RUN: FRAN001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: GERM041L.rwl.conv LOG FILE PROCESSED: GERM041L.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_LATE 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 0.531 0.275 2.495 11.639 0.370 0.211 2 016013 1933 1992 60 0.590 0.278 0.723 3.099 0.370 0.451 3 016016 1932 1992 61 0.569 0.269 0.829 3.797 0.360 0.503 4 016021 1937 1992 56 0.501 0.165 0.659 3.196 0.250 0.468 5 016025 1938 1992 55 0.482 0.155 1.112 4.452 0.286 0.249 6 016027 1937 1992 56 0.561 0.211 0.940 3.506 0.355 0.292 7 016031 1936 1992 57 0.529 0.316 1.803 6.009 0.375 0.661 8 016033 1937 1992 56 0.623 0.378 1.583 4.390 0.439 0.427 9 016034 1937 1992 56 0.429 0.220 2.158 9.195 0.358 0.433 10 016041 1935 1992 58 0.545 0.380 3.266 12.336 0.326 0.432 11 016047 1934 1992 59 0.533 0.257 2.500 12.250 0.350 0.344 12 016054 1934 1992 59 0.358 0.157 2.191 9.018 0.297 0.483 13 016056 1935 1992 58 0.449 0.240 3.000 15.916 0.321 0.324 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 0.516 0.254 1.789 7.600 0.343 0.406 STANDARD DEVIATION 2 0.072 0.074 0.890 4.356 0.048 0.121 MEDIAN (50TH QUANTILE) 58 0.531 0.257 1.803 6.009 0.355 0.432 INTERQUARTILE RANGE 3 0.079 0.068 1.555 7.841 0.048 0.144 MINIMUM VALUE 55 0.358 0.155 0.659 3.099 0.250 0.211 LOWER HINGE (25TH QUANTILE) 56 0.482 0.211 0.940 3.797 0.321 0.324 UPPER HINGE (75TH QUANTILE) 59 0.561 0.278 2.495 11.639 0.370 0.468 MAXIMUM VALUE 61 0.623 0.380 3.266 15.916 0.439 0.661 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.361 0.222 0.025 -0.018 2.177 -0.093 0.828 MINIMUM CORRELATION: -0.093 SERIES 016033 AND 016054 56 YEARS MAXIMUM CORRELATION: 0.828 SERIES 016031 AND 016033 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 0.842 0.136 0.111 0.452 SDEV 0.000 0.336 0.336 0.195 SERR 0.000 0.038 0.038 0.022 EPS 0.983 0.671 0.620 0.915 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 0.479 0.159 1.122 7.230 0.212 0.438 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.852 0.553 -0.090 19 42 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 2.14 1.44 1.16 1.54 2.98 6.99 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.05 0.49 0.86 0.91 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 0.431 0.148 0.063 0.055 0.003 -0.071 -0.167 -0.092 0.011 0.080 PACF 0.431 -0.046 0.021 0.032 -0.041 -0.074 -0.130 0.043 0.063 0.073 95% C.L. 0.256 0.300 0.305 0.305 0.306 0.306 0.307 0.313 0.315 0.315 |------------------ 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 0.205 0.452 |================== 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 -0.00219355 0.59931147 2 016013 3 0.00000000 0.00000000 0.00399667 0.46843502 3 016016 3 0.00000000 0.00000000 -0.00249498 0.64668852 4 016021 3 0.00000000 0.00000000 -0.00390977 0.61285716 5 016025 3 0.00000000 0.00000000 -0.00176263 0.53171718 6 016027 3 0.00000000 0.00000000 -0.00062133 0.57877922 7 016031 3 0.00000000 0.00000000 -0.00597550 0.70258772 8 016033 3 0.00000000 0.00000000 -0.00084313 0.64706492 9 016034 3 0.00000000 0.00000000 -0.00068250 0.44855845 10 016041 1 0.93765026 0.02477117 0.00000000 0.05382347 11 016047 1 0.48115247 0.02139023 0.00000000 0.26213267 12 016054 1 0.32589218 0.08650421 0.00000000 0.29754558 13 016056 3 0.00000000 0.00000000 -0.00856040 0.70201451 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 016011 1932 1992 61 1.000 0.486 1.983 9.169 0.364 0.201 2 016013 1933 1992 60 0.998 0.453 0.696 3.069 0.364 0.364 3 016016 1932 1992 61 0.999 0.454 0.652 3.263 0.354 0.489 4 016021 1937 1992 56 1.000 0.311 0.984 4.472 0.246 0.387 5 016025 1938 1992 55 1.000 0.321 1.288 5.047 0.281 0.234 6 016027 1937 1992 56 1.000 0.376 0.980 3.579 0.348 0.287 7 016031 1936 1992 57 0.993 0.550 1.556 4.655 0.368 0.594 8 016033 1937 1992 56 1.000 0.603 1.527 4.207 0.431 0.414 9 016034 1937 1992 56 1.000 0.512 2.084 8.628 0.352 0.429 10 016041 1935 1992 58 1.001 0.444 2.163 7.764 0.320 0.213 11 016047 1934 1992 59 1.000 0.409 1.424 6.291 0.343 0.266 12 016054 1934 1992 59 0.999 0.356 1.420 5.358 0.291 0.330 13 016056 1935 1992 58 0.997 0.337 2.060 11.332 0.316 -0.054 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 0.999 0.432 1.448 5.910 0.337 0.320 STANDARD DEVIATION 2 0.002 0.091 0.521 2.567 0.047 0.160 MEDIAN (50TH QUANTILE) 58 1.000 0.444 1.424 5.047 0.348 0.330 INTERQUARTILE RANGE 3 0.001 0.130 0.999 3.557 0.048 0.180 MINIMUM VALUE 55 0.993 0.311 0.652 3.069 0.246 -0.054 LOWER HINGE (25TH QUANTILE) 56 0.999 0.356 0.984 4.207 0.316 0.234 UPPER HINGE (75TH QUANTILE) 59 1.000 0.486 1.983 7.764 0.364 0.414 MAXIMUM VALUE 61 1.001 0.603 2.163 11.332 0.431 0.594 |------------------------ 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 0.997 0.483 2.038 9.145 0.364 0.193 2 016013 1933 1992 60 0.994 0.439 1.140 4.108 0.362 0.300 3 016016 1932 1992 61 0.993 0.408 1.600 7.709 0.353 0.275 4 016021 1937 1992 56 0.995 0.288 1.134 4.583 0.244 0.311 5 016025 1938 1992 55 0.995 0.299 1.578 6.420 0.280 0.136 6 016027 1937 1992 56 0.994 0.349 1.167 4.185 0.347 0.207 7 016031 1936 1992 57 0.992 0.456 1.270 3.888 0.366 0.446 8 016033 1937 1992 56 0.992 0.466 1.045 3.239 0.428 0.217 9 016034 1937 1992 56 0.992 0.453 1.522 5.891 0.352 0.379 10 016041 1935 1992 58 0.998 0.435 2.164 7.930 0.321 0.194 11 016047 1934 1992 59 0.996 0.395 1.388 6.287 0.343 0.228 12 016054 1934 1992 59 0.998 0.322 0.876 4.162 0.291 0.227 13 016056 1935 1992 58 0.998 0.336 2.468 13.694 0.317 -0.092 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 0.995 0.395 1.492 6.249 0.336 0.233 STANDARD DEVIATION 2 0.003 0.068 0.476 2.880 0.046 0.128 MEDIAN (50TH QUANTILE) 58 0.995 0.408 1.388 5.891 0.347 0.227 INTERQUARTILE RANGE 3 0.004 0.117 0.461 3.548 0.046 0.106 MINIMUM VALUE 55 0.992 0.288 0.876 3.239 0.244 -0.092 LOWER HINGE (25TH QUANTILE) 56 0.993 0.336 1.140 4.162 0.317 0.194 UPPER HINGE (75TH QUANTILE) 59 0.997 0.453 1.600 7.709 0.362 0.300 MAXIMUM VALUE 61 0.998 0.483 2.468 13.694 0.428 0.446 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.413 0.194 0.022 -0.583 3.030 -0.120 0.742 MINIMUM CORRELATION: -0.120 SERIES 016027 AND 016033 56 YEARS MAXIMUM CORRELATION: 0.742 SERIES 016031 AND 016033 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 0.854 0.149 0.108 0.501 SDEV 0.000 0.318 0.306 0.188 SERR 0.000 0.036 0.035 0.021 EPS 0.985 0.695 0.612 0.929 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 0.954 0.284 1.252 6.552 0.223 0.372 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.705 0.316 -0.027 17 44 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.70 0.89 1.00 1.13 2.02 3.88 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.07 0.58 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 0.366 0.124 -0.044 -0.169 -0.249 -0.281 -0.295 -0.179 -0.054 0.030 PACF 0.366 -0.012 -0.099 -0.139 -0.156 -0.157 -0.185 -0.072 -0.042 -0.053 95% C.L. 0.256 0.288 0.292 0.292 0.299 0.312 0.328 0.345 0.351 0.352 |------------------ 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 0.142 0.377 |======================= 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 0.304 0.120 -0.077 -0.158 -0.240 -0.208 -0.168 -0.193 -0.137 -0.058 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 0.304 2 0.295 0.030 3 0.299 0.070 -0.133 4 0.283 0.078 -0.099 -0.115 5 0.265 0.062 -0.086 -0.069 -0.163 6 0.249 0.055 -0.095 -0.063 -0.137 -0.098 7 0.240 0.042 -0.101 -0.072 -0.132 -0.075 -0.091 8 0.223 0.029 -0.125 -0.085 -0.150 -0.068 -0.047 -0.182 9 0.200 0.023 -0.133 -0.104 -0.161 -0.084 -0.043 -0.153 -0.128 10 0.189 0.010 -0.137 -0.111 -0.174 -0.092 -0.055 -0.151 -0.111 -0.085 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) 398.22 394.31 396.25 397.15 398.33 398.70 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 400.11 401.61 401.56 402.56 404.12 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 0.304 R-SQUARED DUE TO POOLED AUTOREGRESSION: 9.23 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 110.17 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 1) PROCESS OUT TO ORDER 50: 1.0000 0.304 0.092 0.028 0.009 0.003 0.001 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 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 0.103 0.198 2 016013 1 0.096 0.308 3 016016 1 0.081 0.279 4 016021 1 0.100 0.316 5 016025 1 0.039 0.136 6 016027 1 0.068 0.210 7 016031 1 0.202 0.449 8 016033 1 0.095 0.222 9 016034 1 0.160 0.382 10 016041 1 0.039 0.195 11 016047 1 0.083 0.235 12 016054 1 0.078 0.239 13 016056 1 0.009 -0.094 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 1 0.089 0.237 STANDARD DEVIATION 0 0.050 0.130 MEDIAN 1 0.083 0.235 INTERQUARTILE RANGE 0 0.032 0.110 MINIMUM VALUE 1 0.009 -0.094 LOWER HINGE 1 0.068 0.198 UPPER HINGE 1 0.100 0.308 MAXIMUM VALUE 1 0.202 0.449 |------------------- 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 0.474 2.530 11.686 0.373 0.047 2 016013 1933 1992 60 1.000 0.417 1.449 5.124 0.392 0.009 3 016016 1932 1992 61 1.000 0.391 2.069 10.657 0.385 -0.021 4 016021 1937 1992 56 1.000 0.273 1.537 5.432 0.269 -0.005 5 016025 1938 1992 55 1.000 0.296 1.707 7.157 0.303 -0.018 6 016027 1937 1992 56 1.000 0.341 1.253 4.446 0.365 0.030 7 016031 1936 1992 57 1.000 0.407 1.179 4.661 0.435 0.014 8 016033 1937 1992 56 1.000 0.454 1.054 3.212 0.469 -0.051 9 016034 1937 1992 56 1.000 0.418 1.554 6.099 0.420 -0.047 10 016041 1935 1992 58 1.000 0.426 2.319 8.768 0.350 -0.006 11 016047 1934 1992 59 1.000 0.384 1.676 7.708 0.360 0.035 12 016054 1934 1992 59 1.000 0.312 1.012 4.780 0.315 0.034 13 016056 1935 1992 58 1.000 0.334 2.332 13.004 0.302 0.004 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 58 1.000 0.379 1.667 7.133 0.365 0.002 STANDARD DEVIATION 2 0.000 0.062 0.505 3.067 0.057 0.031 MEDIAN (50TH QUANTILE) 58 1.000 0.391 1.554 6.099 0.365 0.004 INTERQUARTILE RANGE 3 0.000 0.084 0.816 3.988 0.077 0.047 MINIMUM VALUE 55 1.000 0.273 1.012 3.212 0.269 -0.051 LOWER HINGE (25TH QUANTILE) 56 1.000 0.334 1.253 4.780 0.315 -0.018 UPPER HINGE (75TH QUANTILE) 59 1.000 0.418 2.069 8.768 0.392 0.030 MAXIMUM VALUE 61 1.000 0.474 2.530 13.004 0.469 0.047 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 78 0.395 0.194 0.022 -0.635 3.104 -0.164 0.730 MINIMUM CORRELATION: -0.164 SERIES 016027 AND 016033 56 YEARS MAXIMUM CORRELATION: 0.730 SERIES 016031 AND 016033 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 0.853 0.159 0.127 0.469 SDEV 0.000 0.308 0.278 0.183 SERR 0.000 0.035 0.031 0.021 EPS 0.985 0.711 0.654 0.920 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 0.963 0.263 1.868 9.140 0.235 0.146 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.727 0.349 -0.068 19 42 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.26 0.57 1.01 1.14 1.71 6.83 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.06 0.56 0.86 0.91 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 0.144 0.071 -0.050 -0.119 -0.205 -0.203 -0.224 -0.120 -0.030 0.072 PACF 0.144 0.051 -0.068 -0.109 -0.173 -0.155 -0.191 -0.111 -0.067 -0.013 95% C.L. 0.256 0.261 0.263 0.263 0.267 0.277 0.286 0.298 0.301 0.301 |------------------ 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 -0.012 0.060 -0.045 -0.086 -0.169 -0.148 -0.183 -0.087 -0.023 0.082 PACF -0.012 0.060 -0.044 -0.091 -0.168 -0.152 -0.195 -0.131 -0.085 -0.004 95% C.L. 0.256 0.256 0.257 0.258 0.259 0.267 0.272 0.280 0.282 0.282 |----------------- 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 0.004 -0.012 |========================= 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 0.963 0.275 1.444 7.363 0.225 0.310 |------------ 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 0.305 0.121 -0.046 -0.152 -0.249 -0.267 -0.280 -0.163 -0.052 0.053 PACF 0.305 0.031 -0.100 -0.129 -0.176 -0.155 -0.184 -0.082 -0.050 -0.026 95% C.L. 0.256 0.279 0.282 0.283 0.288 0.302 0.317 0.333 0.338 0.338 |------------------- 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 0.101 0.314 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.17 MINUTES