RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM042W.rwl.conv LOG FILE PROCESSED: GERM042W.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 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: 021 1 Kaiserstuhl (D), EU-Pr. WIDTH_RING PCAB - 021 2 Germany Norway spruce 270 4803-740 1903 1995 - 021 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 5 021018 MISSING VALUES FOUND: 2 IN 1 GAPS / 1940 1941 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 021014 1931 1995 65 2.432 0.986 0.833 3.337 0.288 0.647 2 021015 1911 1995 85 2.203 1.183 1.195 3.792 0.253 0.850 3 021016 1925 1995 71 1.269 0.564 0.360 2.602 0.250 0.746 4 021017 1911 1995 85 4.518 1.901 0.418 2.676 0.306 0.409 5 021018 1909 1995 87 3.400 1.383 0.086 2.712 0.248 0.775 6 021019 1909 1995 87 2.131 1.099 0.969 3.473 0.222 0.861 7 021020 1909 1995 87 2.830 1.323 0.166 1.917 0.204 0.854 8 021021 1908 1995 88 3.594 1.692 1.252 4.778 0.237 0.800 9 021023 1908 1995 88 3.798 1.876 1.001 3.666 0.242 0.789 10 021025 1907 1995 89 3.549 1.469 1.149 4.893 0.269 0.687 11 021027 1913 1995 83 3.312 1.361 0.872 3.472 0.224 0.777 12 021031 1903 1995 93 2.218 1.090 2.162 7.908 0.241 0.740 13 021033 1903 1995 93 2.529 1.323 1.789 5.865 0.224 0.841 14 021035 1903 1995 93 2.526 1.176 1.745 6.122 0.191 0.847 15 021037 1903 1995 93 2.418 0.947 1.540 5.777 0.199 0.775 16 021041 1911 1995 85 3.297 1.557 0.487 2.625 0.282 0.691 NUMBER OF SERIES READ IN: 16 FROM 1903 TO 1995 93 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 86 2.877 1.308 1.002 4.101 0.243 0.756 STANDARD DEVIATION 7 0.810 0.349 0.607 1.641 0.032 0.113 MEDIAN (50TH QUANTILE) 87 2.680 1.323 0.985 3.570 0.242 0.776 INTERQUARTILE RANGE 6 1.156 0.419 0.944 2.641 0.038 0.129 MINIMUM VALUE 65 1.269 0.564 0.086 1.917 0.191 0.409 LOWER HINGE (25TH QUANTILE) 85 2.318 1.094 0.452 2.694 0.223 0.715 UPPER HINGE (75TH QUANTILE) 91 3.475 1.513 1.396 5.335 0.261 0.844 MAXIMUM VALUE 93 4.518 1.901 2.162 7.908 0.306 0.861 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.360 0.246 0.022 0.173 2.431 -0.145 0.930 MINIMUM CORRELATION: -0.145 SERIES 021016 AND 021021 71 YEARS MAXIMUM CORRELATION: 0.930 SERIES 021033 AND 021035 93 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1913. 1930. 1940. 1950. 1960. 1970. 1980. CORR 6. 91. 105. 120. 120. 120. 120. RBAR 0.917 0.407 0.305 0.190 0.239 0.350 0.184 SDEV 0.025 0.256 0.360 0.496 0.321 0.308 0.303 SERR 0.010 0.027 0.035 0.045 0.029 0.028 0.028 EPS 0.992 0.913 0.875 0.789 0.834 0.896 0.783 NSS 10.7 15.2 15.9 16.0 16.0 16.0 16.0 |======================== 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 1903 1995 93 2.717 0.966 1.124 4.680 0.171 0.824 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.442 0.230 0.460 38 55 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.78 1.64 1.04 1.26 2.90 54.15 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.07 0.69 0.84 0.91 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 87. 6. 65. 85. 91. 93. |----------- 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 0.664 0.513 0.397 0.285 0.229 0.243 0.180 0.117 0.073 PACF 0.815 -0.003 -0.082 0.008 -0.062 0.083 0.186 -0.217 -0.065 0.046 95% C.L. 0.207 0.317 0.372 0.401 0.417 0.426 0.431 0.437 0.440 0.441 |------------------ 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 1 0.676 0.822 |================== 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 021014 3 0.00000000 0.00000000 -0.02044493 3.10699034 2 021015 1 2.74143434 0.04380941 0.00000000 1.49980509 3 021016 3 0.00000000 0.00000000 -0.01237391 1.71419322 4 021017 3 0.00000000 0.00000000 -0.00528181 4.74499989 5 021018 3 0.00000000 0.00000000 0.00689126 3.09914613 6 021019 1 3.23025012 0.03874116 0.00000000 1.22362375 7 021020 3 0.00000000 0.00000000 -0.03931126 4.56015491 8 021021 3 0.00000000 0.00000000 -0.01650593 4.32883215 9 021023 1 2.15743566 0.00568213 0.00000000 2.10543370 10 021025 3 0.00000000 0.00000000 -0.01418659 4.18727255 11 021027 1 2.63508630 0.05053974 0.00000000 2.70897245 12 021031 1 2.17532730 0.02102359 0.00000000 1.27309060 13 021033 1 3.08868814 0.01538747 0.00000000 0.89888430 14 021035 1 3.87041616 0.01139805 0.00000000 0.15341194 15 021037 1 1.94853663 0.01818717 0.00000000 1.48708081 16 021041 1 1.21963668 0.05515792 0.00000000 3.04600883 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 021014 1931 1995 65 0.997 0.344 0.283 2.930 0.284 0.585 2 021015 1911 1995 85 1.000 0.389 -0.027 2.413 0.251 0.684 3 021016 1925 1995 71 0.996 0.380 0.072 2.733 0.247 0.692 4 021017 1911 1995 85 1.000 0.424 0.506 2.807 0.302 0.400 5 021018 1909 1995 87 1.000 0.400 0.107 2.885 0.243 0.756 6 021019 1909 1995 87 1.001 0.349 0.135 2.501 0.221 0.669 7 021020 1909 1995 87 0.994 0.316 0.352 2.472 0.201 0.678 8 021021 1908 1995 88 1.000 0.459 1.202 4.185 0.235 0.789 9 021023 1908 1995 88 1.000 0.510 1.348 4.723 0.240 0.793 10 021025 1907 1995 89 1.000 0.387 0.758 3.583 0.266 0.634 11 021027 1913 1995 83 1.000 0.361 0.797 3.808 0.221 0.710 12 021031 1903 1995 93 1.000 0.367 0.964 4.198 0.238 0.617 13 021033 1903 1995 93 1.001 0.369 0.397 3.560 0.221 0.731 14 021035 1903 1995 93 1.001 0.303 0.431 4.335 0.190 0.684 15 021037 1903 1995 93 1.000 0.328 1.095 4.897 0.198 0.679 16 021041 1911 1995 85 1.000 0.468 0.645 3.340 0.279 0.656 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 86 0.999 0.385 0.567 3.461 0.240 0.672 STANDARD DEVIATION 7 0.002 0.057 0.426 0.825 0.032 0.092 MEDIAN (50TH QUANTILE) 87 1.000 0.375 0.468 3.450 0.239 0.681 INTERQUARTILE RANGE 6 0.001 0.065 0.672 1.421 0.038 0.076 MINIMUM VALUE 65 0.994 0.303 -0.027 2.413 0.190 0.400 LOWER HINGE (25TH QUANTILE) 85 1.000 0.347 0.209 2.770 0.221 0.645 UPPER HINGE (75TH QUANTILE) 91 1.000 0.412 0.880 4.191 0.259 0.720 MAXIMUM VALUE 93 1.001 0.510 1.348 4.897 0.302 0.793 |------------------------ 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 021014 -67 43 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 021015 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 021016 -67 47 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 021017 -67 56 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 021018 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 021019 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 021020 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 021021 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 021023 -67 58 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 021025 -67 59 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 021027 -67 55 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 021031 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 021033 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 021035 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 021037 -67 62 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 021041 -67 56 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 021014 1931 1995 65 0.996 0.321 0.405 3.379 0.283 0.498 2 021015 1911 1995 85 0.991 0.373 0.110 2.493 0.250 0.654 3 021016 1925 1995 71 0.986 0.323 0.106 3.715 0.245 0.537 4 021017 1911 1995 85 0.992 0.387 0.549 3.101 0.303 0.377 5 021018 1909 1995 87 0.985 0.336 0.151 3.094 0.242 0.659 6 021019 1909 1995 87 0.994 0.313 0.154 2.302 0.220 0.579 7 021020 1909 1995 87 0.996 0.292 0.076 2.299 0.199 0.615 8 021021 1908 1995 88 0.995 0.441 1.124 3.933 0.234 0.781 9 021023 1908 1995 88 0.990 0.462 1.105 4.228 0.237 0.761 10 021025 1907 1995 89 0.996 0.370 0.748 3.767 0.265 0.618 11 021027 1913 1995 83 0.997 0.346 0.822 4.339 0.220 0.685 12 021031 1903 1995 93 0.995 0.338 0.826 3.994 0.239 0.566 13 021033 1903 1995 93 0.991 0.330 0.173 3.455 0.221 0.669 14 021035 1903 1995 93 0.993 0.268 0.201 4.273 0.189 0.613 15 021037 1903 1995 93 0.992 0.283 0.939 4.836 0.198 0.595 16 021041 1911 1995 85 0.978 0.388 0.326 2.840 0.278 0.517 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 86 0.992 0.348 0.489 3.503 0.239 0.608 STANDARD DEVIATION 7 0.005 0.053 0.381 0.767 0.032 0.100 MEDIAN (50TH QUANTILE) 87 0.992 0.337 0.366 3.585 0.238 0.614 INTERQUARTILE RANGE 6 0.005 0.063 0.672 1.144 0.037 0.112 MINIMUM VALUE 65 0.978 0.268 0.076 2.299 0.189 0.377 LOWER HINGE (25TH QUANTILE) 85 0.990 0.317 0.153 2.967 0.220 0.552 UPPER HINGE (75TH QUANTILE) 91 0.995 0.380 0.824 4.111 0.257 0.664 MAXIMUM VALUE 93 0.997 0.462 1.124 4.836 0.303 0.781 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.285 0.227 0.021 0.327 2.592 -0.212 0.830 MINIMUM CORRELATION: -0.212 SERIES 021016 AND 021021 71 YEARS MAXIMUM CORRELATION: 0.830 SERIES 021033 AND 021035 93 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1913. 1930. 1940. 1950. 1960. 1970. 1980. CORR 6. 91. 105. 120. 120. 120. 120. RBAR 0.919 0.311 0.285 0.177 0.269 0.332 0.292 SDEV 0.025 0.277 0.372 0.456 0.320 0.307 0.257 SERR 0.010 0.029 0.036 0.042 0.029 0.028 0.023 EPS 0.992 0.873 0.864 0.775 0.855 0.888 0.869 NSS 10.7 15.2 15.9 16.0 16.0 16.0 16.0 |======================== 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 1903 1995 93 0.957 0.233 0.040 3.576 0.160 0.676 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.454 0.233 0.043 37 56 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.19 0.70 1.01 1.04 1.73 98.84 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.08 0.56 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 0.669 0.421 0.254 0.048 -0.152 -0.188 -0.157 -0.241 -0.265 -0.231 PACF 0.669 -0.047 -0.017 -0.187 -0.183 0.066 0.056 -0.215 -0.082 -0.045 95% C.L. 0.207 0.285 0.311 0.320 0.320 0.323 0.328 0.331 0.339 0.347 |------------------ 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 0.456 0.675 |======================= 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 0.621 0.340 0.147 -0.031 -0.231 -0.262 -0.231 -0.305 -0.268 -0.215 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 0.621 2 0.666 -0.073 3 0.662 -0.035 -0.057 4 0.654 -0.040 0.031 -0.133 5 0.625 -0.033 0.022 0.012 -0.221 6 0.629 -0.033 0.022 0.012 -0.234 0.020 7 0.629 -0.036 0.022 0.013 -0.234 0.028 -0.014 8 0.626 -0.030 -0.032 0.016 -0.229 0.020 0.130 -0.229 9 0.626 -0.030 -0.032 0.016 -0.229 0.020 0.130 -0.229 0.000 10 0.626 -0.052 -0.019 0.018 -0.251 0.022 0.127 -0.232 0.061 -0.098 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) 627.49 584.25 585.76 587.46 587.80 585.13 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 587.09 589.07 586.05 588.05 589.15 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 0.621 R-SQUARED DUE TO POOLED AUTOREGRESSION: 38.52 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 162.65 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.621 0.385 0.239 0.148 0.092 0.057 0.035 0.022 0.014 0.0085 0.005 0.003 0.002 0.001 0.001 0.000 0.000 0.000 0.000 0.0001 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 021014 1 0.288 0.515 2 021015 1 0.442 0.662 3 021016 1 0.297 0.545 4 021017 1 0.160 0.382 5 021018 1 0.445 0.667 6 021019 1 0.361 0.588 7 021020 1 0.391 0.625 8 021021 1 0.665 0.791 9 021023 1 0.613 0.781 10 021025 1 0.400 0.633 11 021027 1 0.517 0.689 12 021031 1 0.349 0.571 13 021033 1 0.458 0.675 14 021035 1 0.387 0.622 15 021037 1 0.363 0.601 16 021041 1 0.293 0.524 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.402 0.617 STANDARD DEVIATION 0 0.125 0.101 MEDIAN 1 0.389 0.624 INTERQUARTILE RANGE 0 0.128 0.113 MINIMUM VALUE 1 0.160 0.382 LOWER HINGE 1 0.323 0.558 UPPER HINGE 1 0.451 0.671 MAXIMUM VALUE 1 0.665 0.791 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 021014 1931 1995 65 1.000 0.273 -0.228 2.947 0.338 0.068 2 021015 1911 1995 85 1.000 0.278 0.074 3.672 0.330 -0.062 3 021016 1925 1995 71 1.000 0.271 0.743 4.320 0.274 0.004 4 021017 1911 1995 85 1.002 0.350 0.489 4.490 0.342 -0.024 5 021018 1909 1995 87 1.000 0.249 0.188 3.478 0.292 -0.022 6 021019 1909 1995 87 1.000 0.252 0.147 4.093 0.273 0.082 7 021020 1909 1995 87 1.000 0.227 0.181 3.196 0.255 0.002 8 021021 1908 1995 88 1.000 0.268 0.667 4.368 0.272 0.245 9 021023 1908 1995 88 1.000 0.287 0.335 3.873 0.313 0.079 10 021025 1907 1995 89 1.000 0.284 0.687 3.517 0.318 -0.029 11 021027 1913 1995 83 1.000 0.251 0.314 3.649 0.263 0.198 12 021031 1903 1995 93 1.000 0.277 1.471 7.403 0.279 0.105 13 021033 1903 1995 93 1.000 0.242 0.730 5.136 0.268 0.044 14 021035 1903 1995 93 1.000 0.208 0.422 4.742 0.237 -0.007 15 021037 1903 1995 93 1.000 0.225 0.807 5.030 0.237 0.032 16 021041 1911 1995 85 1.000 0.329 0.699 4.519 0.329 0.077 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 86 1.000 0.267 0.483 4.277 0.289 0.050 STANDARD DEVIATION 7 0.001 0.037 0.396 1.049 0.035 0.083 MEDIAN (50TH QUANTILE) 87 1.000 0.269 0.455 4.206 0.277 0.038 INTERQUARTILE RANGE 6 0.000 0.035 0.530 1.048 0.058 0.095 MINIMUM VALUE 65 1.000 0.208 -0.228 2.947 0.237 -0.062 LOWER HINGE (25TH QUANTILE) 85 1.000 0.246 0.185 3.583 0.266 -0.014 UPPER HINGE (75TH QUANTILE) 91 1.000 0.281 0.715 4.631 0.323 0.081 MAXIMUM VALUE 93 1.002 0.350 1.471 7.403 0.342 0.245 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.288 0.180 0.016 0.549 2.746 -0.046 0.726 MINIMUM CORRELATION: -0.046 SERIES 021016 AND 021021 71 YEARS MAXIMUM CORRELATION: 0.726 SERIES 021031 AND 021033 93 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 88.02 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1913. 1930. 1940. 1950. 1960. 1970. 1980. CORR 6. 91. 105. 120. 120. 120. 120. RBAR 0.841 0.238 0.235 0.226 0.255 0.260 0.254 SDEV 0.057 0.262 0.265 0.285 0.276 0.252 0.196 SERR 0.023 0.027 0.026 0.026 0.025 0.023 0.018 EPS 0.983 0.826 0.830 0.823 0.845 0.849 0.845 NSS 10.7 15.2 15.9 16.0 16.0 16.0 16.0 |======================== 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 1903 1995 93 0.985 0.160 0.125 3.918 0.176 0.097 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.379 0.195 0.008 30 63 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.32 0.85 1.00 1.10 1.95 4.85 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.10 0.66 0.84 0.93 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 0.096 0.032 0.041 -0.031 -0.200 -0.144 0.113 -0.157 -0.091 -0.121 PACF 0.096 0.023 0.036 -0.039 -0.198 -0.114 0.157 -0.166 -0.081 -0.166 95% C.L. 0.207 0.209 0.209 0.210 0.210 0.218 0.222 0.225 0.229 0.231 |------------------ 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 -0.003 0.020 0.040 -0.016 -0.187 -0.139 0.145 -0.161 -0.066 -0.114 PACF -0.003 0.020 0.040 -0.016 -0.189 -0.148 0.158 -0.144 -0.079 -0.173 95% C.L. 0.207 0.207 0.207 0.208 0.208 0.215 0.219 0.223 0.228 0.229 |----------------- 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 0.000 -0.003 |========================= 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 1903 1995 93 0.983 0.204 0.107 3.718 0.148 0.622 |------------ 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 0.615 0.370 0.191 0.006 -0.165 -0.195 -0.130 -0.231 -0.228 -0.210 PACF 0.615 -0.013 -0.051 -0.144 -0.163 0.019 0.087 -0.248 -0.038 -0.073 95% C.L. 0.207 0.275 0.296 0.301 0.301 0.305 0.310 0.312 0.320 0.327 |------------------- 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 0.384 0.620 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.19 MINUTES