RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM043L.rwl.conv LOG FILE PROCESSED: GERM043L.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: 022 1 Kaiserstuhl (D), EU-Pr. WIDTH_LATE ABAL - 022 2 Germany silver fir, European fir 440 4805-741 1926 1995 - 022 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 022011 1927 1995 69 0.801 0.388 0.804 3.896 0.482 0.294 2 022013 1928 1995 68 0.832 0.366 0.572 3.482 0.416 0.344 3 022015 1928 1995 68 0.848 0.368 0.488 2.718 0.435 0.261 4 022017 1928 1995 68 0.781 0.356 0.990 4.772 0.447 0.098 5 022021 1929 1995 67 1.118 0.685 1.115 4.001 0.465 0.390 6 022023 1935 1995 61 1.405 0.744 1.338 5.050 0.521 0.235 7 022025 1929 1995 67 1.041 0.480 0.523 3.382 0.459 0.229 8 022027 1929 1995 67 0.889 0.481 0.846 3.639 0.474 0.331 9 022031 1927 1995 69 0.923 0.468 0.557 2.359 0.522 0.346 10 022033 1929 1995 67 0.723 0.383 0.386 2.411 0.483 0.429 11 022037 1926 1995 70 0.658 0.365 0.465 2.649 0.528 0.362 12 022043 1928 1995 68 0.799 0.370 1.351 6.553 0.410 0.354 13 022047 1928 1995 68 0.691 0.311 0.537 3.166 0.428 0.306 14 022053 1931 1995 65 1.084 0.625 1.234 5.064 0.582 0.370 15 022055 1929 1995 67 0.877 0.469 1.532 6.209 0.466 0.419 16 022057 1928 1995 68 0.623 0.309 0.598 3.124 0.480 0.220 NUMBER OF SERIES READ IN: 16 FROM 1926 TO 1995 70 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 0.881 0.448 0.834 3.905 0.475 0.312 STANDARD DEVIATION 2 0.201 0.131 0.375 1.291 0.046 0.086 MEDIAN (50TH QUANTILE) 68 0.840 0.385 0.701 3.561 0.470 0.337 INTERQUARTILE RANGE 1 0.229 0.115 0.644 1.990 0.061 0.118 MINIMUM VALUE 61 0.623 0.309 0.386 2.359 0.410 0.098 LOWER HINGE (25TH QUANTILE) 67 0.752 0.366 0.530 2.921 0.441 0.248 UPPER HINGE (75TH QUANTILE) 68 0.982 0.481 1.174 4.911 0.502 0.366 MAXIMUM VALUE 70 1.405 0.744 1.532 6.553 0.582 0.429 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.370 0.185 0.017 0.033 2.897 -0.133 0.804 MINIMUM CORRELATION: -0.133 SERIES 022013 AND 022037 68 YEARS MAXIMUM CORRELATION: 0.804 SERIES 022033 AND 022037 67 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.77 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1950. 1960. 1970. 1980. CORR 120. 120. 120. 120. RBAR 0.462 0.544 0.504 0.415 SDEV 0.222 0.184 0.212 0.226 SERR 0.020 0.017 0.019 0.021 EPS 0.932 0.950 0.942 0.919 NSS 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 1926 1995 70 0.814 0.285 -0.108 2.289 0.349 0.281 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.612 0.377 0.029 29 41 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.65 1.66 1.04 1.21 2.87 5.34 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.85 0.92 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 68. 1. 61. 67. 68. 70. |----------- 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 0.277 0.251 0.251 0.023 0.049 -0.148 -0.090 -0.267 -0.144 0.055 PACF 0.277 0.189 0.160 -0.125 -0.012 -0.205 -0.001 -0.234 0.070 0.197 95% C.L. 0.239 0.257 0.270 0.283 0.284 0.284 0.288 0.290 0.304 0.308 |------------------ 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 3 0.155 0.193 0.156 0.179 |================== 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 022011 3 0.00000000 0.00000000 -0.00140811 0.85000855 2 022013 3 0.00000000 0.00000000 0.00961427 0.49992537 3 022015 3 0.00000000 0.00000000 0.00504733 0.67366111 4 022017 3 0.00000000 0.00000000 0.00520441 0.60162425 5 022021 3 0.00000000 0.00000000 0.00279751 1.02279508 6 022023 3 0.00000000 0.00000000 0.01213009 1.02904916 7 022025 3 0.00000000 0.00000000 0.00628262 0.82713705 8 022027 3 0.00000000 0.00000000 -0.00287972 0.98686564 9 022031 3 0.00000000 0.00000000 -0.00885787 1.23277915 10 022033 3 0.00000000 0.00000000 -0.00880517 1.02280867 11 022037 3 0.00000000 0.00000000 -0.00783116 0.93643481 12 022043 3 0.00000000 0.00000000 0.00568195 0.60250217 13 022047 3 0.00000000 0.00000000 0.00294900 0.58899474 14 022053 3 0.00000000 0.00000000 0.00860402 0.80052882 15 022055 3 0.00000000 0.00000000 0.00333027 0.76363635 16 022057 3 0.00000000 0.00000000 -0.00081326 0.65143985 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 022011 1927 1995 69 1.000 0.489 0.923 4.264 0.475 0.284 2 022013 1928 1995 68 0.996 0.380 0.442 2.965 0.410 0.159 3 022015 1928 1995 68 0.999 0.422 0.449 2.491 0.428 0.253 4 022017 1928 1995 68 0.998 0.427 0.702 3.518 0.440 0.022 5 022021 1929 1995 67 0.999 0.603 1.059 3.974 0.458 0.366 6 022023 1935 1995 61 0.997 0.501 1.306 4.749 0.511 0.140 7 022025 1929 1995 67 0.999 0.442 0.476 3.619 0.451 0.157 8 022027 1929 1995 67 1.000 0.539 0.871 3.696 0.467 0.328 9 022031 1927 1995 69 0.995 0.460 0.459 2.392 0.516 0.191 10 022033 1929 1995 67 1.000 0.497 0.497 2.624 0.475 0.318 11 022037 1926 1995 70 1.002 0.536 0.786 3.602 0.520 0.310 12 022043 1928 1995 68 0.997 0.439 1.208 6.120 0.404 0.308 13 022047 1928 1995 68 0.999 0.453 0.813 4.176 0.421 0.292 14 022053 1931 1995 65 0.999 0.535 0.726 3.262 0.572 0.258 15 022055 1929 1995 67 0.999 0.529 1.410 5.408 0.459 0.396 16 022057 1928 1995 68 1.000 0.498 0.664 3.389 0.473 0.213 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 0.999 0.484 0.799 3.766 0.467 0.250 STANDARD DEVIATION 2 0.002 0.057 0.314 1.021 0.045 0.097 MEDIAN (50TH QUANTILE) 68 0.999 0.493 0.756 3.610 0.463 0.271 INTERQUARTILE RANGE 1 0.002 0.092 0.504 1.107 0.059 0.139 MINIMUM VALUE 61 0.995 0.380 0.442 2.392 0.404 0.022 LOWER HINGE (25TH QUANTILE) 67 0.998 0.440 0.486 3.113 0.434 0.175 UPPER HINGE (75TH QUANTILE) 68 1.000 0.532 0.991 4.220 0.493 0.314 MAXIMUM VALUE 70 1.002 0.603 1.410 6.120 0.572 0.396 |------------------------ 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 022011 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 022013 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 022015 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 022017 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 022021 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 022023 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 022025 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 022027 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 022031 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 022033 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 022037 -67 46 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 022043 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 022047 -67 45 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 14 022053 -67 43 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 15 022055 -67 44 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 16 022057 -67 45 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 022011 1927 1995 69 0.990 0.445 0.709 3.943 0.471 0.200 2 022013 1928 1995 68 0.995 0.362 0.622 3.726 0.408 0.106 3 022015 1928 1995 68 0.991 0.395 0.562 2.520 0.425 0.178 4 022017 1928 1995 68 0.991 0.385 0.629 3.873 0.439 -0.085 5 022021 1929 1995 67 0.973 0.493 1.067 3.898 0.452 0.245 6 022023 1935 1995 61 0.994 0.443 0.994 4.617 0.509 0.034 7 022025 1929 1995 67 0.996 0.417 0.233 3.262 0.450 0.134 8 022027 1929 1995 67 0.990 0.494 0.766 3.577 0.466 0.295 9 022031 1927 1995 69 0.994 0.400 0.135 2.457 0.516 0.007 10 022033 1929 1995 67 0.982 0.423 0.249 2.465 0.475 0.144 11 022037 1926 1995 70 0.981 0.444 0.282 2.410 0.519 0.089 12 022043 1928 1995 68 0.992 0.395 0.952 4.520 0.403 0.208 13 022047 1928 1995 68 0.988 0.411 0.637 3.429 0.417 0.218 14 022053 1931 1995 65 0.992 0.512 0.655 3.107 0.572 0.220 15 022055 1929 1995 67 0.989 0.443 0.962 4.048 0.457 0.249 16 022057 1928 1995 68 0.991 0.471 0.800 4.001 0.472 0.163 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 0.989 0.433 0.641 3.491 0.466 0.150 STANDARD DEVIATION 2 0.006 0.043 0.290 0.726 0.046 0.101 MEDIAN (50TH QUANTILE) 68 0.991 0.433 0.646 3.652 0.461 0.170 INTERQUARTILE RANGE 1 0.005 0.061 0.455 1.158 0.060 0.122 MINIMUM VALUE 61 0.973 0.362 0.135 2.410 0.403 -0.085 LOWER HINGE (25TH QUANTILE) 67 0.988 0.397 0.422 2.814 0.432 0.097 UPPER HINGE (75TH QUANTILE) 68 0.993 0.458 0.876 3.972 0.492 0.219 MAXIMUM VALUE 70 0.996 0.512 1.067 4.617 0.572 0.295 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.421 0.139 0.013 0.522 3.325 0.123 0.866 MINIMUM CORRELATION: 0.123 SERIES 022011 AND 022017 68 YEARS MAXIMUM CORRELATION: 0.866 SERIES 022011 AND 022033 67 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.77 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1950. 1960. 1970. 1980. CORR 120. 120. 120. 120. RBAR 0.476 0.574 0.532 0.430 SDEV 0.225 0.186 0.192 0.209 SERR 0.021 0.017 0.018 0.019 EPS 0.936 0.956 0.948 0.924 NSS 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 1926 1995 70 0.963 0.297 -0.191 2.537 0.345 0.145 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.590 0.268 0.049 18 52 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.17 0.57 1.03 1.06 1.63 4.55 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.06 0.00 0.85 0.91 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 0.143 0.074 0.136 -0.092 -0.118 -0.210 -0.200 -0.343 -0.211 0.091 PACF 0.143 0.055 0.121 -0.135 -0.107 -0.197 -0.120 -0.304 -0.141 0.141 95% C.L. 0.239 0.244 0.245 0.249 0.251 0.255 0.264 0.273 0.296 0.305 |------------------ 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 0 0.000 |======================= 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 0.123 0.044 0.113 -0.113 -0.138 -0.213 -0.220 -0.323 -0.202 0.084 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 0.123 2 0.120 0.029 3 0.117 0.016 0.105 4 0.132 0.019 0.122 -0.144 5 0.115 0.033 0.124 -0.128 -0.119 6 0.091 0.008 0.149 -0.122 -0.096 -0.199 7 0.060 -0.007 0.130 -0.098 -0.095 -0.185 -0.156 8 0.013 -0.063 0.102 -0.128 -0.055 -0.187 -0.138 -0.303 9 -0.044 -0.089 0.067 -0.138 -0.079 -0.168 -0.150 -0.301 -0.187 10 -0.031 -0.068 0.077 -0.127 -0.073 -0.159 -0.154 -0.294 -0.184 0.071 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) 511.54 512.47 514.41 515.63 516.16 517.17 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 516.34 516.61 511.87 511.38 513.03 SELECTED AUTOREGRESSION ORDER: 9 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 -0.044 -0.089 0.067 -0.138 -0.079 -0.168 -0.150 -0.301 -0.187 R-SQUARED DUE TO POOLED AUTOREGRESSION: 22.85 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 129.62 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 9) PROCESS OUT TO ORDER 50: 1.0000 -0.044 -0.087 0.074 -0.137 -0.079 -0.132 -0.142 -0.254 -0.136 0.0900 0.049 0.088 0.130 0.106 0.104 0.086 0.036 -0.051 -0.085 -.0826 -0.093 -0.076 -0.048 -0.021 0.015 0.051 0.071 0.067 0.057 0.0391 0.013 -0.011 -0.031 -0.047 -0.051 -0.044 -0.029 -0.012 0.007 0.0222 0.032 0.036 0.033 0.023 0.010 -0.004 -0.015 -0.023 -0.026 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 022011 9 0.309 0.109 -0.027 -0.059 0.078 -0.228 -0.229 0.043 -0.354 -0.046 2 022013 9 0.167 0.055 0.079 -0.129 0.109 -0.098 -0.207 -0.005 -0.121 -0.192 3 022015 9 0.219 0.145 -0.154 0.122 0.048 -0.181 -0.270 -0.074 -0.040 0.048 4 022017 9 0.301 -0.140 0.392 0.077 -0.176 -0.128 -0.139 -0.165 0.040 0.226 5 022021 9 0.271 0.151 -0.034 0.166 -0.059 0.061 0.042 -0.007 -0.364 -0.167 6 022023 9 0.161 -0.028 -0.044 0.235 -0.045 -0.073 -0.284 -0.100 -0.089 -0.019 7 022025 9 0.360 -0.037 0.084 0.081 -0.481 -0.197 -0.095 0.025 -0.337 -0.214 8 022027 9 0.335 0.093 0.096 0.082 -0.275 -0.003 -0.076 -0.179 -0.287 -0.047 9 022031 9 0.114 -0.059 -0.130 -0.037 -0.161 -0.055 -0.132 -0.088 -0.240 -0.159 10 022033 9 0.215 0.055 0.006 0.039 -0.015 -0.022 -0.175 0.003 -0.323 -0.120 11 022037 9 0.118 0.043 0.055 -0.029 -0.123 0.087 0.024 -0.166 -0.145 -0.140 12 022043 9 0.290 0.188 -0.138 -0.103 0.322 -0.162 -0.015 -0.142 -0.250 -0.135 13 022047 9 0.114 0.230 -0.018 0.104 -0.115 -0.017 -0.194 0.077 0.053 -0.068 14 022053 9 0.216 0.107 0.049 -0.023 -0.173 0.040 -0.008 -0.285 -0.163 -0.102 15 022055 9 0.233 0.181 0.271 -0.002 -0.325 -0.008 0.078 -0.050 -0.083 -0.096 16 022057 9 0.216 0.059 0.031 0.064 -0.166 0.036 -0.046 -0.238 -0.280 0.018 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 9 0.227 0.072 0.032 0.037 -0.097 -0.059 -0.108 -0.085 -0.186 -0.076 STANDARD DEVIATION 0 0.079 0.100 0.142 0.098 0.189 0.098 0.114 0.105 0.137 0.109 MEDIAN 9 0.217 0.076 0.018 0.052 -0.119 -0.039 -0.114 -0.081 -0.201 -0.099 INTERQUARTILE RANGE 0 0.132 0.140 0.120 0.126 0.191 0.162 0.189 0.165 0.219 0.117 MINIMUM VALUE 9 0.114 -0.140 -0.154 -0.129 -0.481 -0.228 -0.284 -0.285 -0.364 -0.214 LOWER HINGE 9 0.164 0.008 -0.039 -0.033 -0.175 -0.145 -0.201 -0.166 -0.305 -0.150 UPPER HINGE 9 0.296 0.148 0.082 0.093 0.017 0.017 -0.012 -0.001 -0.086 -0.032 MAXIMUM VALUE 9 0.360 0.230 0.392 0.235 0.322 0.087 0.078 0.077 0.053 0.226 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 022011 1927 1995 69 1.000 0.373 0.612 3.667 0.437 0.000 2 022013 1928 1995 68 1.000 0.332 0.189 3.336 0.416 0.017 3 022015 1928 1995 68 1.000 0.349 0.298 2.677 0.420 -0.017 4 022017 1928 1995 68 1.000 0.329 0.343 3.021 0.362 0.033 5 022021 1929 1995 67 1.000 0.419 0.567 2.836 0.456 -0.024 6 022023 1935 1995 61 1.000 0.407 1.056 4.446 0.470 0.000 7 022025 1929 1995 67 1.000 0.331 -0.056 2.895 0.415 0.009 8 022027 1929 1995 67 1.000 0.402 0.562 3.782 0.456 0.000 9 022031 1927 1995 69 1.000 0.375 0.143 2.558 0.471 -0.012 10 022033 1929 1995 67 1.000 0.377 0.195 3.187 0.431 0.019 11 022037 1926 1995 70 1.000 0.418 0.318 2.372 0.477 0.013 12 022043 1928 1995 68 1.000 0.335 0.706 4.315 0.398 -0.036 13 022047 1928 1995 68 1.000 0.387 0.809 4.201 0.445 -0.007 14 022053 1931 1995 65 1.000 0.451 0.339 2.302 0.562 -0.010 15 022055 1929 1995 67 1.000 0.395 0.624 3.160 0.463 -0.021 16 022057 1928 1995 68 1.000 0.419 0.871 4.456 0.469 -0.006 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.381 0.474 3.326 0.447 -0.003 STANDARD DEVIATION 2 0.000 0.038 0.301 0.737 0.044 0.018 MEDIAN (50TH QUANTILE) 68 1.000 0.382 0.452 3.173 0.450 -0.003 INTERQUARTILE RANGE 1 0.000 0.071 0.419 1.235 0.052 0.026 MINIMUM VALUE 61 1.000 0.329 -0.056 2.302 0.362 -0.036 LOWER HINGE (25TH QUANTILE) 67 1.000 0.342 0.246 2.757 0.418 -0.015 UPPER HINGE (75TH QUANTILE) 68 1.000 0.413 0.665 3.992 0.470 0.011 MAXIMUM VALUE 70 1.000 0.451 1.056 4.456 0.562 0.033 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.353 0.165 0.015 0.404 2.949 -0.040 0.816 MINIMUM CORRELATION: -0.040 SERIES 022011 AND 022017 68 YEARS MAXIMUM CORRELATION: 0.816 SERIES 022011 AND 022033 67 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 94.77 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1950. 1960. 1970. 1980. CORR 120. 120. 120. 120. RBAR 0.441 0.532 0.433 0.331 SDEV 0.240 0.207 0.246 0.223 SERR 0.022 0.019 0.022 0.020 EPS 0.927 0.948 0.924 0.888 NSS 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 1926 1995 70 0.982 0.244 0.003 2.624 0.294 -0.054 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.410 0.186 0.116 11 59 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.27 0.14 1.02 1.14 1.28 1.52 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.00 0.86 0.92 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.053 -0.019 0.117 -0.018 -0.040 -0.039 -0.076 -0.135 -0.096 0.086 PACF -0.053 -0.022 0.115 -0.007 -0.038 -0.058 -0.081 -0.139 -0.110 0.086 95% C.L. 0.239 0.240 0.240 0.243 0.243 0.243 0.244 0.245 0.249 0.251 |------------------ 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 0.005 0.022 0.032 0.008 -0.021 -0.038 -0.057 -0.027 -0.014 0.079 PACF 0.005 0.022 0.031 0.007 -0.022 -0.039 -0.056 -0.024 -0.009 0.085 95% C.L. 0.239 0.239 0.239 0.239 0.239 0.240 0.240 0.241 0.241 0.241 |----------------- 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 9 0.016 -0.001 0.020 0.033 0.011 -0.019 -0.039 -0.059 -0.026 -0.011 |========================= 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 1926 1995 70 0.979 0.269 -0.214 2.565 0.300 0.113 |------------ 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 0.111 0.019 0.084 -0.119 -0.120 -0.185 -0.170 -0.287 -0.152 0.154 PACF 0.111 0.007 0.082 -0.140 -0.095 -0.174 -0.119 -0.284 -0.138 0.136 95% C.L. 0.239 0.242 0.242 0.244 0.247 0.250 0.258 0.264 0.282 0.286 |------------------- 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 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.18 MINUTES