RUN: FILE NAMES FILE PROCESSED: run_me2 DATA FILE PROCESSED: SWIT178E.rwl.conv LOG FILE PROCESSED: SWIT178E.rwl.conv_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 50 25 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: 326 1 Krauchthal BE WIDTH_EARLY PISY - 326 2 Switzerland Scots pine, Scotch pine 550 4700-734 1714 1976 - 326 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 13 326071 MISSING VALUES FOUND: 5 IN 4 GAPS / 1870 1870 / 1892 1893 / 1911 1911 / 1958 1958 / -------------------------------------------------------------------- 17 326101 MISSING VALUES FOUND: 2 IN 1 GAPS / 1865 1866 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 326011 1764 1976 213 0.503 0.372 1.643 5.305 0.280 0.864 2 326012 1768 1976 209 0.555 0.292 1.832 7.326 0.268 0.752 3 326021 1785 1960 176 0.401 0.225 1.033 3.784 0.309 0.800 4 326022 1778 1976 199 0.452 0.342 1.959 8.523 0.304 0.786 5 326031 1863 1975 113 0.422 0.149 0.710 3.476 0.333 0.388 6 326032 1870 1973 104 0.489 0.151 1.160 5.114 0.269 0.261 7 326041 1892 1976 85 0.374 0.126 0.869 3.441 0.297 0.358 8 326042 1888 1976 89 0.368 0.156 1.135 3.709 0.324 0.514 9 326051 1791 1975 185 0.481 0.243 0.702 2.901 0.307 0.740 10 326052 1790 1976 187 0.381 0.190 0.842 3.038 0.286 0.736 11 326061 1770 1976 207 0.650 0.278 1.453 5.996 0.297 0.585 12 326062 1811 1976 166 0.603 0.172 0.047 3.309 0.315 0.119 13 326071 1714 1975 262 0.235 0.215 4.105 22.561 0.389 0.865 14 326072 1735 1976 242 0.493 0.368 4.504 29.085 0.290 0.853 15 326081 1835 1973 139 0.384 0.176 0.734 4.135 0.308 0.690 16 326082 1797 1961 165 0.372 0.213 1.385 4.477 0.325 0.783 17 326101 1789 1976 188 0.426 0.228 0.755 4.267 0.317 0.758 18 326102 1750 1976 227 0.369 0.189 1.329 5.521 0.364 0.531 NUMBER OF SERIES READ IN: 18 FROM 1714 TO 1976 263 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 175 0.442 0.227 1.455 6.998 0.310 0.632 STANDARD DEVIATION 51 0.098 0.076 1.137 7.098 0.031 0.224 MEDIAN (50TH QUANTILE) 185 0.424 0.214 1.147 4.372 0.307 0.738 INTERQUARTILE RANGE 70 0.119 0.106 0.888 2.520 0.034 0.271 MINIMUM VALUE 85 0.235 0.126 0.047 2.901 0.268 0.119 LOWER HINGE (25TH QUANTILE) 139 0.374 0.172 0.755 3.476 0.290 0.514 UPPER HINGE (75TH QUANTILE) 209 0.493 0.278 1.643 5.996 0.324 0.786 MAXIMUM VALUE 257 0.650 0.372 4.504 29.085 0.389 0.865 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 153 0.391 0.266 0.021 -0.273 2.625 -0.296 0.880 MINIMUM CORRELATION: -0.296 SERIES 326031 AND 326051 113 YEARS MAXIMUM CORRELATION: 0.880 SERIES 326011 AND 326012 209 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 54.78 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 1. 15. 55. 78. 91. 120. 153. 120. RBAR 0.898 0.490 0.315 0.337 0.399 0.446 0.445 0.441 SDEV 0.000 0.222 0.447 0.253 0.227 0.170 0.200 0.147 SERR 0.000 0.057 0.060 0.029 0.024 0.016 0.016 0.013 EPS 0.979 0.906 0.855 0.875 0.911 0.933 0.935 0.933 NSS 5.4 10.0 12.8 13.8 15.3 17.2 18.0 17.7 |======================== 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 1714 1976 263 0.456 0.246 2.221 9.607 0.263 0.839 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.811 0.428 0.000 37 226 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.66 1.01 1.08 1.74 5.47 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.11 0.00 0.83 0.94 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 186. 70. 85. 139. 209. 262. |----------- 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 0.835 0.781 0.719 0.636 0.589 0.505 0.482 0.452 0.439 0.383 PACF 0.835 0.275 0.058 -0.087 0.038 -0.101 0.114 0.059 0.089 -0.153 95% C.L. 0.123 0.191 0.235 0.266 0.288 0.306 0.318 0.329 0.339 0.347 |------------------ 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 0.732 0.604 0.282 |================== 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 326011 1 1.39300799 0.02261695 0.00000000 0.21946041 2 326012 1 0.97169995 0.02263799 0.00000000 0.35357147 3 326021 1 0.74434680 0.02082992 0.00000000 0.20529746 4 326022 1 1.12974370 0.01747471 0.00000000 0.13947490 5 326031 3 0.00000000 0.00000000 0.00215209 0.29954329 6 326032 3 0.00000000 0.00000000 0.00130310 0.42081776 7 326041 1 0.14557418 0.04347612 0.00000000 0.33606258 8 326042 3 0.00000000 0.00000000 -0.00306742 0.50567418 9 326051 3 0.00000000 0.00000000 -0.00230535 0.69510049 10 326052 3 0.00000000 0.00000000 -0.00165674 0.53696394 11 326061 1 0.99629605 0.05358124 0.00000000 0.56251299 12 326062 3 0.00000000 0.00000000 0.00013015 0.59238553 13 326071 3 0.00000000 0.00000000 -0.00111954 0.37926987 14 326072 3 0.00000000 0.00000000 -0.00227878 0.76943415 15 326081 3 0.00000000 0.00000000 -0.00323071 0.61017829 16 326082 3 0.00000000 0.00000000 -0.00187169 0.52783519 17 326101 1 0.92166775 0.10199165 0.00000000 0.37693590 18 326102 1 0.59530950 0.05350693 0.00000000 0.32114282 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 326011 1764 1976 213 1.002 0.303 0.471 3.294 0.278 0.352 2 326012 1768 1976 209 0.999 0.278 0.223 2.886 0.266 0.294 3 326021 1785 1960 176 0.999 0.354 0.963 5.838 0.307 0.408 4 326022 1778 1976 199 0.995 0.368 0.807 4.187 0.303 0.437 5 326031 1863 1975 113 0.998 0.303 0.489 3.160 0.330 0.151 6 326032 1870 1973 104 1.000 0.300 1.288 5.266 0.267 0.178 7 326041 1892 1976 85 1.000 0.316 0.667 3.125 0.294 0.291 8 326042 1888 1976 89 0.998 0.339 0.891 3.927 0.320 0.308 9 326051 1791 1975 185 0.989 0.414 0.909 4.103 0.306 0.645 10 326052 1790 1976 187 0.992 0.397 0.756 3.902 0.284 0.650 11 326061 1770 1976 207 0.999 0.314 0.403 3.812 0.296 0.364 12 326062 1811 1976 166 1.000 0.285 0.053 3.282 0.313 0.115 13 326071 1714 1975 262 1.010 0.686 3.052 15.696 0.402 0.740 14 326072 1735 1976 242 1.001 0.510 3.637 23.635 0.289 0.739 15 326081 1835 1973 139 0.996 0.311 0.246 3.038 0.306 0.302 16 326082 1797 1961 165 0.996 0.461 0.924 3.923 0.324 0.672 17 326101 1789 1976 188 1.000 0.473 0.083 2.373 0.315 0.713 18 326102 1750 1976 227 1.000 0.419 0.501 3.380 0.363 0.448 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 175 0.999 0.380 0.909 5.490 0.309 0.434 STANDARD DEVIATION 51 0.004 0.104 0.951 5.397 0.033 0.209 MEDIAN (50TH QUANTILE) 186 0.999 0.347 0.712 3.857 0.306 0.386 INTERQUARTILE RANGE 70 0.004 0.116 0.521 1.026 0.032 0.356 MINIMUM VALUE 85 0.989 0.278 0.053 2.373 0.266 0.115 LOWER HINGE (25TH QUANTILE) 139 0.996 0.303 0.403 3.160 0.289 0.294 UPPER HINGE (75TH QUANTILE) 209 1.000 0.419 0.924 4.187 0.320 0.650 MAXIMUM VALUE 262 1.010 0.686 3.637 23.635 0.402 0.740 |------------------------ 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 326011 -67 142 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 326012 -67 140 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 326021 -67 117 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 326022 -67 133 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 326031 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 326032 -67 69 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 326041 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 326042 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 326051 -67 123 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 326052 -67 125 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 326061 -67 138 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 326062 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 326071 -67 175 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 326072 -67 162 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 326081 -67 93 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 326082 -67 110 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 17 326101 -67 125 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 18 326102 -67 152 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 326011 1764 1976 213 0.997 0.268 0.294 3.605 0.278 0.148 2 326012 1768 1976 209 0.999 0.269 0.158 2.771 0.267 0.263 3 326021 1785 1960 176 0.998 0.341 0.912 5.991 0.307 0.358 4 326022 1778 1976 199 0.999 0.359 0.687 4.014 0.303 0.398 5 326031 1863 1975 113 0.997 0.281 0.326 2.905 0.329 0.027 6 326032 1870 1973 104 0.997 0.277 0.934 4.257 0.267 0.070 7 326041 1892 1976 85 0.998 0.305 0.596 2.983 0.294 0.255 8 326042 1888 1976 89 0.999 0.326 0.630 3.184 0.320 0.275 9 326051 1791 1975 185 0.993 0.330 0.360 3.057 0.306 0.441 10 326052 1790 1976 187 0.995 0.346 0.852 5.775 0.284 0.482 11 326061 1770 1976 207 0.998 0.308 0.513 4.085 0.296 0.341 12 326062 1811 1976 166 0.998 0.275 -0.011 3.307 0.313 0.045 13 326071 1714 1975 262 0.973 0.533 2.742 14.290 0.402 0.630 14 326072 1735 1976 242 0.991 0.470 3.620 23.673 0.289 0.698 15 326081 1835 1973 139 0.998 0.305 0.369 3.134 0.306 0.260 16 326082 1797 1961 165 0.991 0.413 0.498 2.963 0.323 0.601 17 326101 1789 1976 188 0.979 0.411 0.209 2.461 0.315 0.600 18 326102 1750 1976 227 0.998 0.411 0.473 3.205 0.363 0.420 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 175 0.994 0.346 0.787 5.315 0.309 0.351 STANDARD DEVIATION 51 0.007 0.075 0.920 5.312 0.033 0.204 MEDIAN (50TH QUANTILE) 186 0.998 0.328 0.506 3.256 0.306 0.350 INTERQUARTILE RANGE 70 0.005 0.130 0.526 1.274 0.031 0.227 MINIMUM VALUE 85 0.973 0.268 -0.011 2.461 0.267 0.027 LOWER HINGE (25TH QUANTILE) 139 0.993 0.281 0.326 2.983 0.289 0.255 UPPER HINGE (75TH QUANTILE) 209 0.998 0.411 0.852 4.257 0.320 0.482 MAXIMUM VALUE 262 0.999 0.533 3.620 23.673 0.402 0.698 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 153 0.400 0.141 0.011 0.051 3.596 -0.090 0.775 MINIMUM CORRELATION: -0.090 SERIES 326082 AND 326101 165 YEARS MAXIMUM CORRELATION: 0.775 SERIES 326041 AND 326042 85 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 54.78 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 1. 15. 55. 78. 91. 120. 153. 120. RBAR 0.894 0.353 0.301 0.333 0.408 0.477 0.518 0.433 SDEV 0.000 0.125 0.223 0.228 0.199 0.148 0.125 0.141 SERR 0.000 0.032 0.030 0.026 0.021 0.014 0.010 0.013 EPS 0.978 0.845 0.847 0.873 0.913 0.940 0.951 0.931 NSS 5.4 10.0 12.8 13.8 15.3 17.2 18.0 17.7 |======================== 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 1714 1976 263 0.956 0.300 1.249 8.541 0.275 0.467 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.686 0.508 -0.234 53 210 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.25 0.43 1.00 1.10 1.52 5.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.11 0.00 0.84 0.94 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 0.465 0.352 0.246 0.092 0.084 -0.015 -0.007 -0.017 0.004 -0.071 PACF 0.465 0.172 0.040 -0.099 0.034 -0.076 0.021 -0.006 0.042 -0.113 95% C.L. 0.123 0.148 0.160 0.166 0.166 0.167 0.167 0.167 0.167 0.167 |------------------ 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 0.245 0.388 0.174 |======================= 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 0.276 0.156 0.065 -0.066 -0.041 -0.118 -0.075 -0.082 0.030 0.002 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 0.276 2 0.252 0.087 3 0.252 0.087 0.002 4 0.252 0.096 0.028 -0.105 5 0.251 0.096 0.029 -0.103 -0.007 6 0.250 0.086 0.032 -0.094 0.017 -0.094 7 0.249 0.086 0.030 -0.094 0.018 -0.091 -0.012 8 0.249 0.082 0.031 -0.098 0.019 -0.087 -0.001 -0.046 9 0.253 0.082 0.039 -0.099 0.027 -0.090 -0.008 -0.067 0.085 10 0.255 0.080 0.038 -0.102 0.028 -0.093 -0.006 -0.064 0.092 -0.028 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) 2035.28 2016.48 2016.48 2018.48 2017.58 2019.57 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 2019.22 2021.18 2022.63 2022.73 2024.51 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 0.252 0.087 R-SQUARED DUE TO POOLED AUTOREGRESSION: 8.30 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 109.05 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.252 0.150 0.060 0.028 0.012 0.006 0.002 0.001 0.000 0.0002 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 326011 2 0.032 0.149 -0.008 2 326012 2 0.077 0.248 0.068 3 326021 2 0.135 0.332 0.074 4 326022 2 0.177 0.387 0.032 5 326031 2 0.003 0.026 0.047 6 326032 2 0.058 0.056 0.203 7 326041 2 0.068 0.265 -0.039 8 326042 2 0.093 0.302 -0.098 9 326051 2 0.278 0.344 0.236 10 326052 2 0.304 0.414 0.199 11 326061 2 0.163 0.282 0.177 12 326062 2 0.033 0.041 0.090 13 326071 2 0.424 0.519 0.184 14 326072 2 0.497 0.656 0.064 15 326081 2 0.134 0.201 0.239 16 326082 2 0.438 0.411 0.322 17 326101 2 0.417 0.426 0.293 18 326102 2 0.207 0.345 0.181 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.197 0.300 0.126 STANDARD DEVIATION 0 0.159 0.166 0.117 MEDIAN 2 0.149 0.317 0.134 INTERQUARTILE RANGE 0 0.235 0.210 0.156 MINIMUM VALUE 2 0.003 0.026 -0.098 LOWER HINGE 2 0.068 0.201 0.047 UPPER HINGE 2 0.304 0.411 0.203 MAXIMUM VALUE 2 0.497 0.656 0.322 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 326011 1764 1976 213 1.000 0.265 0.296 3.707 0.297 0.001 2 326012 1768 1976 209 1.000 0.258 0.086 2.868 0.293 -0.004 3 326021 1785 1960 176 1.000 0.318 0.844 6.474 0.360 0.003 4 326022 1778 1976 199 1.000 0.328 0.415 4.284 0.358 0.004 5 326031 1863 1975 113 1.000 0.280 0.320 2.960 0.332 0.000 6 326032 1870 1973 104 1.000 0.270 0.721 4.008 0.282 -0.023 7 326041 1892 1976 85 1.000 0.295 0.463 2.787 0.329 0.001 8 326042 1888 1976 89 1.000 0.312 0.603 2.905 0.348 -0.009 9 326051 1791 1975 185 1.000 0.285 -0.035 2.680 0.352 -0.056 10 326052 1790 1976 187 1.000 0.284 0.269 4.311 0.339 -0.057 11 326061 1770 1976 207 1.000 0.284 0.452 3.672 0.334 -0.025 12 326062 1811 1976 166 1.000 0.274 0.023 3.271 0.320 -0.013 13 326071 1714 1975 262 1.000 0.403 0.866 6.467 0.479 -0.006 14 326072 1735 1976 242 1.000 0.334 1.572 10.363 0.367 0.005 15 326081 1835 1973 139 1.000 0.285 0.243 3.076 0.331 -0.026 16 326082 1797 1961 165 1.000 0.310 0.175 2.782 0.363 -0.032 17 326101 1789 1976 188 1.000 0.314 0.119 3.128 0.351 -0.003 18 326102 1750 1976 227 1.000 0.366 0.521 3.343 0.405 -0.010 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 175 1.000 0.304 0.442 4.060 0.347 -0.014 STANDARD DEVIATION 51 0.000 0.037 0.387 1.938 0.044 0.019 MEDIAN (50TH QUANTILE) 186 1.000 0.290 0.367 3.307 0.343 -0.007 INTERQUARTILE RANGE 70 0.000 0.037 0.428 1.379 0.031 0.026 MINIMUM VALUE 85 1.000 0.258 -0.035 2.680 0.282 -0.057 LOWER HINGE (25TH QUANTILE) 139 1.000 0.280 0.175 2.905 0.329 -0.025 UPPER HINGE (75TH QUANTILE) 209 1.000 0.318 0.603 4.284 0.360 0.001 MAXIMUM VALUE 262 1.000 0.403 1.572 10.363 0.479 0.005 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 153 0.431 0.098 0.008 0.709 3.607 0.232 0.753 MINIMUM CORRELATION: 0.232 SERIES 326052 AND 326102 187 YEARS MAXIMUM CORRELATION: 0.753 SERIES 326021 AND 326022 176 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 54.78 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1770. 1795. 1820. 1845. 1870. 1895. 1920. 1945. CORR 1. 15. 55. 78. 91. 120. 153. 120. RBAR 0.809 0.353 0.397 0.481 0.457 0.442 0.498 0.450 SDEV 0.000 0.108 0.157 0.124 0.123 0.116 0.111 0.105 SERR 0.000 0.028 0.021 0.014 0.013 0.011 0.009 0.010 EPS 0.958 0.845 0.894 0.928 0.928 0.932 0.947 0.935 NSS 5.4 10.0 12.8 13.8 15.3 17.2 18.0 17.7 |======================== 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 1714 1976 263 0.990 0.243 0.373 4.915 0.288 -0.023 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.436 0.246 -0.039 69 194 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.23 0.86 1.00 1.05 1.91 8.20 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.11 0.00 0.85 0.96 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 -0.023 0.004 0.075 -0.088 0.026 -0.113 -0.016 -0.032 0.041 -0.034 PACF -0.023 0.003 0.075 -0.085 0.022 -0.118 -0.006 -0.045 0.064 -0.054 95% C.L. 0.123 0.123 0.123 0.124 0.125 0.125 0.127 0.127 0.127 0.127 |------------------ 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 0.000 0.002 0.073 -0.086 0.021 -0.112 -0.019 -0.031 0.040 -0.034 PACF 0.000 0.002 0.073 -0.086 0.022 -0.119 -0.005 -0.043 0.064 -0.057 95% C.L. 0.123 0.123 0.123 0.124 0.125 0.125 0.126 0.127 0.127 0.127 |----------------- 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 0.005 0.000 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 1714 1976 263 0.990 0.254 0.832 6.740 0.257 0.281 |------------ 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 0.280 0.162 0.107 -0.049 -0.013 -0.119 -0.055 -0.054 -0.006 -0.069 PACF 0.280 0.090 0.045 -0.111 0.011 -0.115 0.019 -0.028 0.044 -0.097 95% C.L. 0.123 0.133 0.136 0.137 0.137 0.137 0.139 0.139 0.139 0.139 |------------------- 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 0.089 0.256 0.090 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES