RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN018X.rwl LOG FILE PROCESSED: FRAN018X.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 DENSITY_MAXIMUM 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 0.926 0.050 0.076 3.024 0.046 0.407 2 260120 1843 1975 133 0.892 0.061 -0.009 3.408 0.069 0.213 3 260130 1890 1975 86 0.958 0.074 -1.375 7.610 0.077 0.191 4 260140 1859 1975 117 0.820 0.071 -1.136 5.505 0.063 0.576 5 260150 1828 1975 148 1.007 0.084 -1.360 5.368 0.056 0.672 6 260160 1828 1975 148 0.945 0.058 -0.627 3.137 0.044 0.530 7 260170 1795 1975 181 0.919 0.060 -1.722 13.225 0.050 0.478 8 260180 1829 1975 147 0.925 0.048 0.015 3.742 0.040 0.481 9 260190 1852 1975 124 0.922 0.049 -0.610 3.467 0.043 0.453 10 260200 1874 1975 102 0.982 0.053 -0.464 4.548 0.042 0.497 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 0.930 0.061 -0.721 5.303 0.053 0.450 STANDARD DEVIATION 26 0.051 0.012 0.648 3.127 0.013 0.149 MEDIAN (50TH QUANTILE) 133 0.926 0.059 -0.619 4.145 0.048 0.480 INTERQUARTILE RANGE 31 0.039 0.020 1.350 2.098 0.020 0.123 MINIMUM VALUE 86 0.820 0.048 -1.722 3.024 0.040 0.191 LOWER HINGE (25TH QUANTILE) 117 0.919 0.050 -1.360 3.408 0.043 0.407 UPPER HINGE (75TH QUANTILE) 148 0.958 0.071 -0.009 5.505 0.063 0.530 MAXIMUM VALUE 181 1.007 0.084 0.076 13.225 0.077 0.672 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.346 0.156 0.023 -0.111 2.593 -0.022 0.668 MINIMUM CORRELATION: -0.022 SERIES 260140 AND 260160 117 YEARS MAXIMUM CORRELATION: 0.668 SERIES 260190 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 0.552 0.260 0.257 0.243 0.318 0.280 0.327 0.250 0.364 0.440 SDEV 0.253 0.217 0.292 0.238 0.225 0.314 0.263 0.277 0.255 0.260 SERR 0.103 0.089 0.075 0.045 0.043 0.052 0.039 0.041 0.038 0.039 EPS 0.854 0.685 0.720 0.727 0.804 0.787 0.829 0.770 0.851 0.887 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 0.358 0.296 0.473 SDEV 0.258 0.290 0.265 SERR 0.038 0.043 0.040 EPS 0.848 0.808 0.900 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 0.926 0.040 -0.485 3.673 0.036 0.461 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.157 0.123 -0.062 42 139 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.44 2.23 1.03 1.18 3.41 61.43 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.27 0.00 0.63 0.90 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 0.459 0.395 0.308 0.218 0.193 0.082 0.087 0.021 0.107 0.038 PACF 0.459 0.233 0.084 -0.005 0.035 -0.081 0.021 -0.045 0.128 -0.041 95% C.L. 0.149 0.177 0.196 0.206 0.211 0.215 0.216 0.216 0.216 0.218 |------------------ 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 0.267 0.347 0.247 |================== 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 -0.00005933 0.92990011 2 260120 3 0.00000000 0.00000000 0.00039532 0.86546820 3 260130 3 0.00000000 0.00000000 -0.00124846 1.01233101 4 260140 3 0.00000000 0.00000000 0.00037832 0.79810637 5 260150 3 0.00000000 0.00000000 0.00022024 0.99095696 6 260160 3 0.00000000 0.00000000 0.00024365 0.92657751 7 260170 3 0.00000000 0.00000000 -0.00007207 0.92589504 8 260180 3 0.00000000 0.00000000 0.00054572 0.88499117 9 260190 3 0.00000000 0.00000000 0.00012721 0.91382378 10 260200 3 0.00000000 0.00000000 -0.00027232 0.99618131 |-------------------- 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 0.054 0.101 3.058 0.046 0.401 2 260120 1843 1975 133 1.000 0.066 -0.274 3.616 0.068 0.154 3 260130 1890 1975 86 1.000 0.072 -1.267 7.238 0.076 0.008 4 260140 1859 1975 117 1.000 0.085 -1.156 5.277 0.062 0.559 5 260150 1828 1975 148 1.000 0.083 -1.511 6.006 0.055 0.660 6 260160 1828 1975 148 1.000 0.060 -0.669 3.342 0.044 0.507 7 260170 1795 1975 181 1.000 0.066 -1.633 12.811 0.050 0.473 8 260180 1829 1975 147 1.000 0.045 -0.328 3.441 0.040 0.321 9 260190 1852 1975 124 1.000 0.053 -0.660 3.713 0.042 0.441 10 260200 1874 1975 102 1.000 0.054 -0.311 4.357 0.041 0.483 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.064 -0.771 5.286 0.052 0.401 STANDARD DEVIATION 26 0.000 0.013 0.589 2.967 0.012 0.194 MEDIAN (50TH QUANTILE) 133 1.000 0.063 -0.665 4.035 0.048 0.457 INTERQUARTILE RANGE 31 0.000 0.018 0.956 2.565 0.020 0.186 MINIMUM VALUE 86 1.000 0.045 -1.633 3.058 0.040 0.008 LOWER HINGE (25TH QUANTILE) 117 1.000 0.054 -1.267 3.441 0.042 0.321 UPPER HINGE (75TH QUANTILE) 148 1.000 0.072 -0.311 6.006 0.062 0.507 MAXIMUM VALUE 181 1.000 0.085 0.101 12.811 0.076 0.660 |------------------------ 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 1.000 0.053 0.092 2.995 0.046 0.379 2 260120 1843 1975 133 1.000 0.063 -0.336 3.386 0.068 0.075 3 260130 1890 1975 86 1.000 0.071 -1.274 7.011 0.076 -0.005 4 260140 1859 1975 117 1.000 0.079 -1.276 5.501 0.062 0.479 5 260150 1828 1975 148 0.999 0.067 -1.253 5.093 0.055 0.476 6 260160 1828 1975 148 1.000 0.055 -0.508 3.480 0.044 0.414 7 260170 1795 1975 181 1.000 0.057 -1.649 14.049 0.050 0.261 8 260180 1829 1975 147 1.000 0.043 -0.212 3.532 0.040 0.268 9 260190 1852 1975 124 1.000 0.042 -0.470 3.164 0.043 0.146 10 260200 1874 1975 102 1.000 0.044 0.096 3.377 0.041 0.260 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.058 -0.679 5.159 0.052 0.275 STANDARD DEVIATION 26 0.000 0.012 0.631 3.384 0.012 0.166 MEDIAN (50TH QUANTILE) 133 1.000 0.056 -0.489 3.506 0.048 0.265 INTERQUARTILE RANGE 31 0.000 0.023 1.061 2.124 0.020 0.268 MINIMUM VALUE 86 0.999 0.042 -1.649 2.995 0.040 -0.005 LOWER HINGE (25TH QUANTILE) 117 1.000 0.044 -1.274 3.377 0.043 0.146 UPPER HINGE (75TH QUANTILE) 148 1.000 0.067 -0.212 5.501 0.062 0.414 MAXIMUM VALUE 181 1.000 0.079 0.096 14.049 0.076 0.479 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.313 0.165 0.025 -0.328 3.175 -0.153 0.594 MINIMUM CORRELATION: -0.153 SERIES 260140 AND 260160 117 YEARS MAXIMUM CORRELATION: 0.594 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 0.503 0.274 0.223 0.252 0.312 0.280 0.330 0.239 0.357 0.440 SDEV 0.223 0.207 0.303 0.230 0.233 0.304 0.274 0.287 0.253 0.245 SERR 0.091 0.085 0.078 0.043 0.044 0.051 0.041 0.043 0.038 0.037 EPS 0.828 0.701 0.682 0.736 0.800 0.787 0.831 0.759 0.847 0.887 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 0.375 0.290 0.444 SDEV 0.258 0.289 0.238 SERR 0.038 0.043 0.035 EPS 0.857 0.803 0.889 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 1.002 0.037 -0.723 4.890 0.037 0.172 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.124 -0.079 0.115 33 148 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.70 2.56 1.01 1.29 3.84 56.55 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.85 0.21 0.00 0.68 0.89 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 0.171 0.112 0.035 -0.013 -0.045 -0.134 -0.114 -0.155 -0.002 -0.114 PACF 0.171 0.085 0.003 -0.029 -0.043 -0.121 -0.070 -0.108 0.060 -0.107 95% C.L. 0.149 0.153 0.155 0.155 0.155 0.155 0.158 0.160 0.163 0.163 |------------------ 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 0.036 0.171 |======================= 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 0.173 0.073 0.068 -0.022 -0.056 -0.138 -0.085 -0.184 0.030 -0.070 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 0.173 2 0.165 0.044 3 0.163 0.036 0.050 4 0.165 0.037 0.057 -0.046 5 0.163 0.041 0.059 -0.037 -0.053 6 0.156 0.036 0.067 -0.032 -0.033 -0.125 7 0.152 0.035 0.066 -0.030 -0.032 -0.120 -0.036 8 0.146 0.016 0.061 -0.034 -0.021 -0.114 -0.013 -0.155 9 0.163 0.018 0.073 -0.032 -0.018 -0.121 -0.014 -0.170 0.108 10 0.172 0.003 0.072 -0.043 -0.019 -0.124 -0.008 -0.169 0.122 -0.087 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) 491.60 488.12 489.77 491.32 492.94 494.42 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 493.57 495.33 492.96 492.83 493.45 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 0.173 R-SQUARED DUE TO POOLED AUTOREGRESSION: 2.98 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 103.07 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.173 0.030 0.005 0.001 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 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 0.151 0.384 2 260120 1 0.057 0.075 3 260130 1 0.000 -0.005 4 260140 1 0.240 0.481 5 260150 1 0.241 0.478 6 260160 1 0.232 0.415 7 260170 1 0.089 0.262 8 260180 1 0.078 0.279 9 260190 1 0.030 0.147 10 260200 1 0.080 0.262 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.120 0.278 STANDARD DEVIATION 0 0.090 0.167 MEDIAN 1 0.085 0.271 INTERQUARTILE RANGE 0 0.175 0.268 MINIMUM VALUE 1 0.000 -0.005 LOWER HINGE 1 0.057 0.147 UPPER HINGE 1 0.232 0.415 MAXIMUM VALUE 1 0.241 0.481 |------------------- 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 0.049 0.158 3.248 0.053 -0.024 2 260120 1843 1975 133 1.000 0.063 -0.295 3.382 0.071 -0.017 3 260130 1890 1975 86 1.000 0.071 -1.269 6.995 0.076 0.000 4 260140 1859 1975 117 1.000 0.069 -1.373 6.915 0.079 -0.052 5 260150 1828 1975 148 1.000 0.059 -0.617 3.320 0.069 -0.059 6 260160 1828 1975 148 1.000 0.050 -0.461 4.674 0.055 -0.110 7 260170 1795 1975 181 1.000 0.055 -1.691 14.763 0.056 -0.037 8 260180 1829 1975 147 1.000 0.041 -0.167 3.668 0.046 0.013 9 260190 1852 1975 124 1.000 0.042 -0.419 3.145 0.045 0.013 10 260200 1874 1975 102 1.000 0.042 0.081 3.705 0.045 0.030 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.054 -0.605 5.382 0.060 -0.024 STANDARD DEVIATION 26 0.000 0.011 0.633 3.606 0.013 0.042 MEDIAN (50TH QUANTILE) 133 1.000 0.053 -0.440 3.686 0.056 -0.020 INTERQUARTILE RANGE 31 0.000 0.021 1.102 3.595 0.026 0.065 MINIMUM VALUE 86 1.000 0.041 -1.691 3.145 0.045 -0.110 LOWER HINGE (25TH QUANTILE) 117 1.000 0.042 -1.269 3.320 0.046 -0.052 UPPER HINGE (75TH QUANTILE) 148 1.000 0.063 -0.167 6.915 0.071 0.013 MAXIMUM VALUE 181 1.000 0.071 0.158 14.763 0.079 0.030 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.338 0.151 0.022 -0.336 2.985 -0.069 0.595 MINIMUM CORRELATION: -0.069 SERIES 260140 AND 260160 117 YEARS MAXIMUM CORRELATION: 0.595 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 0.478 0.312 0.296 0.303 0.323 0.309 0.349 0.231 0.316 0.434 SDEV 0.257 0.170 0.266 0.184 0.283 0.294 0.259 0.245 0.238 0.203 SERR 0.105 0.070 0.069 0.035 0.053 0.049 0.039 0.036 0.035 0.030 EPS 0.813 0.737 0.758 0.783 0.808 0.810 0.843 0.750 0.822 0.885 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 0.376 0.283 0.442 SDEV 0.238 0.254 0.239 SERR 0.035 0.038 0.036 EPS 0.858 0.798 0.888 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 1.002 0.035 -0.496 3.976 0.042 -0.123 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.126 -0.079 0.112 30 151 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.74 2.74 1.03 1.12 3.86 55.57 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.85 0.16 0.00 0.74 0.89 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 -0.123 0.057 0.016 -0.002 -0.019 -0.090 -0.053 -0.152 0.064 -0.060 PACF -0.123 0.043 0.028 0.001 -0.022 -0.097 -0.075 -0.163 0.035 -0.033 95% C.L. 0.149 0.151 0.151 0.151 0.151 0.151 0.153 0.153 0.156 0.157 |------------------ 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 0.017 -0.123 |---------- 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 0.005 0.046 0.023 -0.002 -0.031 -0.102 -0.085 -0.156 0.039 -0.075 PACF 0.005 0.046 0.023 -0.004 -0.033 -0.102 -0.082 -0.148 0.050 -0.061 95% C.L. 0.149 0.149 0.149 0.149 0.149 0.149 0.151 0.152 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 0.002 0.005 |========================= 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 1.002 0.036 -0.540 3.777 0.036 0.187 |------------ 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 0.186 0.080 0.034 -0.003 -0.051 -0.126 -0.128 -0.169 -0.010 -0.106 PACF 0.186 0.047 0.012 -0.016 -0.052 -0.112 -0.086 -0.124 0.057 -0.103 95% C.L. 0.149 0.154 0.155 0.155 0.155 0.155 0.157 0.160 0.164 0.164 |------------------- 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 0.037 0.186 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.09 MINUTES