RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN017L.rwl LOG FILE PROCESSED: FRAN017L.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_LATE 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 1.289 0.481 0.843 5.141 0.214 0.693 2 259020 1876 1975 100 0.563 0.161 0.856 3.387 0.225 0.473 3 259030 1895 1975 81 1.007 0.645 1.345 4.542 0.292 0.790 4 259040 1849 1975 127 0.591 0.197 1.355 5.003 0.166 0.702 5 259050 1848 1975 128 0.512 0.329 2.765 12.373 0.188 0.839 6 259060 1844 1975 132 0.609 0.149 0.379 2.925 0.190 0.550 7 259070 1860 1975 116 0.711 0.403 0.918 3.509 0.210 0.905 8 259080 1861 1975 115 0.492 0.198 1.623 7.258 0.217 0.681 9 259090 1908 1975 68 0.470 0.235 0.767 3.373 0.219 0.881 10 259100 1838 1975 138 0.570 0.288 1.361 6.005 0.289 0.736 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 0.681 0.309 1.221 5.352 0.221 0.725 STANDARD DEVIATION 31 0.263 0.160 0.657 2.813 0.041 0.138 MEDIAN (50TH QUANTILE) 115 0.581 0.262 1.131 4.773 0.215 0.719 INTERQUARTILE RANGE 47 0.199 0.206 0.517 2.619 0.035 0.157 MINIMUM VALUE 41 0.470 0.149 0.379 2.925 0.166 0.473 LOWER HINGE (25TH QUANTILE) 81 0.512 0.197 0.843 3.387 0.190 0.681 UPPER HINGE (75TH QUANTILE) 128 0.711 0.403 1.361 6.005 0.225 0.839 MAXIMUM VALUE 138 1.289 0.645 2.765 12.373 0.292 0.905 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.351 0.194 0.029 0.039 2.939 -0.106 0.735 MINIMUM CORRELATION: -0.106 SERIES 259070 AND 259080 115 YEARS MAXIMUM CORRELATION: 0.735 SERIES 259010 AND 259090 41 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 0.328 0.161 0.172 0.201 0.096 0.111 0.172 0.409 0.559 0.116 SDEV 0.448 0.276 0.249 0.264 0.369 0.360 0.356 0.225 0.345 0.351 SERR 0.183 0.087 0.064 0.058 0.081 0.068 0.059 0.038 0.058 0.052 EPS 0.707 0.541 0.582 0.645 0.456 0.518 0.651 0.865 0.925 0.568 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 0.384 SDEV 0.309 SERR 0.046 EPS 0.862 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 0.593 0.182 1.417 4.708 0.154 0.821 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.510 0.392 -0.014 39 99 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.42 3.74 1.01 1.17 4.92 166.31 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.12 0.00 0.80 0.92 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 0.815 0.762 0.737 0.647 0.573 0.451 0.387 0.320 0.214 0.107 PACF 0.815 0.289 0.195 -0.106 -0.092 -0.263 -0.010 0.008 -0.069 -0.170 95% C.L. 0.170 0.260 0.318 0.364 0.396 0.419 0.433 0.443 0.450 0.453 |------------------ 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 0.709 0.513 0.175 0.209 |================== 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 -0.00394599 1.37140238 2 259020 3 0.00000000 0.00000000 0.00163660 0.48035151 3 259030 3 0.00000000 0.00000000 0.00090447 0.97020060 4 259040 3 0.00000000 0.00000000 0.00270593 0.41815898 5 259050 3 0.00000000 0.00000000 0.00237685 0.35856792 6 259060 1 0.18448359 0.02692204 0.00000000 0.55926359 7 259070 3 0.00000000 0.00000000 0.00194549 0.59705096 8 259080 3 0.00000000 0.00000000 0.00196607 0.37840274 9 259090 3 0.00000000 0.00000000 0.00340020 0.35225198 10 259100 1 0.43583050 0.02568668 0.00000000 0.45220721 |-------------------- 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 0.365 0.791 5.409 0.208 0.663 2 259020 1876 1975 100 1.000 0.266 0.600 2.916 0.223 0.411 3 259030 1895 1975 81 1.000 0.631 1.271 4.389 0.288 0.777 4 259040 1849 1975 127 1.000 0.267 0.683 3.034 0.165 0.633 5 259050 1848 1975 128 1.003 0.563 2.221 10.377 0.186 0.808 6 259060 1844 1975 132 1.000 0.232 0.232 2.484 0.189 0.479 7 259070 1860 1975 116 0.998 0.534 0.699 3.065 0.208 0.886 8 259080 1861 1975 115 1.003 0.362 0.744 3.837 0.215 0.690 9 259090 1908 1975 68 1.000 0.467 0.481 2.922 0.216 0.843 10 259100 1838 1975 138 1.000 0.517 2.549 12.826 0.287 0.680 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.420 1.027 5.126 0.219 0.687 STANDARD DEVIATION 31 0.002 0.141 0.766 3.567 0.040 0.152 MEDIAN (50TH QUANTILE) 115 1.000 0.416 0.722 3.451 0.212 0.685 INTERQUARTILE RANGE 47 0.000 0.266 0.672 2.486 0.034 0.174 MINIMUM VALUE 41 0.998 0.232 0.232 2.484 0.165 0.411 LOWER HINGE (25TH QUANTILE) 81 1.000 0.267 0.600 2.922 0.189 0.633 UPPER HINGE (75TH QUANTILE) 128 1.000 0.534 1.271 5.409 0.223 0.808 MAXIMUM VALUE 138 1.003 0.631 2.549 12.826 0.288 0.886 |------------------------ 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 0.985 0.234 0.696 3.854 0.197 0.418 2 259020 1876 1975 100 0.999 0.255 0.544 2.806 0.222 0.377 3 259030 1895 1975 81 0.953 0.380 0.632 3.535 0.290 0.599 4 259040 1849 1975 127 0.997 0.252 0.765 4.219 0.165 0.544 5 259050 1848 1975 128 0.972 0.402 2.052 11.978 0.186 0.743 6 259060 1844 1975 132 0.999 0.224 0.169 2.395 0.189 0.442 7 259070 1860 1975 116 0.972 0.360 0.827 3.921 0.204 0.759 8 259080 1861 1975 115 0.995 0.280 0.699 4.220 0.213 0.573 9 259090 1908 1975 68 0.960 0.263 0.028 3.336 0.209 0.594 10 259100 1838 1975 138 0.991 0.462 2.069 10.385 0.287 0.642 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 0.982 0.311 0.848 5.065 0.216 0.569 STANDARD DEVIATION 31 0.017 0.083 0.688 3.298 0.041 0.129 MEDIAN (50TH QUANTILE) 115 0.988 0.272 0.697 3.887 0.207 0.584 INTERQUARTILE RANGE 47 0.026 0.129 0.283 0.884 0.033 0.200 MINIMUM VALUE 41 0.953 0.224 0.028 2.395 0.165 0.377 LOWER HINGE (25TH QUANTILE) 81 0.972 0.252 0.544 3.336 0.189 0.442 UPPER HINGE (75TH QUANTILE) 128 0.997 0.380 0.827 4.220 0.222 0.642 MAXIMUM VALUE 138 0.999 0.462 2.069 11.978 0.290 0.759 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.316 0.163 0.024 -0.430 2.640 -0.094 0.588 MINIMUM CORRELATION: -0.094 SERIES 259020 AND 259080 100 YEARS MAXIMUM CORRELATION: 0.588 SERIES 259070 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 0.329 0.146 0.180 0.207 0.143 0.158 0.244 0.452 0.497 0.129 SDEV 0.415 0.339 0.245 0.252 0.295 0.278 0.293 0.218 0.346 0.320 SERR 0.169 0.107 0.063 0.055 0.064 0.053 0.049 0.036 0.058 0.048 EPS 0.708 0.513 0.595 0.655 0.567 0.618 0.744 0.884 0.906 0.597 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 0.311 SDEV 0.269 SERR 0.040 EPS 0.819 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 0.980 0.184 -0.064 3.444 0.146 0.562 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.256 0.163 0.065 23 115 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.81 4.00 1.00 1.33 5.32 41.41 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.10 0.00 0.82 0.92 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 0.558 0.462 0.461 0.325 0.295 0.142 0.127 0.141 0.001 -0.108 PACF 0.558 0.218 0.210 -0.050 0.041 -0.181 0.031 0.054 -0.112 -0.195 95% C.L. 0.170 0.217 0.244 0.268 0.279 0.288 0.290 0.292 0.294 0.294 |------------------ 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 3 0.378 0.397 0.124 0.207 |======================= 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 0.639 0.546 0.540 0.419 0.354 0.172 0.150 0.147 -0.003 -0.149 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 0.639 2 0.490 0.233 3 0.438 0.124 0.222 4 0.450 0.131 0.244 -0.051 5 0.449 0.133 0.245 -0.046 -0.010 6 0.446 0.121 0.312 -0.011 0.111 -0.270 7 0.456 0.117 0.312 -0.021 0.107 -0.285 0.035 8 0.453 0.136 0.305 -0.020 0.086 -0.293 0.004 0.067 9 0.461 0.136 0.270 -0.010 0.084 -0.257 0.021 0.120 -0.118 10 0.429 0.169 0.276 -0.079 0.106 -0.260 0.093 0.157 0.006 -0.269 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) 824.63 754.31 748.61 743.66 745.30 747.28 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 738.86 740.69 742.07 742.13 733.77 SELECTED AUTOREGRESSION ORDER: 3 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 0.438 0.124 0.222 R-SQUARED DUE TO POOLED AUTOREGRESSION: 46.75 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 187.81 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.438 0.316 0.415 0.318 0.261 0.246 0.211 0.181 0.160 0.1394 0.121 0.106 0.092 0.080 0.070 0.061 0.053 0.047 0.041 0.0354 0.031 0.027 0.024 0.021 0.018 0.016 0.014 0.012 0.010 0.0090 0.008 0.007 0.006 0.005 0.005 0.004 0.003 0.003 0.003 0.0023 0.002 0.002 0.002 0.001 0.001 0.001 0.001 0.001 0.001 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 259010 3 0.365 0.455 -0.072 -0.374 2 259020 3 0.157 0.405 -0.094 0.101 3 259030 3 0.392 0.475 0.226 -0.019 4 259040 3 0.394 0.433 0.205 0.062 5 259050 3 0.576 0.574 0.176 0.060 6 259060 3 0.228 0.408 0.071 0.045 7 259070 3 0.592 0.641 0.144 0.017 8 259080 3 0.395 0.555 0.127 -0.092 9 259090 3 0.380 0.480 0.206 -0.016 10 259100 3 0.426 0.604 0.016 0.065 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.390 0.503 0.100 -0.015 STANDARD DEVIATION 0 0.132 0.084 0.116 0.138 MEDIAN 3 0.393 0.478 0.135 0.031 INTERQUARTILE RANGE 0 0.061 0.141 0.189 0.082 MINIMUM VALUE 3 0.157 0.405 -0.094 -0.374 LOWER HINGE 3 0.365 0.433 0.016 -0.019 UPPER HINGE 3 0.426 0.574 0.205 0.062 MAXIMUM VALUE 3 0.592 0.641 0.226 0.101 |------------------- 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 0.185 0.262 3.225 0.209 -0.005 2 259020 1876 1975 100 1.000 0.234 0.503 3.030 0.270 0.002 3 259030 1895 1975 81 1.000 0.297 0.261 2.692 0.343 0.000 4 259040 1849 1975 127 1.000 0.198 1.454 10.615 0.202 0.014 5 259050 1848 1975 128 1.000 0.261 2.383 17.836 0.239 0.002 6 259060 1844 1975 132 1.000 0.198 0.319 2.745 0.220 0.005 7 259070 1860 1975 116 1.000 0.230 -0.217 4.417 0.269 -0.003 8 259080 1861 1975 115 1.000 0.224 0.066 3.107 0.258 0.003 9 259090 1908 1975 68 1.000 0.207 0.653 3.017 0.238 -0.001 10 259100 1838 1975 138 1.002 0.345 1.588 12.358 0.377 0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.238 0.727 6.304 0.263 0.003 STANDARD DEVIATION 31 0.001 0.050 0.816 5.362 0.057 0.006 MEDIAN (50TH QUANTILE) 115 1.000 0.227 0.411 3.166 0.249 0.002 INTERQUARTILE RANGE 47 0.000 0.063 1.193 7.598 0.051 0.006 MINIMUM VALUE 41 1.000 0.185 -0.217 2.692 0.202 -0.005 LOWER HINGE (25TH QUANTILE) 81 1.000 0.198 0.261 3.017 0.220 -0.001 UPPER HINGE (75TH QUANTILE) 128 1.000 0.261 1.454 10.615 0.270 0.005 MAXIMUM VALUE 138 1.002 0.345 2.383 17.836 0.377 0.014 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.276 0.118 0.018 -0.990 4.886 -0.076 0.510 MINIMUM CORRELATION: -0.076 SERIES 259010 AND 259070 41 YEARS MAXIMUM CORRELATION: 0.510 SERIES 259010 AND 259030 41 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 0.361 0.186 0.341 0.434 0.238 0.226 0.338 0.402 0.367 0.213 SDEV 0.151 0.242 0.182 0.156 0.153 0.152 0.196 0.179 0.192 0.218 SERR 0.062 0.077 0.047 0.034 0.033 0.029 0.033 0.030 0.032 0.032 EPS 0.737 0.584 0.776 0.848 0.710 0.715 0.821 0.862 0.850 0.730 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 0.250 SDEV 0.211 SERR 0.031 EPS 0.770 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 0.996 0.138 -0.117 3.208 0.172 -0.102 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.130 0.072 0.094 31 107 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.65 2.27 1.00 1.15 3.43 147.83 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.07 0.00 0.84 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 -0.101 -0.031 0.223 -0.041 0.175 -0.178 -0.001 0.183 -0.023 -0.062 PACF -0.101 -0.041 0.218 0.002 0.194 -0.212 -0.009 0.093 0.108 -0.094 95% C.L. 0.170 0.172 0.172 0.180 0.181 0.185 0.190 0.190 0.195 0.195 |------------------ 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 -0.002 -0.042 0.054 0.021 0.142 -0.229 0.018 0.189 0.024 -0.075 PACF -0.002 -0.042 0.054 0.019 0.147 -0.236 0.039 0.162 0.045 -0.094 95% C.L. 0.170 0.170 0.171 0.171 0.171 0.175 0.183 0.183 0.189 0.189 |----------------- 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 3 0.005 0.001 -0.043 0.055 |========================= 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 0.996 0.176 -0.137 3.770 0.132 0.606 |------------ 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 0.602 0.490 0.496 0.394 0.344 0.138 0.155 0.165 0.020 -0.101 PACF 0.602 0.200 0.228 -0.006 0.030 -0.290 0.085 0.047 -0.099 -0.214 95% C.L. 0.170 0.224 0.253 0.280 0.295 0.307 0.308 0.311 0.313 0.313 |------------------- 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 3 0.421 0.439 0.087 0.229 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.08 MINUTES