RUN: fran FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: FRAN018N.rwl LOG FILE PROCESSED: FRAN018N.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_MINIMUM 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 2 260120 MISSING VALUES FOUND: 5 IN 1 GAPS / 1852 1856 / -------------------------------------------------------------------- 4 260140 MISSING VALUES FOUND: 5 IN 1 GAPS / 1953 1957 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 260110 1842 1975 134 0.292 0.027 0.488 3.449 0.060 0.610 2 260120 1843 1975 133 0.293 0.021 -0.017 2.926 0.055 0.446 3 260130 1890 1975 86 0.311 0.031 -0.177 2.967 0.059 0.741 4 260140 1859 1975 117 0.229 0.027 0.263 2.968 0.080 0.646 5 260150 1828 1975 148 0.319 0.035 0.160 2.510 0.074 0.606 6 260160 1828 1975 148 0.290 0.025 0.216 3.209 0.065 0.547 7 260170 1795 1975 181 0.326 0.039 0.238 2.554 0.069 0.729 8 260180 1829 1975 147 0.333 0.026 0.384 2.775 0.065 0.421 9 260190 1852 1975 124 0.297 0.026 0.193 2.018 0.057 0.644 10 260200 1874 1975 102 0.287 0.029 0.191 2.309 0.055 0.766 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 131 0.298 0.029 0.194 2.768 0.064 0.616 STANDARD DEVIATION 27 0.029 0.005 0.187 0.428 0.008 0.118 MEDIAN (50TH QUANTILE) 131 0.295 0.027 0.205 2.850 0.063 0.627 INTERQUARTILE RANGE 36 0.029 0.005 0.103 0.459 0.012 0.182 MINIMUM VALUE 86 0.229 0.021 -0.177 2.018 0.055 0.421 LOWER HINGE (25TH QUANTILE) 112 0.290 0.026 0.160 2.510 0.057 0.547 UPPER HINGE (75TH QUANTILE) 148 0.319 0.031 0.263 2.968 0.069 0.729 MAXIMUM VALUE 181 0.333 0.039 0.488 3.449 0.080 0.766 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.366 0.158 0.023 -0.138 2.713 0.046 0.672 MINIMUM CORRELATION: 0.046 SERIES 260150 AND 260170 148 YEARS MAXIMUM CORRELATION: 0.672 SERIES 260130 AND 260200 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 0.331 0.155 0.257 0.180 0.281 0.392 0.098 0.244 0.331 0.394 SDEV 0.159 0.257 0.190 0.208 0.218 0.284 0.321 0.347 0.237 0.213 SERR 0.065 0.105 0.049 0.039 0.041 0.047 0.048 0.052 0.035 0.032 EPS 0.701 0.533 0.720 0.646 0.775 0.860 0.520 0.764 0.832 0.867 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 0.681 0.421 0.374 SDEV 0.111 0.195 0.201 SERR 0.017 0.029 0.030 EPS 0.955 0.879 0.856 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 0.310 0.029 1.199 5.455 0.056 0.676 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.520 -0.300 0.121 64 117 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.39 1.32 1.01 1.15 2.46 9999.00 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.84 0.90 0.00 0.00 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 0.673 0.573 0.602 0.583 0.429 0.494 0.445 0.373 0.354 0.417 PACF 0.673 0.220 0.295 0.149 -0.166 0.211 -0.074 -0.014 0.032 0.103 95% C.L. 0.149 0.205 0.238 0.269 0.296 0.309 0.326 0.339 0.348 0.356 |------------------ 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 6 0.591 0.451 0.036 0.205 0.207 -0.248 0.224 |================== 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 -0.00034222 0.31541353 2 260120 3 0.00000000 0.00000000 -0.00020459 0.30683249 3 260130 1 0.06782459 0.04111342 0.00000000 0.29257098 4 260140 3 0.00000000 0.00000000 -0.00028615 0.24483769 5 260150 3 0.00000000 0.00000000 0.00033668 0.29437673 6 260160 3 0.00000000 0.00000000 0.00013924 0.28009927 7 260170 3 0.00000000 0.00000000 -0.00041026 0.36379743 8 260180 3 0.00000000 0.00000000 -0.00006381 0.33751094 9 260190 3 0.00000000 0.00000000 -0.00008699 0.30221087 10 260200 3 0.00000000 0.00000000 -0.00068329 0.32264027 |-------------------- 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 0.079 0.604 3.965 0.060 0.464 2 260120 1843 1975 133 1.000 0.066 0.049 2.738 0.055 0.387 3 260130 1890 1975 86 1.000 0.082 -0.485 3.483 0.059 0.571 4 260140 1859 1975 117 1.000 0.110 0.406 3.081 0.081 0.556 5 260150 1828 1975 148 1.000 0.099 0.142 2.469 0.074 0.519 6 260160 1828 1975 148 1.000 0.085 0.300 2.952 0.065 0.516 7 260170 1795 1975 181 1.000 0.099 0.532 2.795 0.069 0.621 8 260180 1829 1975 147 1.000 0.076 0.365 2.734 0.065 0.410 9 260190 1852 1975 124 1.000 0.085 0.122 2.104 0.057 0.638 10 260200 1874 1975 102 1.000 0.074 0.111 2.231 0.055 0.535 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.086 0.215 2.855 0.064 0.522 STANDARD DEVIATION 26 0.000 0.013 0.309 0.560 0.009 0.082 MEDIAN (50TH QUANTILE) 133 1.000 0.084 0.221 2.767 0.062 0.527 INTERQUARTILE RANGE 31 0.000 0.023 0.295 0.612 0.012 0.107 MINIMUM VALUE 86 1.000 0.066 -0.485 2.104 0.055 0.387 LOWER HINGE (25TH QUANTILE) 117 1.000 0.076 0.111 2.469 0.057 0.464 UPPER HINGE (75TH QUANTILE) 148 1.000 0.099 0.406 3.081 0.069 0.571 MAXIMUM VALUE 181 1.000 0.110 0.604 3.965 0.081 0.638 |------------------------ 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 0.072 0.650 4.543 0.060 0.364 2 260120 1843 1975 133 1.000 0.059 -0.093 2.686 0.055 0.239 3 260130 1890 1975 86 0.999 0.064 -0.513 4.058 0.058 0.318 4 260140 1859 1975 117 1.000 0.095 0.198 3.389 0.081 0.417 5 260150 1828 1975 148 1.000 0.089 0.226 2.854 0.074 0.402 6 260160 1828 1975 148 1.000 0.071 0.337 2.905 0.065 0.319 7 260170 1795 1975 181 1.000 0.095 0.424 2.875 0.069 0.592 8 260180 1829 1975 147 1.000 0.073 0.200 2.497 0.065 0.361 9 260190 1852 1975 124 1.000 0.063 0.353 3.329 0.057 0.312 10 260200 1874 1975 102 1.000 0.069 0.129 2.244 0.055 0.474 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.075 0.191 3.138 0.064 0.380 STANDARD DEVIATION 26 0.000 0.013 0.315 0.710 0.009 0.099 MEDIAN (50TH QUANTILE) 133 1.000 0.071 0.213 2.890 0.062 0.362 INTERQUARTILE RANGE 31 0.000 0.025 0.225 0.703 0.012 0.099 MINIMUM VALUE 86 0.999 0.059 -0.513 2.244 0.055 0.239 LOWER HINGE (25TH QUANTILE) 117 1.000 0.064 0.129 2.686 0.057 0.318 UPPER HINGE (75TH QUANTILE) 148 1.000 0.089 0.353 3.389 0.069 0.417 MAXIMUM VALUE 181 1.000 0.095 0.650 4.543 0.081 0.592 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.323 0.109 0.016 0.283 2.823 0.119 0.578 MINIMUM CORRELATION: 0.119 SERIES 260130 AND 260180 86 YEARS MAXIMUM CORRELATION: 0.578 SERIES 260170 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 0.389 0.168 0.250 0.190 0.302 0.403 0.094 0.265 0.370 0.453 SDEV 0.162 0.221 0.213 0.205 0.217 0.283 0.329 0.298 0.215 0.183 SERR 0.066 0.090 0.055 0.039 0.041 0.047 0.049 0.044 0.032 0.027 EPS 0.752 0.556 0.713 0.661 0.792 0.865 0.509 0.783 0.855 0.892 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 0.613 0.477 0.418 SDEV 0.150 0.184 0.181 SERR 0.022 0.027 0.027 EPS 0.941 0.901 0.878 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 0.999 0.056 0.290 2.892 0.055 0.283 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.077 0.042 0.007 32 149 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.61 1.55 1.03 1.27 2.81 47.32 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.86 0.18 0.00 0.72 0.90 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 0.282 0.119 0.250 0.161 -0.066 0.021 0.007 -0.123 -0.074 -0.008 PACF 0.282 0.043 0.224 0.040 -0.159 0.021 -0.043 -0.090 0.004 0.010 95% C.L. 0.149 0.160 0.162 0.170 0.174 0.174 0.174 0.174 0.176 0.177 |------------------ 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 0.081 0.282 |======================= 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 0.336 0.258 0.264 0.160 -0.023 -0.021 -0.051 -0.167 -0.094 -0.145 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 0.336 2 0.281 0.164 3 0.255 0.119 0.158 4 0.254 0.118 0.155 0.011 5 0.255 0.143 0.174 0.053 -0.165 6 0.247 0.146 0.183 0.060 -0.152 -0.052 7 0.245 0.140 0.185 0.067 -0.146 -0.042 -0.038 8 0.240 0.135 0.168 0.075 -0.124 -0.026 -0.009 -0.118 9 0.244 0.136 0.169 0.080 -0.127 -0.031 -0.014 -0.126 0.034 10 0.247 0.126 0.168 0.077 -0.136 -0.025 -0.001 -0.116 0.052 -0.077 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) 597.55 577.86 574.95 572.40 574.38 571.39 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 572.90 574.64 574.10 575.90 576.82 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 0.255 0.119 0.158 R-SQUARED DUE TO POOLED AUTOREGRESSION: 15.81 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 118.78 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 3) PROCESS OUT TO ORDER 50: 1.0000 0.255 0.184 0.235 0.122 0.088 0.074 0.049 0.035 0.026 0.0186 0.013 0.010 0.007 0.005 0.004 0.003 0.002 0.001 0.001 0.0007 0.001 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 3 0.156 0.340 0.023 0.094 2 260120 3 0.109 0.237 -0.044 0.227 3 260130 3 0.185 0.209 0.193 0.175 4 260140 3 0.212 0.335 0.137 0.096 5 260150 3 0.222 0.311 0.088 0.198 6 260160 3 0.123 0.280 0.065 0.109 7 260170 3 0.370 0.487 0.144 0.043 8 260180 3 0.156 0.309 0.162 -0.009 9 260190 3 0.124 0.279 0.132 -0.009 10 260200 3 0.272 0.359 0.224 0.023 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 3 0.193 0.315 0.112 0.095 STANDARD DEVIATION 0 0.080 0.076 0.081 0.084 MEDIAN 3 0.170 0.310 0.134 0.095 INTERQUARTILE RANGE 0 0.098 0.061 0.097 0.152 MINIMUM VALUE 3 0.109 0.209 -0.044 -0.009 LOWER HINGE 3 0.124 0.279 0.065 0.023 UPPER HINGE 3 0.222 0.340 0.162 0.175 MAXIMUM VALUE 3 0.370 0.487 0.224 0.227 |------------------- 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 0.066 0.887 5.403 0.072 -0.012 2 260120 1843 1975 133 1.000 0.055 -0.239 2.980 0.062 -0.010 3 260130 1890 1975 86 1.000 0.058 -0.628 3.673 0.065 -0.016 4 260140 1859 1975 117 1.000 0.084 0.414 3.690 0.097 0.004 5 260150 1828 1975 148 1.000 0.079 0.243 3.282 0.085 0.015 6 260160 1828 1975 148 1.000 0.066 0.357 3.030 0.075 -0.006 7 260170 1795 1975 181 1.000 0.075 0.155 2.711 0.085 0.001 8 260180 1829 1975 147 1.000 0.067 0.320 2.531 0.075 0.000 9 260190 1852 1975 124 1.000 0.059 0.594 3.205 0.066 -0.005 10 260200 1874 1975 102 1.000 0.059 -0.119 2.465 0.067 0.001 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 132 1.000 0.067 0.198 3.297 0.075 -0.003 STANDARD DEVIATION 26 0.000 0.010 0.434 0.852 0.011 0.009 MEDIAN (50TH QUANTILE) 133 1.000 0.066 0.281 3.118 0.073 -0.002 INTERQUARTILE RANGE 31 0.000 0.017 0.533 0.962 0.019 0.012 MINIMUM VALUE 86 1.000 0.055 -0.628 2.465 0.062 -0.016 LOWER HINGE (25TH QUANTILE) 117 1.000 0.059 -0.119 2.711 0.066 -0.010 UPPER HINGE (75TH QUANTILE) 148 1.000 0.075 0.414 3.673 0.085 0.001 MAXIMUM VALUE 181 1.000 0.084 0.887 5.403 0.097 0.015 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 45 0.358 0.088 0.013 0.061 2.801 0.207 0.568 MINIMUM CORRELATION: 0.207 SERIES 260140 AND 260160 117 YEARS MAXIMUM CORRELATION: 0.568 SERIES 260140 AND 260180 117 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 0.437 0.238 0.321 0.249 0.322 0.369 0.196 0.407 0.456 0.378 SDEV 0.174 0.213 0.184 0.203 0.183 0.220 0.262 0.181 0.156 0.179 SERR 0.071 0.087 0.048 0.038 0.035 0.037 0.039 0.027 0.023 0.027 EPS 0.787 0.659 0.779 0.734 0.807 0.848 0.710 0.873 0.894 0.859 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 0.480 0.557 0.420 SDEV 0.161 0.106 0.171 SERR 0.024 0.016 0.026 EPS 0.902 0.926 0.879 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 1.000 0.053 0.329 2.939 0.065 -0.107 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.071 0.037 0.005 32 149 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.05 1.94 1.01 1.10 3.05 22.69 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.85 0.16 0.00 0.74 0.90 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 -0.106 -0.130 0.090 0.084 -0.179 0.018 0.039 -0.095 -0.055 0.099 PACF -0.106 -0.143 0.061 0.086 -0.145 -0.003 -0.010 -0.079 -0.049 0.044 95% C.L. 0.149 0.150 0.153 0.154 0.155 0.159 0.160 0.160 0.161 0.161 |------------------ 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 2 0.035 -0.121 -0.143 |---------- 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 -0.006 0.021 -0.012 0.068 -0.148 -0.001 -0.011 -0.070 -0.058 0.048 PACF -0.006 0.021 -0.011 0.068 -0.147 -0.004 -0.004 -0.079 -0.039 0.030 95% C.L. 0.149 0.149 0.149 0.149 0.149 0.153 0.153 0.153 0.153 0.154 |----------------- 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 -0.006 0.021 -0.012 |========================= 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 1.000 0.056 0.310 3.064 0.054 0.321 |------------ 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 0.319 0.237 0.222 0.143 -0.057 0.001 -0.027 -0.114 -0.112 -0.043 PACF 0.319 0.150 0.125 0.023 -0.178 0.007 -0.017 -0.080 -0.038 0.021 95% C.L. 0.149 0.163 0.171 0.177 0.179 0.180 0.180 0.180 0.181 0.183 |------------------- 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 0.137 0.253 0.116 0.125 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.09 MINUTES