RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM043T.rwl.conv LOG FILE PROCESSED: GERM043T.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. DENSITY_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 7.319 0.674 0.353 2.454 0.092 0.195 2 022013 1928 1995 68 7.269 0.574 0.332 2.747 0.095 -0.146 3 022015 1928 1995 68 7.038 0.611 0.518 3.224 0.108 -0.139 4 022017 1928 1995 68 7.249 0.812 -0.228 2.959 0.096 0.456 5 022021 1929 1995 67 6.907 0.810 0.082 2.780 0.122 0.101 6 022023 1935 1995 61 6.834 0.781 0.686 2.805 0.124 -0.014 7 022025 1929 1995 67 6.840 0.755 0.807 3.492 0.118 -0.029 8 022027 1929 1995 67 6.981 0.777 0.359 2.956 0.126 -0.037 9 022031 1927 1995 69 7.474 0.638 0.076 2.136 0.091 0.107 10 022033 1929 1995 67 7.203 0.648 0.371 2.720 0.107 -0.006 11 022037 1926 1995 70 7.586 0.581 0.664 2.721 0.085 0.077 12 022043 1928 1995 68 7.223 0.744 0.924 4.360 0.113 -0.020 13 022047 1928 1995 68 7.237 0.649 0.325 2.662 0.096 0.062 14 022053 1931 1995 65 7.219 0.749 0.425 2.612 0.107 0.183 15 022055 1929 1995 67 7.325 0.852 0.144 3.199 0.106 0.358 16 022057 1928 1995 68 7.489 0.676 -0.300 3.387 0.098 0.162 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 7.200 0.708 0.346 2.951 0.105 0.082 STANDARD DEVIATION 2 0.227 0.088 0.340 0.511 0.013 0.164 MEDIAN (50TH QUANTILE) 68 7.230 0.710 0.356 2.792 0.107 0.070 INTERQUARTILE RANGE 1 0.312 0.136 0.478 0.521 0.020 0.197 MINIMUM VALUE 61 6.834 0.574 -0.300 2.136 0.085 -0.146 LOWER HINGE (25TH QUANTILE) 67 7.010 0.643 0.113 2.691 0.095 -0.024 UPPER HINGE (75TH QUANTILE) 68 7.322 0.779 0.591 3.212 0.116 0.172 MAXIMUM VALUE 70 7.586 0.852 0.924 4.360 0.126 0.456 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.537 0.132 0.012 -0.225 3.045 0.197 0.814 MINIMUM CORRELATION: 0.197 SERIES 022037 AND 022055 67 YEARS MAXIMUM CORRELATION: 0.814 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 0.618 0.766 0.637 0.535 SDEV 0.175 0.096 0.158 0.189 SERR 0.016 0.009 0.014 0.017 EPS 0.963 0.981 0.966 0.949 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 7.231 0.560 0.786 3.803 0.083 -0.028 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.230 -0.075 1.056 17 53 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.29 0.95 1.01 1.14 2.09 3.54 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.07 0.00 0.86 0.93 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 -0.028 -0.006 0.208 0.049 0.044 0.068 0.110 -0.104 -0.071 0.117 PACF -0.028 -0.007 0.208 0.063 0.052 0.030 0.096 -0.124 -0.111 0.062 95% C.L. 0.239 0.239 0.239 0.249 0.250 0.250 0.251 0.254 0.257 0.258 |------------------ 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 0 0.000 |================== 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 1 1.30206358 0.01493230 0.00000000 6.51233959 2 022013 1 0.39236066 0.02481170 0.00000000 7.08223677 3 022015 3 0.00000000 0.00000000 0.00082242 7.00971460 4 022017 1 1.78075707 0.01470117 0.00000000 6.13101196 5 022021 3 0.00000000 0.00000000 0.00417591 6.76533222 6 022023 1 1.19185805 0.09767195 0.00000000 6.64399719 7 022025 3 0.00000000 0.00000000 -0.00419427 6.98260498 8 022027 3 0.00000000 0.00000000 0.01020353 6.63442326 9 022031 1 0.65710610 0.03094741 0.00000000 7.20732498 10 022033 3 0.00000000 0.00000000 -0.00621718 7.41481686 11 022037 1 0.54006571 0.07270557 0.00000000 7.48432636 12 022043 1 1.06496990 0.00737445 0.00000000 6.38884115 13 022047 3 0.00000000 0.00000000 0.00075906 7.21101856 14 022053 3 0.00000000 0.00000000 -0.00890297 7.51302862 15 022055 3 0.00000000 0.00000000 -0.01911366 7.97449112 16 022057 3 0.00000000 0.00000000 -0.01060179 7.85473204 |-------------------- 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 0.086 0.362 2.379 0.091 0.073 2 022013 1928 1995 68 1.000 0.078 0.473 2.853 0.093 -0.183 3 022015 1928 1995 68 1.000 0.087 0.511 3.256 0.106 -0.137 4 022017 1928 1995 68 1.000 0.104 0.050 2.926 0.095 0.344 5 022021 1929 1995 67 1.000 0.117 0.064 2.941 0.120 0.087 6 022023 1935 1995 61 1.000 0.107 0.756 3.474 0.122 -0.135 7 022025 1929 1995 67 1.000 0.110 0.800 3.364 0.117 -0.038 8 022027 1929 1995 67 1.000 0.108 0.567 3.502 0.124 -0.117 9 022031 1927 1995 69 1.000 0.083 0.262 2.271 0.090 0.035 10 022033 1929 1995 67 1.000 0.088 0.361 2.791 0.106 -0.040 11 022037 1926 1995 70 1.000 0.074 0.464 2.451 0.084 0.048 12 022043 1928 1995 68 1.000 0.101 0.836 3.836 0.111 -0.052 13 022047 1928 1995 68 1.000 0.090 0.325 2.675 0.095 0.062 14 022053 1931 1995 65 1.000 0.101 0.472 2.594 0.106 0.130 15 022055 1929 1995 67 1.000 0.105 0.187 3.162 0.104 0.200 16 022057 1928 1995 68 1.000 0.086 -0.128 2.961 0.097 0.060 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.095 0.398 2.965 0.104 0.021 STANDARD DEVIATION 2 0.000 0.013 0.273 0.443 0.012 0.137 MEDIAN (50TH QUANTILE) 68 1.000 0.095 0.413 2.934 0.105 0.041 INTERQUARTILE RANGE 1 0.000 0.020 0.315 0.675 0.020 0.165 MINIMUM VALUE 61 1.000 0.074 -0.128 2.271 0.084 -0.183 LOWER HINGE (25TH QUANTILE) 67 1.000 0.086 0.224 2.635 0.094 -0.085 UPPER HINGE (75TH QUANTILE) 68 1.000 0.106 0.539 3.310 0.114 0.080 MAXIMUM VALUE 70 1.000 0.117 0.836 3.836 0.124 0.344 |------------------------ 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 1.000 0.085 0.409 2.445 0.091 0.046 2 022013 1928 1995 68 1.000 0.076 0.653 3.357 0.093 -0.269 3 022015 1928 1995 68 1.000 0.085 0.612 3.434 0.106 -0.198 4 022017 1928 1995 68 0.999 0.084 0.293 3.157 0.094 -0.020 5 022021 1929 1995 67 1.000 0.112 0.137 2.982 0.120 0.010 6 022023 1935 1995 61 1.000 0.106 0.785 3.504 0.122 -0.166 7 022025 1929 1995 67 1.000 0.106 0.865 3.281 0.117 -0.114 8 022027 1929 1995 67 1.000 0.107 0.642 3.602 0.124 -0.140 9 022031 1927 1995 69 1.000 0.079 0.494 2.748 0.090 -0.067 10 022033 1929 1995 67 1.000 0.086 0.426 2.885 0.106 -0.085 11 022037 1926 1995 70 1.000 0.074 0.471 2.478 0.084 0.039 12 022043 1928 1995 68 1.000 0.096 1.038 4.249 0.111 -0.164 13 022047 1928 1995 68 1.000 0.085 0.360 2.888 0.095 -0.025 14 022053 1931 1995 65 0.999 0.090 0.555 2.866 0.106 -0.097 15 022055 1929 1995 67 0.999 0.091 0.141 2.910 0.104 -0.044 16 022057 1928 1995 68 1.000 0.081 -0.297 2.840 0.097 -0.044 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.090 0.474 3.102 0.104 -0.084 STANDARD DEVIATION 2 0.000 0.012 0.319 0.458 0.013 0.088 MEDIAN (50TH QUANTILE) 68 1.000 0.086 0.483 2.946 0.105 -0.076 INTERQUARTILE RANGE 1 0.000 0.019 0.321 0.543 0.020 0.129 MINIMUM VALUE 61 0.999 0.074 -0.297 2.445 0.084 -0.269 LOWER HINGE (25TH QUANTILE) 67 1.000 0.082 0.327 2.853 0.094 -0.152 UPPER HINGE (75TH QUANTILE) 68 1.000 0.101 0.647 3.396 0.114 -0.023 MAXIMUM VALUE 70 1.000 0.112 1.038 4.249 0.124 0.046 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.562 0.125 0.011 -0.036 3.097 0.215 0.867 MINIMUM CORRELATION: 0.215 SERIES 022037 AND 022055 67 YEARS MAXIMUM CORRELATION: 0.867 SERIES 022023 AND 022027 61 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 0.634 0.769 0.663 0.544 SDEV 0.169 0.091 0.142 0.181 SERR 0.015 0.008 0.013 0.016 EPS 0.965 0.982 0.969 0.950 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 0.999 0.070 0.947 4.053 0.083 -0.193 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.041 0.013 0.045 12 58 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.51 0.92 1.01 1.11 2.03 5.51 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.00 0.86 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 -0.190 -0.130 0.093 -0.083 -0.001 -0.015 0.027 -0.208 -0.174 0.071 PACF -0.190 -0.172 0.033 -0.083 -0.017 -0.049 0.022 -0.230 -0.290 -0.140 95% C.L. 0.239 0.248 0.251 0.253 0.255 0.255 0.255 0.255 0.265 0.271 |------------------ 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 0.066 -0.192 |======================= 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 -0.189 -0.134 0.098 -0.091 0.018 -0.014 0.032 -0.206 -0.175 0.081 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 -0.189 2 -0.222 -0.176 3 -0.216 -0.168 0.037 4 -0.212 -0.183 0.018 -0.092 5 -0.212 -0.183 0.018 -0.092 0.002 6 -0.212 -0.187 0.019 -0.100 -0.008 -0.044 7 -0.210 -0.187 0.022 -0.100 -0.001 -0.036 0.038 8 -0.202 -0.195 0.022 -0.123 0.004 -0.079 -0.010 -0.227 9 -0.265 -0.198 0.000 -0.122 -0.030 -0.072 -0.064 -0.283 -0.279 10 -0.299 -0.233 -0.008 -0.131 -0.034 -0.087 -0.064 -0.307 -0.311 -0.122 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) 309.63 309.09 308.88 310.78 312.19 314.19 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 316.05 317.95 316.25 312.60 313.55 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 -0.222 -0.176 R-SQUARED DUE TO POOLED AUTOREGRESSION: 6.57 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 107.03 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 -0.222 -0.127 0.067 0.007 -0.014 0.002 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 022011 2 0.043 0.056 -0.196 2 022013 2 0.083 -0.285 -0.053 3 022015 2 0.085 -0.242 -0.205 4 022017 2 0.034 -0.019 0.049 5 022021 2 0.056 0.009 0.083 6 022023 2 0.060 -0.165 0.017 7 022025 2 0.034 -0.121 -0.036 8 022027 2 0.023 -0.144 -0.006 9 022031 2 0.043 -0.077 -0.124 10 022033 2 0.030 -0.098 -0.147 11 022037 2 0.013 0.044 -0.107 12 022043 2 0.039 -0.176 -0.061 13 022047 2 0.026 -0.027 -0.061 14 022053 2 0.010 -0.097 0.005 15 022055 2 0.051 -0.047 -0.059 16 022057 2 0.043 -0.051 -0.173 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.042 -0.090 -0.067 STANDARD DEVIATION 0 0.022 0.097 0.086 MEDIAN 2 0.041 -0.087 -0.060 INTERQUARTILE RANGE 0 0.026 0.132 0.135 MINIMUM VALUE 2 0.010 -0.285 -0.205 LOWER HINGE 2 0.028 -0.155 -0.136 UPPER HINGE 2 0.054 -0.023 -0.001 MAXIMUM VALUE 2 0.085 0.056 0.083 |------------------- 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 0.083 0.532 2.738 0.091 -0.005 2 022013 1928 1995 68 1.000 0.073 0.631 2.967 0.079 -0.005 3 022015 1928 1995 68 1.000 0.081 0.594 3.464 0.093 -0.011 4 022017 1928 1995 68 1.000 0.083 0.296 3.093 0.093 -0.009 5 022021 1929 1995 67 1.000 0.111 0.108 3.019 0.122 -0.018 6 022023 1935 1995 61 1.000 0.104 0.575 3.478 0.113 -0.004 7 022025 1929 1995 67 1.000 0.105 0.847 3.229 0.109 0.007 8 022027 1929 1995 67 1.000 0.106 0.474 3.633 0.118 0.003 9 022031 1927 1995 69 1.000 0.078 0.327 2.658 0.086 -0.021 10 022033 1929 1995 67 1.000 0.085 0.344 2.845 0.099 -0.004 11 022037 1926 1995 70 1.000 0.073 0.510 2.613 0.085 -0.001 12 022043 1928 1995 68 1.000 0.095 1.053 4.552 0.101 -0.004 13 022047 1928 1995 68 1.000 0.085 0.364 2.896 0.094 -0.009 14 022053 1931 1995 65 1.000 0.089 0.466 2.722 0.102 0.000 15 022055 1929 1995 67 1.000 0.091 0.063 2.932 0.102 0.013 16 022057 1928 1995 68 1.000 0.080 -0.379 3.291 0.092 0.018 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 67 1.000 0.089 0.425 3.133 0.099 -0.003 STANDARD DEVIATION 2 0.000 0.012 0.327 0.488 0.012 0.010 MEDIAN (50TH QUANTILE) 68 1.000 0.085 0.470 2.993 0.097 -0.004 INTERQUARTILE RANGE 1 0.000 0.019 0.273 0.586 0.014 0.010 MINIMUM VALUE 61 1.000 0.073 -0.379 2.613 0.079 -0.021 LOWER HINGE (25TH QUANTILE) 67 1.000 0.081 0.311 2.792 0.092 -0.009 UPPER HINGE (75TH QUANTILE) 68 1.000 0.100 0.585 3.378 0.105 0.001 MAXIMUM VALUE 70 1.000 0.111 1.053 4.552 0.122 0.018 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 120 0.545 0.125 0.011 -0.004 3.030 0.206 0.858 MINIMUM CORRELATION: 0.206 SERIES 022037 AND 022055 67 YEARS MAXIMUM CORRELATION: 0.858 SERIES 022023 AND 022027 61 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 0.621 0.758 0.648 0.519 SDEV 0.171 0.093 0.147 0.184 SERR 0.016 0.009 0.013 0.017 EPS 0.963 0.980 0.967 0.945 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 0.999 0.068 0.917 4.003 0.078 -0.118 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.031 0.009 0.050 15 55 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.31 0.54 1.04 1.07 1.61 3.44 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 -0.116 -0.089 0.078 -0.087 -0.017 -0.036 -0.012 -0.221 -0.200 0.050 PACF -0.116 -0.104 0.056 -0.082 -0.025 -0.063 -0.018 -0.248 -0.286 -0.102 95% C.L. 0.239 0.242 0.244 0.246 0.247 0.247 0.248 0.248 0.259 0.267 |------------------ 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 0.007 -0.002 0.042 -0.097 -0.029 -0.077 -0.075 -0.261 -0.230 0.026 PACF 0.007 -0.003 0.042 -0.097 -0.027 -0.080 -0.067 -0.275 -0.260 -0.024 95% C.L. 0.239 0.239 0.239 0.239 0.242 0.242 0.243 0.245 0.260 0.272 |----------------- 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 0.002 0.007 -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 1926 1995 70 0.999 0.070 0.946 3.951 0.083 -0.195 |------------ 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 -0.192 -0.134 0.124 -0.082 -0.024 -0.017 0.023 -0.196 -0.178 0.061 PACF -0.192 -0.178 0.064 -0.070 -0.029 -0.063 0.013 -0.219 -0.290 -0.150 95% C.L. 0.239 0.248 0.252 0.255 0.257 0.257 0.257 0.257 0.266 0.272 |------------------- 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 0.073 -0.229 -0.179 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.22 MINUTES