.366 SDEV 0.206 SERR 0.031 EPS 0.852 NSS 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 1838 1975 138 1.000 0.108 -0.186 2.799 0.138 -0.142 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.036 0.017 0.088 36 102 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.75 2.83 1.00 1.17 4.01 32.47 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.12 0.00 0.82 0.94 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.141 0.086 0.133 -0.120 0.040 -0.112 0.154 -0.039 0.035 -0.057 PACF -0.141 0.068 0.158 -0.091 -0.015 -0.115 0.164 0.007 0.038 -0.129 95% C.L. 0.170 0.174 0.175 0.178 0.180 0.180 0.182 0.186 0.186 0.186 |------------------ 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 0.025 -0.141 |---------- 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 -0.011 0.028 0.141 -0.102 -0.005 -0.081 0.136 -0.003 0.013 -0.057 PACF -0.011 0.028 0.142 -0.101 -0.015 -0.098 0.172 -0.007 0.032 -0.135 95% C.L. 0.170 0.170 0.170 0.174 0.175 0.176 0.177 0.180 0.180 0.180 |----------------- 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 0.022 -0.011 0.028 |========================= 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 1838 1975 138 1.005 0.164 -0.289 3.254 0.103 0.749 |------------ 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 0.744 0.657 0.560 0.399 0.322 0.228 0.213 0.113 0.052 -0.030 PACF 0.744 0.231 0.030 -0.189 0.007 -0.028 0.139 -0.157 -0.066 -0.140 95% C.L. 0.170 0.247 0.293 0.323 0.337 0.346 0.350 0.354 0.355 0.355 |------------------- 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 0.581 0.565 0.241 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.08 MINUTES