RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN017N.rwl LOG FILE PROCESSED: FRAN017N.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 DENSITY_MINIMUM 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 2 259020 MISSING VALUES FOUND: 5 IN 1 GAPS / 1955 1959 / -------------------------------------------------------------------- 4 259040 MISSING VALUES FOUND: 7 IN 1 GAPS / 1950 1956 / -------------------------------------------------------------------- 6 259060 MISSING VALUES FOUND: 5 IN 1 GAPS / 1942 1946 / -------------------------------------------------------------------- 7 259070 MISSING VALUES FOUND: 5 IN 1 GAPS / 1897 1901 / -------------------------------------------------------------------- 9 259090 MISSING VALUES FOUND: 5 IN 1 GAPS / 1963 1967 / -------------------------------------------------------------------- 10 259100 MISSING VALUES FOUND: 5 IN 1 GAPS / 1848 1852 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 259010 1935 1975 41 0.223 0.031 1.149 5.576 0.087 0.723 2 259020 1876 1975 100 0.225 0.017 -0.339 7.135 0.053 0.494 3 259030 1895 1975 81 0.243 0.022 1.198 4.064 0.055 0.650 4 259040 1849 1975 127 0.263 0.031 2.230 10.248 0.047 0.815 5 259050 1848 1975 128 0.240 0.020 0.818 4.151 0.060 0.523 6 259060 1844 1975 132 0.258 0.017 0.121 3.125 0.051 0.467 7 259070 1860 1975 116 0.276 0.030 2.316 9.143 0.049 0.801 8 259080 1861 1975 115 0.262 0.020 0.997 5.018 0.053 0.586 9 259090 1908 1975 68 0.247 0.024 0.727 3.255 0.061 0.670 10 259100 1838 1975 138 0.301 0.022 0.482 3.384 0.048 0.609 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 101 0.254 0.023 0.970 5.510 0.056 0.634 STANDARD DEVIATION 30 0.023 0.006 0.833 2.533 0.012 0.122 MEDIAN (50TH QUANTILE) 113 0.253 0.022 0.907 4.584 0.053 0.630 INTERQUARTILE RANGE 46 0.022 0.011 0.716 3.752 0.010 0.201 MINIMUM VALUE 41 0.223 0.017 -0.339 3.125 0.047 0.467 LOWER HINGE (25TH QUANTILE) 81 0.240 0.020 0.482 3.384 0.049 0.523 UPPER HINGE (75TH QUANTILE) 127 0.263 0.030 1.198 7.135 0.060 0.723 MAXIMUM VALUE 133 0.301 0.031 2.316 10.248 0.087 0.815 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.161 0.215 0.032 0.349 3.207 -0.199 0.746 MINIMUM CORRELATION: -0.199 SERIES 259090 AND 259100 68 YEARS MAXIMUM CORRELATION: 0.746 SERIES 259010 AND 259040 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 -0.056 0.452 0.457 0.374 0.344 0.240 0.286 0.256 0.148 0.246 SDEV 0.544 0.168 0.181 0.226 0.213 0.276 0.318 0.305 0.264 0.264 SERR 0.222 0.053 0.047 0.049 0.046 0.052 0.053 0.051 0.044 0.039 EPS -0.357 0.835 0.849 0.813 0.805 0.731 0.783 0.761 0.629 0.765 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 0.157 SDEV 0.330 SERR 0.049 EPS 0.651 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 0.257 0.013 0.607 3.029 0.043 0.465 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.033 -0.026 0.034 35 103 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.52 2.04 1.03 1.22 3.26 8.16 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.87 0.14 0.00 0.80 0.94 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 0.461 0.503 0.330 0.293 0.221 0.156 0.093 0.055 0.047 0.041 PACF 0.461 0.368 0.020 0.011 0.009 -0.036 -0.052 -0.023 0.025 0.030 95% C.L. 0.170 0.203 0.237 0.250 0.259 0.265 0.267 0.268 0.269 0.269 |------------------ 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 0.339 0.283 0.393 |================== 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 0.00102962 0.20106098 2 259020 3 0.00000000 0.00000000 -0.00011165 0.23125161 3 259030 3 0.00000000 0.00000000 0.00043338 0.22482407 4 259040 1 0.15758431 0.13664849 0.00000000 0.25470981 5 259050 3 0.00000000 0.00000000 0.00017885 0.22885458 6 259060 1 0.00958770 0.00915431 0.00000000 0.25210351 7 259070 3 0.00000000 0.00000000 0.00049524 0.24566935 8 259080 3 0.00000000 0.00000000 0.00033102 0.24254005 9 259090 3 0.00000000 0.00000000 -0.00050411 0.26402733 10 259100 3 0.00000000 0.00000000 0.00014179 0.28942481 |-------------------- 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 0.129 1.740 6.616 0.085 0.660 2 259020 1876 1975 100 1.000 0.071 -0.440 7.073 0.052 0.450 3 259030 1895 1975 81 1.000 0.078 1.129 4.164 0.054 0.534 4 259040 1849 1975 127 1.000 0.071 0.125 3.297 0.048 0.573 5 259050 1848 1975 128 1.000 0.077 0.702 4.189 0.059 0.452 6 259060 1844 1975 132 1.000 0.066 0.104 3.046 0.050 0.485 7 259070 1860 1975 116 1.000 0.089 1.742 7.467 0.052 0.667 8 259080 1861 1975 115 1.000 0.065 0.548 4.680 0.053 0.397 9 259090 1908 1975 68 1.000 0.087 0.591 3.640 0.062 0.516 10 259100 1838 1975 138 1.000 0.074 0.482 3.463 0.049 0.602 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.081 0.672 4.764 0.056 0.534 STANDARD DEVIATION 31 0.000 0.019 0.700 1.661 0.011 0.091 MEDIAN (50TH QUANTILE) 115 1.000 0.075 0.570 4.176 0.053 0.525 INTERQUARTILE RANGE 47 0.000 0.016 1.005 3.153 0.009 0.149 MINIMUM VALUE 41 1.000 0.065 -0.440 3.046 0.048 0.397 LOWER HINGE (25TH QUANTILE) 81 1.000 0.071 0.125 3.463 0.050 0.452 UPPER HINGE (75TH QUANTILE) 128 1.000 0.087 1.129 6.616 0.059 0.602 MAXIMUM VALUE 138 1.000 0.129 1.742 7.467 0.085 0.667 |------------------------ 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 0.999 0.090 1.041 6.337 0.083 0.341 2 259020 1876 1975 100 1.000 0.067 -0.813 7.234 0.052 0.366 3 259030 1895 1975 81 1.000 0.070 0.876 3.975 0.054 0.442 4 259040 1849 1975 127 1.000 0.066 0.207 3.638 0.048 0.504 5 259050 1848 1975 128 1.000 0.069 0.318 4.071 0.059 0.318 6 259060 1844 1975 132 1.000 0.059 0.186 3.034 0.050 0.369 7 259070 1860 1975 116 1.000 0.073 1.732 7.914 0.052 0.526 8 259080 1861 1975 115 1.000 0.059 0.807 4.439 0.053 0.263 9 259090 1908 1975 68 0.999 0.070 0.126 3.776 0.063 0.301 10 259100 1838 1975 138 1.000 0.069 0.343 3.410 0.049 0.542 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.069 0.482 4.783 0.056 0.397 STANDARD DEVIATION 31 0.000 0.009 0.679 1.725 0.010 0.100 MEDIAN (50TH QUANTILE) 115 1.000 0.069 0.331 4.023 0.053 0.367 INTERQUARTILE RANGE 47 0.000 0.004 0.690 2.699 0.009 0.187 MINIMUM VALUE 41 0.999 0.059 -0.813 3.034 0.048 0.263 LOWER HINGE (25TH QUANTILE) 81 1.000 0.066 0.186 3.638 0.050 0.318 UPPER HINGE (75TH QUANTILE) 128 1.000 0.070 0.876 6.337 0.059 0.504 MAXIMUM VALUE 138 1.000 0.090 1.732 7.914 0.083 0.542 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.211 0.183 0.027 -0.454 3.398 -0.277 0.621 MINIMUM CORRELATION: -0.277 SERIES 259030 AND 259070 81 YEARS MAXIMUM CORRELATION: 0.621 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 0.240 0.498 0.450 0.368 0.342 0.247 0.294 0.280 0.163 0.185 SDEV 0.228 0.149 0.170 0.232 0.195 0.259 0.291 0.282 0.301 0.283 SERR 0.093 0.047 0.044 0.051 0.043 0.049 0.048 0.047 0.050 0.042 EPS 0.609 0.859 0.846 0.809 0.803 0.738 0.789 0.783 0.655 0.694 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 0.164 SDEV 0.322 SERR 0.048 EPS 0.662 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 0.996 0.039 0.406 3.430 0.039 0.211 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.132 0.083 -0.034 35 103 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.10 3.77 1.02 1.42 5.19 124.29 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.08 0.00 0.85 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 0.210 0.305 0.039 0.052 -0.008 -0.014 -0.074 -0.158 -0.088 -0.129 PACF 0.210 0.273 -0.073 -0.030 -0.002 -0.018 -0.070 -0.143 0.000 -0.036 95% C.L. 0.170 0.178 0.192 0.192 0.193 0.193 0.193 0.194 0.197 0.198 |------------------ 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 0.121 0.152 0.274 |======================= 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 0.265 0.274 0.028 -0.028 -0.067 -0.093 -0.141 -0.134 -0.074 -0.074 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 0.265 2 0.207 0.220 3 0.229 0.240 -0.099 4 0.220 0.260 -0.080 -0.085 5 0.218 0.258 -0.072 -0.079 -0.027 6 0.217 0.255 -0.076 -0.067 -0.017 -0.046 7 0.212 0.253 -0.082 -0.074 0.008 -0.024 -0.100 8 0.206 0.251 -0.082 -0.079 0.003 -0.008 -0.086 -0.065 9 0.207 0.253 -0.082 -0.079 0.004 -0.006 -0.091 -0.069 0.020 10 0.208 0.251 -0.085 -0.080 0.005 -0.009 -0.094 -0.061 0.027 -0.032 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) 341.81 333.74 328.92 329.57 330.57 332.47 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 334.18 334.79 336.21 338.15 340.01 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 0.207 0.220 R-SQUARED DUE TO POOLED AUTOREGRESSION: 11.52 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 113.02 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.207 0.262 0.100 0.078 0.038 0.025 0.014 0.008 0.005 0.0028 0.002 0.001 0.001 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 259010 2 0.171 0.333 0.055 2 259020 2 0.174 0.297 0.193 3 259030 2 0.239 0.421 0.055 4 259040 2 0.286 0.420 0.180 5 259050 2 0.116 0.291 0.083 6 259060 2 0.196 0.283 0.249 7 259070 2 0.290 0.475 0.099 8 259080 2 0.176 0.176 0.334 9 259090 2 0.179 0.220 0.291 10 259100 2 0.343 0.401 0.262 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.217 0.332 0.180 STANDARD DEVIATION 0 0.070 0.096 0.103 MEDIAN 2 0.187 0.315 0.186 INTERQUARTILE RANGE 0 0.112 0.137 0.179 MINIMUM VALUE 2 0.116 0.176 0.055 LOWER HINGE 2 0.174 0.283 0.083 UPPER HINGE 2 0.286 0.420 0.262 MAXIMUM VALUE 2 0.343 0.475 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 0.084 0.710 5.094 0.095 0.006 2 259020 1876 1975 100 1.000 0.061 -0.834 9.160 0.062 -0.020 3 259030 1895 1975 81 1.000 0.062 0.903 5.206 0.067 0.011 4 259040 1849 1975 127 1.000 0.056 0.560 4.502 0.062 0.001 5 259050 1848 1975 128 1.000 0.065 0.530 4.566 0.070 0.008 6 259060 1844 1975 132 1.000 0.052 0.161 3.171 0.060 -0.017 7 259070 1860 1975 116 1.000 0.062 1.301 7.316 0.064 0.009 8 259080 1861 1975 115 1.000 0.053 1.057 5.060 0.057 0.023 9 259090 1908 1975 68 1.000 0.063 0.117 2.914 0.071 -0.028 10 259100 1838 1975 138 1.000 0.056 0.037 3.279 0.059 0.008 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 105 1.000 0.061 0.454 5.027 0.067 0.000 STANDARD DEVIATION 31 0.000 0.009 0.614 1.938 0.011 0.016 MEDIAN (50TH QUANTILE) 115 1.000 0.061 0.545 4.813 0.063 0.007 INTERQUARTILE RANGE 47 0.000 0.008 0.785 1.927 0.010 0.026 MINIMUM VALUE 41 1.000 0.052 -0.834 2.914 0.057 -0.028 LOWER HINGE (25TH QUANTILE) 81 1.000 0.056 0.117 3.279 0.060 -0.017 UPPER HINGE (75TH QUANTILE) 128 1.000 0.063 0.903 5.206 0.070 0.009 MAXIMUM VALUE 138 1.000 0.084 1.301 9.160 0.095 0.023 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.244 0.124 0.019 -0.516 3.224 -0.089 0.459 MINIMUM CORRELATION: -0.089 SERIES 259010 AND 259070 41 YEARS MAXIMUM CORRELATION: 0.459 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 0.210 0.547 0.546 0.439 0.322 0.288 0.331 0.305 0.231 0.188 SDEV 0.170 0.108 0.136 0.146 0.170 0.175 0.179 0.225 0.197 0.200 SERR 0.069 0.034 0.035 0.032 0.037 0.033 0.030 0.037 0.033 0.030 EPS 0.569 0.881 0.889 0.850 0.789 0.777 0.817 0.802 0.745 0.698 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 0.173 SDEV 0.260 SERR 0.039 EPS 0.677 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 0.998 0.035 0.450 3.390 0.043 -0.188 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.078 0.046 -0.003 25 113 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.54 1.98 1.03 1.28 3.26 143.96 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.12 0.00 0.81 0.92 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 -0.187 0.130 -0.068 -0.003 0.012 0.020 -0.053 -0.083 -0.012 -0.069 PACF -0.187 0.098 -0.029 -0.034 0.017 0.029 -0.053 -0.109 -0.030 -0.064 95% C.L. 0.170 0.176 0.179 0.180 0.180 0.180 0.180 0.180 0.181 0.181 |------------------ 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 0.044 -0.187 |---------- 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 -0.002 -0.035 -0.029 0.028 0.025 -0.068 -0.095 -0.033 -0.052 PACF 0.003 -0.002 -0.035 -0.029 0.028 0.024 -0.071 -0.094 -0.030 -0.057 95% C.L. 0.170 0.170 0.170 0.170 0.171 0.171 0.171 0.172 0.173 0.173 |----------------- 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 0.003 -0.002 |========================= 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 0.999 0.036 0.346 3.288 0.035 0.255 |------------ 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 0.254 0.255 0.069 0.039 0.022 -0.010 -0.093 -0.135 -0.102 -0.129 PACF 0.254 0.204 -0.038 -0.022 0.015 -0.020 -0.104 -0.100 -0.013 -0.058 95% C.L. 0.170 0.181 0.191 0.192 0.192 0.192 0.192 0.193 0.196 0.198 |------------------- 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 0.105 0.202 0.205 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.09 MINUTES