RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM041W.rwl.conv LOG FILE PROCESSED: GERM041W.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: 016 1 Schluchsee (D), EU-Pr. WIDTH_RING PCAB - 016 2 Germany Norway spruce 1200 4748-805 1932 1992 - 016 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 016011 1932 1992 61 3.057 1.154 0.257 2.290 0.199 0.751 2 016013 1933 1992 60 3.008 1.041 0.233 2.929 0.200 0.693 3 016016 1932 1992 61 2.957 0.918 -0.194 2.497 0.175 0.732 4 016021 1937 1992 56 3.220 1.314 0.494 2.301 0.200 0.858 5 016025 1938 1992 55 3.272 1.172 0.598 3.159 0.214 0.723 6 016027 1937 1992 56 3.269 1.173 0.139 2.199 0.166 0.872 7 016031 1936 1992 57 3.690 1.487 0.105 2.217 0.180 0.854 8 016033 1937 1992 56 4.124 1.303 0.374 2.960 0.165 0.799 9 016034 1937 1992 56 3.098 1.296 0.182 1.882 0.186 0.865 10 016041 1935 1992 58 3.171 1.549 0.230 1.698 0.156 0.911 11 016047 1934 1992 59 3.151 1.160 0.209 1.908 0.183 0.799 12 016054 1934 1992 59 2.302 0.942 1.228 3.494 0.199 0.813 13 016056 1935 1992 58 2.474 1.202 0.827 2.978 0.189 0.855 NUMBER OF SERIES READ IN: 13 FROM 1932 TO 1992 61 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 3.138 1.209 0.360 2.501 0.185 0.810 STANDARD DEVIATION 2 0.458 0.185 0.361 0.553 0.017 0.067 MEDIAN (50TH QUANTILE) 58 3.151 1.173 0.233 2.301 0.186 0.813 INTERQUARTILE RANGE 3 0.261 0.149 0.312 0.760 0.025 0.107 MINIMUM VALUE 55 2.302 0.918 -0.194 1.698 0.156 0.693 LOWER HINGE (25TH QUANTILE) 56 3.008 1.154 0.182 2.199 0.175 0.751 UPPER HINGE (75TH QUANTILE) 59 3.269 1.303 0.494 2.960 0.199 0.858 MAXIMUM VALUE 61 4.124 1.549 1.228 3.494 0.214 0.911 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.693 0.177 0.020 -1.551 6.179 0.084 0.932 MINIMUM CORRELATION: 0.084 SERIES 016027 AND 016054 56 YEARS MAXIMUM CORRELATION: 0.932 SERIES 016021 AND 016027 56 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 92.88 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1942. 1960. 1970. 1980. CORR 1. 78. 78. 78. RBAR 0.689 0.598 0.610 0.712 SDEV 0.000 0.197 0.244 0.205 SERR 0.000 0.022 0.028 0.023 EPS 0.960 0.951 0.953 0.970 NSS 10.9 13.0 13.0 13.0 |======================== 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 1932 1992 61 3.061 1.092 0.089 2.199 0.151 0.838 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.700 0.211 0.117 11 50 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.50 1.20 1.01 1.27 2.47 4.79 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.90 0.06 0.46 0.87 0.93 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 58. 3. 55. 56. 59. 61. |----------- 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 0.824 0.707 0.620 0.523 0.457 0.405 0.344 0.334 0.298 0.267 PACF 0.824 0.087 0.053 -0.055 0.038 0.024 -0.033 0.117 -0.046 0.011 95% C.L. 0.256 0.393 0.469 0.520 0.554 0.578 0.596 0.609 0.621 0.630 |------------------ 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 0.735 0.855 |================== 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 016011 3 0.00000000 0.00000000 -0.03693919 4.20232773 2 016013 3 0.00000000 0.00000000 -0.01991831 3.61550856 3 016016 3 0.00000000 0.00000000 -0.01757007 3.50139356 4 016021 3 0.00000000 0.00000000 -0.03950342 4.34566879 5 016025 3 0.00000000 0.00000000 -0.03782612 4.33113146 6 016027 3 0.00000000 0.00000000 -0.03220540 4.18731833 7 016031 3 0.00000000 0.00000000 -0.06571428 5.59606504 8 016033 3 0.00000000 0.00000000 -0.04279562 5.34396124 9 016034 3 0.00000000 0.00000000 -0.06498735 4.94981813 10 016041 3 0.00000000 0.00000000 -0.07852872 5.48711443 11 016047 3 0.00000000 0.00000000 -0.04984804 4.64611912 12 016054 1 2.46208906 0.04369869 0.00000000 1.43872404 13 016056 3 0.00000000 0.00000000 -0.05824972 4.19284916 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 016011 1932 1992 61 0.994 0.285 -0.029 3.336 0.195 0.598 2 016013 1933 1992 60 0.999 0.315 -0.139 2.703 0.196 0.646 3 016016 1932 1992 61 0.998 0.280 -0.469 3.106 0.173 0.666 4 016021 1937 1992 56 0.993 0.343 0.530 2.233 0.197 0.775 5 016025 1938 1992 55 0.996 0.294 0.527 3.122 0.210 0.606 6 016027 1937 1992 56 0.996 0.318 0.130 2.027 0.165 0.794 7 016031 1936 1992 57 0.989 0.262 0.512 3.169 0.178 0.639 8 016033 1937 1992 56 0.995 0.263 0.720 3.023 0.162 0.696 9 016034 1937 1992 56 1.000 0.250 0.293 2.551 0.181 0.614 10 016041 1935 1992 58 1.000 0.241 0.344 3.094 0.153 0.637 11 016047 1934 1992 59 0.996 0.235 0.123 3.305 0.180 0.499 12 016054 1934 1992 59 1.000 0.292 1.158 5.545 0.196 0.609 13 016056 1935 1992 58 1.004 0.241 0.818 5.268 0.187 0.423 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 0.997 0.278 0.347 3.268 0.182 0.631 STANDARD DEVIATION 2 0.004 0.033 0.434 1.032 0.016 0.098 MEDIAN (50TH QUANTILE) 58 0.996 0.280 0.344 3.106 0.181 0.637 INTERQUARTILE RANGE 3 0.005 0.044 0.407 0.602 0.023 0.059 MINIMUM VALUE 55 0.989 0.235 -0.469 2.027 0.153 0.423 LOWER HINGE (25TH QUANTILE) 56 0.995 0.250 0.123 2.703 0.173 0.606 UPPER HINGE (75TH QUANTILE) 59 1.000 0.294 0.530 3.305 0.196 0.666 MAXIMUM VALUE 61 1.004 0.343 1.158 5.545 0.210 0.794 |------------------------ 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 016011 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 016013 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 016016 -67 40 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 016021 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 016025 -67 36 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 016027 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 016031 -67 38 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 016033 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 016034 -67 37 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 016041 -67 38 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 016047 -67 39 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 016054 -67 39 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 13 016056 -67 38 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 016011 1932 1992 61 0.993 0.232 0.133 2.913 0.195 0.429 2 016013 1933 1992 60 0.996 0.302 0.656 3.581 0.194 0.616 3 016016 1932 1992 61 0.995 0.227 0.198 3.423 0.173 0.475 4 016021 1937 1992 56 0.990 0.213 0.255 2.864 0.191 0.447 5 016025 1938 1992 55 0.994 0.222 0.592 3.130 0.207 0.321 6 016027 1937 1992 56 0.989 0.202 -0.305 2.773 0.164 0.527 7 016031 1936 1992 57 0.997 0.209 0.570 3.041 0.175 0.465 8 016033 1937 1992 56 0.998 0.173 0.377 3.058 0.159 0.377 9 016034 1937 1992 56 0.996 0.218 0.620 3.508 0.179 0.518 10 016041 1935 1992 58 0.993 0.168 0.033 3.563 0.150 0.353 11 016047 1934 1992 59 0.997 0.213 0.085 3.058 0.180 0.423 12 016054 1934 1992 59 0.996 0.228 0.062 3.598 0.195 0.423 13 016056 1935 1992 58 0.998 0.222 0.687 5.413 0.185 0.376 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 0.995 0.218 0.305 3.379 0.181 0.442 STANDARD DEVIATION 2 0.003 0.032 0.306 0.678 0.016 0.080 MEDIAN (50TH QUANTILE) 58 0.996 0.218 0.255 3.130 0.180 0.429 INTERQUARTILE RANGE 3 0.004 0.018 0.507 0.523 0.021 0.098 MINIMUM VALUE 55 0.989 0.168 -0.305 2.773 0.150 0.321 LOWER HINGE (25TH QUANTILE) 56 0.993 0.209 0.085 3.041 0.173 0.377 UPPER HINGE (75TH QUANTILE) 59 0.997 0.227 0.592 3.563 0.194 0.475 MAXIMUM VALUE 61 0.998 0.302 0.687 5.413 0.207 0.616 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.559 0.122 0.014 0.119 2.653 0.311 0.820 MINIMUM CORRELATION: 0.311 SERIES 016034 AND 016047 56 YEARS MAXIMUM CORRELATION: 0.820 SERIES 016025 AND 016027 55 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 92.88 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1942. 1960. 1970. 1980. CORR 1. 78. 78. 78. RBAR 0.612 0.541 0.508 0.628 SDEV 0.000 0.178 0.217 0.202 SERR 0.000 0.020 0.025 0.023 EPS 0.945 0.939 0.931 0.956 NSS 10.9 13.0 13.0 13.0 |======================== 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 1932 1992 61 0.971 0.191 -0.134 3.322 0.152 0.526 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.270 0.080 0.058 18 43 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.38 1.02 1.10 1.48 2.23 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.76 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 0.518 0.229 0.042 -0.151 -0.260 -0.233 -0.244 -0.145 -0.117 -0.042 PACF 0.518 -0.053 -0.076 -0.181 -0.130 -0.015 -0.126 0.022 -0.114 0.006 95% C.L. 0.256 0.317 0.328 0.328 0.333 0.346 0.356 0.367 0.371 0.373 |------------------ 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 0.293 0.540 |======================= 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 0.426 0.114 -0.051 -0.116 -0.192 -0.198 -0.178 -0.142 -0.182 -0.095 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 0.426 2 0.461 -0.082 3 0.454 -0.043 -0.085 4 0.449 -0.046 -0.055 -0.064 5 0.440 -0.053 -0.062 -0.004 -0.135 6 0.429 -0.054 -0.067 -0.008 -0.099 -0.082 7 0.422 -0.062 -0.067 -0.014 -0.103 -0.047 -0.083 8 0.416 -0.065 -0.075 -0.015 -0.108 -0.051 -0.051 -0.075 9 0.404 -0.074 -0.084 -0.033 -0.111 -0.064 -0.062 -0.005 -0.167 10 0.401 -0.074 -0.085 -0.034 -0.113 -0.064 -0.064 -0.007 -0.160 -0.018 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) 339.82 329.58 331.17 332.73 334.48 335.36 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 336.95 338.53 340.18 340.45 342.43 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 0.426 R-SQUARED DUE TO POOLED AUTOREGRESSION: 18.17 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 122.21 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.426 0.182 0.077 0.033 0.014 0.006 0.003 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 016011 1 0.226 0.447 2 016013 1 0.469 0.625 3 016016 1 0.251 0.495 4 016021 1 0.204 0.451 5 016025 1 0.108 0.325 6 016027 1 0.317 0.551 7 016031 1 0.294 0.487 8 016033 1 0.143 0.378 9 016034 1 0.277 0.521 10 016041 1 0.141 0.366 11 016047 1 0.255 0.434 12 016054 1 0.233 0.452 13 016056 1 0.183 0.406 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.239 0.457 STANDARD DEVIATION 0 0.093 0.081 MEDIAN 1 0.233 0.451 INTERQUARTILE RANGE 0 0.094 0.089 MINIMUM VALUE 1 0.108 0.325 LOWER HINGE 1 0.183 0.406 UPPER HINGE 1 0.277 0.495 MAXIMUM VALUE 1 0.469 0.625 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 016011 1932 1992 61 1.000 0.206 0.325 2.554 0.227 0.060 2 016013 1933 1992 60 1.000 0.234 0.794 4.139 0.227 0.211 3 016016 1932 1992 61 1.000 0.195 0.700 3.933 0.212 0.025 4 016021 1937 1992 56 1.000 0.191 0.359 3.168 0.227 -0.015 5 016025 1938 1992 55 1.000 0.210 0.566 3.227 0.246 -0.020 6 016027 1937 1992 56 1.000 0.168 -0.004 3.100 0.204 -0.058 7 016031 1936 1992 57 1.000 0.181 0.529 3.039 0.191 0.114 8 016033 1937 1992 56 1.000 0.160 0.468 3.144 0.186 0.012 9 016034 1937 1992 56 1.000 0.186 0.691 3.628 0.210 0.043 10 016041 1935 1992 58 1.000 0.155 -0.061 3.651 0.172 0.020 11 016047 1934 1992 59 1.000 0.191 0.134 3.005 0.198 0.111 12 016054 1934 1992 59 1.000 0.201 0.085 2.914 0.222 0.060 13 016056 1935 1992 58 1.000 0.201 0.414 4.063 0.220 0.030 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 1.000 0.191 0.385 3.351 0.211 0.046 STANDARD DEVIATION 2 0.000 0.021 0.278 0.486 0.020 0.069 MEDIAN (50TH QUANTILE) 58 1.000 0.191 0.414 3.168 0.212 0.030 INTERQUARTILE RANGE 3 0.000 0.020 0.433 0.612 0.029 0.048 MINIMUM VALUE 55 1.000 0.155 -0.061 2.554 0.172 -0.058 LOWER HINGE (25TH QUANTILE) 56 1.000 0.181 0.134 3.039 0.198 0.012 UPPER HINGE (75TH QUANTILE) 59 1.000 0.201 0.566 3.651 0.227 0.060 MAXIMUM VALUE 61 1.000 0.234 0.794 4.139 0.246 0.211 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.569 0.104 0.012 0.345 3.451 0.316 0.855 MINIMUM CORRELATION: 0.316 SERIES 016011 AND 016056 58 YEARS MAXIMUM CORRELATION: 0.855 SERIES 016025 AND 016027 55 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 92.88 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1942. 1960. 1970. 1980. CORR 1. 78. 78. 78. RBAR 0.518 0.590 0.552 0.608 SDEV 0.000 0.142 0.172 0.163 SERR 0.000 0.016 0.019 0.018 EPS 0.922 0.949 0.941 0.953 NSS 10.9 13.0 13.0 13.0 |======================== 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 1932 1992 61 0.986 0.159 0.116 2.992 0.178 0.117 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.536 0.173 -0.056 14 47 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.56 1.01 1.01 1.57 101.10 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.91 0.06 0.81 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 0.115 0.026 0.003 -0.114 -0.190 -0.089 -0.136 -0.011 -0.100 0.001 PACF 0.115 0.013 -0.002 -0.116 -0.168 -0.050 -0.121 0.005 -0.143 -0.026 95% C.L. 0.256 0.259 0.260 0.260 0.263 0.272 0.274 0.278 0.278 0.280 |------------------ 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 -0.006 0.011 0.013 -0.093 -0.169 -0.052 -0.127 0.017 -0.103 0.013 PACF -0.006 0.011 0.014 -0.093 -0.171 -0.057 -0.128 0.007 -0.141 -0.035 95% C.L. 0.256 0.256 0.256 0.256 0.258 0.265 0.266 0.270 0.270 0.273 |----------------- 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 -0.006 |========================= 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 1932 1992 61 0.983 0.177 -0.137 3.303 0.150 0.431 |------------ 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 0.424 0.178 0.024 -0.150 -0.246 -0.195 -0.200 -0.102 -0.112 -0.035 PACF 0.424 -0.002 -0.062 -0.169 -0.143 -0.019 -0.103 0.007 -0.131 0.000 95% C.L. 0.256 0.299 0.306 0.306 0.310 0.323 0.331 0.338 0.340 0.343 |------------------- 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 0.196 0.442 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.08 MINUTES