RUN: SWIT001 FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: SWIT112N.rwl.conv LOG FILE PROCESSED: SWIT112N.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 50 25 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: 372 1 Lauenen BE BrŸchli DENSITY_MINIMUM PCAB - 372 2 Switzerland Norway spruce 1500 4625-719 1701 1976 - 372 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 1 372011 MISSING VALUES FOUND: 5 IN 1 GAPS / 1839 1843 / -------------------------------------------------------------------- 6 372032 MISSING VALUES FOUND: 5 IN 1 GAPS / 1804 1808 / -------------------------------------------------------------------- 11 372091 MISSING VALUES FOUND: 5 IN 1 GAPS / 1898 1902 / -------------------------------------------------------------------- 12 372092 MISSING VALUES FOUND: 6 IN 1 GAPS / 1899 1904 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 372011 1814 1976 163 0.294 0.023 0.153 2.963 0.057 0.574 2 372012 1810 1976 167 0.290 0.025 0.437 3.272 0.066 0.573 3 372021 1705 1976 272 0.321 0.028 0.224 2.825 0.050 0.746 4 372022 1726 1976 251 0.332 0.027 -0.513 4.061 0.050 0.659 5 372031 1701 1976 276 0.332 0.038 1.394 9.512 0.054 0.755 6 372032 1709 1976 268 0.344 0.047 0.448 2.426 0.049 0.897 7 372041 1769 1976 208 0.359 0.029 0.245 2.755 0.045 0.760 8 372042 1748 1976 229 0.332 0.022 0.137 2.908 0.052 0.536 9 372051 1734 1976 243 0.322 0.030 0.822 4.043 0.050 0.755 10 372052 1755 1976 222 0.317 0.028 0.185 2.536 0.048 0.766 11 372091 1813 1976 164 0.311 0.029 0.352 3.158 0.058 0.684 12 372092 1788 1976 189 0.307 0.021 0.552 2.976 0.058 0.440 NUMBER OF SERIES READ IN: 12 FROM 1701 TO 1976 276 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 219 0.322 0.029 0.370 3.620 0.053 0.679 STANDARD DEVIATION 43 0.020 0.007 0.452 1.925 0.006 0.127 MEDIAN (50TH QUANTILE) 225 0.322 0.028 0.298 2.969 0.051 0.715 INTERQUARTILE RANGE 82 0.023 0.006 0.331 0.868 0.008 0.185 MINIMUM VALUE 158 0.290 0.021 -0.513 2.426 0.045 0.440 LOWER HINGE (25TH QUANTILE) 175 0.309 0.024 0.169 2.790 0.049 0.573 UPPER HINGE (75TH QUANTILE) 257 0.332 0.030 0.500 3.658 0.058 0.758 MAXIMUM VALUE 276 0.359 0.047 1.394 9.512 0.066 0.897 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.212 0.258 0.032 -0.136 2.926 -0.497 0.806 MINIMUM CORRELATION: -0.497 SERIES 372032 AND 372091 164 YEARS MAXIMUM CORRELATION: 0.806 SERIES 372011 AND 372012 163 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 70.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 10. 21. 28. 45. 66. 66. 66. 66. RBAR 0.450 0.273 0.335 0.317 0.359 0.364 0.408 0.318 SDEV 0.217 0.304 0.225 0.179 0.221 0.362 0.273 0.217 SERR 0.069 0.066 0.042 0.027 0.027 0.045 0.034 0.027 EPS 0.845 0.756 0.838 0.846 0.871 0.873 0.892 0.849 NSS 6.7 8.3 10.3 11.9 12.0 12.0 12.0 12.0 |======================== 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 1701 1976 276 0.322 0.020 0.046 2.941 0.039 0.660 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.332 0.197 -0.036 79 197 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.64 1.46 1.00 1.23 2.69 8.53 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.14 0.00 0.84 0.98 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 226. 82. 163. 178. 260. 276. |----------- 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 0.657 0.575 0.505 0.500 0.495 0.491 0.482 0.497 0.396 0.385 PACF 0.657 0.252 0.106 0.152 0.126 0.100 0.081 0.115 -0.120 0.010 95% C.L. 0.120 0.164 0.191 0.210 0.226 0.242 0.256 0.269 0.282 0.289 |------------------ 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 6 0.504 0.443 0.140 -0.001 0.084 0.083 0.095 |================== 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 372011 1 0.03880584 0.06854176 0.00000000 0.29006517 2 372012 1 0.05473056 0.06733379 0.00000000 0.28511530 3 372021 3 0.00000000 0.00000000 0.00009269 0.30878174 4 372022 1 0.03821713 0.00807369 0.00000000 0.31568760 5 372031 3 0.00000000 0.00000000 -0.00011384 0.34768671 6 372032 3 0.00000000 0.00000000 -0.00010111 0.35857821 7 372041 3 0.00000000 0.00000000 0.00019872 0.33822465 8 372042 3 0.00000000 0.00000000 -0.00005371 0.33814180 9 372051 1 0.07027967 0.01475518 0.00000000 0.30301791 10 372052 3 0.00000000 0.00000000 -0.00008314 0.32584649 11 372091 3 0.00000000 0.00000000 0.00026842 0.28996664 12 372092 3 0.00000000 0.00000000 0.00001587 0.30469128 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 372011 1814 1976 163 1.000 0.073 0.138 2.722 0.056 0.511 2 372012 1810 1976 167 1.000 0.080 0.270 2.805 0.065 0.489 3 372021 1705 1976 272 1.000 0.084 0.136 2.990 0.050 0.723 4 372022 1726 1976 251 1.000 0.078 -0.492 4.090 0.050 0.614 5 372031 1701 1976 276 1.000 0.112 1.381 9.768 0.054 0.739 6 372032 1709 1976 268 1.000 0.133 0.398 2.535 0.048 0.888 7 372041 1769 1976 208 1.000 0.073 0.120 2.727 0.045 0.705 8 372042 1748 1976 229 1.000 0.067 0.091 3.108 0.052 0.520 9 372051 1734 1976 243 1.000 0.073 0.457 3.702 0.050 0.589 10 372052 1755 1976 222 1.000 0.087 0.107 2.584 0.048 0.750 11 372091 1813 1976 164 1.000 0.086 0.726 3.370 0.057 0.635 12 372092 1788 1976 189 1.000 0.066 0.558 2.966 0.057 0.431 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.000 0.084 0.324 3.614 0.053 0.633 STANDARD DEVIATION 42 0.000 0.020 0.451 1.993 0.006 0.133 MEDIAN (50TH QUANTILE) 225 1.000 0.079 0.204 2.978 0.051 0.625 INTERQUARTILE RANGE 81 0.000 0.014 0.394 0.812 0.008 0.215 MINIMUM VALUE 163 1.000 0.066 -0.492 2.535 0.045 0.431 LOWER HINGE (25TH QUANTILE) 178 1.000 0.073 0.114 2.724 0.049 0.516 UPPER HINGE (75TH QUANTILE) 259 1.000 0.087 0.507 3.536 0.057 0.731 MAXIMUM VALUE 276 1.000 0.133 1.381 9.768 0.065 0.888 |------------------------ 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 372011 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 372012 -67 111 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 372021 -67 182 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 372022 -67 168 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 372031 -67 184 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 372032 -67 179 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 372041 -67 139 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 372042 -67 153 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 372051 -67 162 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 372052 -67 148 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 372091 -67 109 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 372092 -67 126 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 372011 1814 1976 163 1.000 0.066 0.143 2.768 0.057 0.396 2 372012 1810 1976 167 1.000 0.073 0.233 2.831 0.065 0.387 3 372021 1705 1976 272 1.000 0.070 -0.162 3.372 0.050 0.610 4 372022 1726 1976 251 1.000 0.073 -0.375 3.970 0.050 0.569 5 372031 1701 1976 276 0.999 0.082 2.025 14.050 0.054 0.522 6 372032 1709 1976 268 0.998 0.086 -0.206 2.629 0.048 0.726 7 372041 1769 1976 208 1.000 0.061 0.310 2.963 0.045 0.589 8 372042 1748 1976 229 1.000 0.061 0.085 3.398 0.052 0.436 9 372051 1734 1976 243 1.000 0.064 0.297 3.802 0.050 0.483 10 372052 1755 1976 222 0.999 0.063 -0.059 3.041 0.049 0.520 11 372091 1813 1976 164 1.000 0.071 0.313 2.789 0.057 0.455 12 372092 1788 1976 189 1.000 0.061 0.367 2.810 0.057 0.348 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.000 0.069 0.247 4.035 0.053 0.503 STANDARD DEVIATION 42 0.000 0.008 0.609 3.183 0.006 0.109 MEDIAN (50TH QUANTILE) 225 1.000 0.068 0.188 3.002 0.051 0.502 INTERQUARTILE RANGE 81 0.000 0.011 0.422 0.800 0.008 0.164 MINIMUM VALUE 163 0.998 0.061 -0.375 2.629 0.045 0.348 LOWER HINGE (25TH QUANTILE) 178 0.999 0.062 -0.111 2.800 0.049 0.416 UPPER HINGE (75TH QUANTILE) 259 1.000 0.073 0.312 3.600 0.057 0.579 MAXIMUM VALUE 276 1.000 0.086 2.025 14.050 0.065 0.726 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.328 0.147 0.018 0.325 3.410 0.019 0.744 MINIMUM CORRELATION: 0.019 SERIES 372011 AND 372021 163 YEARS MAXIMUM CORRELATION: 0.744 SERIES 372011 AND 372012 163 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 70.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 10. 21. 28. 45. 66. 66. 66. 66. RBAR 0.416 0.322 0.351 0.342 0.414 0.443 0.456 0.358 SDEV 0.317 0.221 0.165 0.180 0.188 0.265 0.245 0.185 SERR 0.100 0.048 0.031 0.027 0.023 0.033 0.030 0.023 EPS 0.826 0.797 0.848 0.861 0.894 0.905 0.910 0.870 NSS 6.7 8.3 10.3 11.9 12.0 12.0 12.0 12.0 |======================== 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 1701 1976 276 0.998 0.048 0.356 3.357 0.039 0.413 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED -0.114 -0.048 0.100 52 224 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.22 0.71 1.01 1.07 1.78 20.08 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.12 0.00 0.85 0.96 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 0.411 0.300 0.181 0.162 0.167 0.150 0.165 0.197 0.049 0.061 PACF 0.411 0.157 0.016 0.058 0.078 0.039 0.066 0.097 -0.124 0.007 95% C.L. 0.120 0.139 0.148 0.151 0.154 0.157 0.159 0.161 0.165 0.165 |------------------ 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 2 0.195 0.359 0.148 |======================= 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 0.467 0.310 0.193 0.107 0.148 0.136 0.180 0.163 0.036 0.043 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 0.467 2 0.413 0.117 3 0.411 0.111 0.014 4 0.411 0.113 0.021 -0.017 5 0.413 0.111 0.008 -0.062 0.109 6 0.409 0.113 0.008 -0.066 0.093 0.039 7 0.405 0.105 0.014 -0.067 0.082 0.000 0.095 8 0.403 0.105 0.012 -0.065 0.082 -0.003 0.084 0.027 9 0.406 0.114 0.012 -0.056 0.074 -0.002 0.096 0.074 -0.115 10 0.408 0.113 0.010 -0.056 0.072 0.000 0.096 0.071 -0.124 0.022 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) 1110.66 1044.66 1042.85 1044.80 1046.72 1045.44 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 1047.02 1046.51 1048.31 1046.60 1048.47 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 0.413 0.117 R-SQUARED DUE TO POOLED AUTOREGRESSION: 22.91 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 129.71 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 2) PROCESS OUT TO ORDER 50: 1.0000 0.413 0.287 0.167 0.102 0.062 0.037 0.023 0.014 0.008 0.0050 0.003 0.002 0.001 0.001 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 372011 2 0.162 0.397 0.012 2 372012 2 0.164 0.346 0.112 3 372021 2 0.432 0.428 0.300 4 372022 2 0.339 0.526 0.081 5 372031 2 0.344 0.413 0.224 6 372032 2 0.607 0.467 0.359 7 372041 2 0.380 0.469 0.207 8 372042 2 0.232 0.339 0.224 9 372051 2 0.297 0.354 0.274 10 372052 2 0.305 0.411 0.212 11 372091 2 0.228 0.401 0.129 12 372092 2 0.176 0.272 0.222 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 2 0.305 0.402 0.196 STANDARD DEVIATION 0 0.129 0.068 0.098 MEDIAN 2 0.301 0.406 0.217 INTERQUARTILE RANGE 0 0.160 0.097 0.128 MINIMUM VALUE 2 0.162 0.272 0.012 LOWER HINGE 2 0.202 0.350 0.120 UPPER HINGE 2 0.362 0.447 0.249 MAXIMUM VALUE 2 0.607 0.526 0.359 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 372011 1814 1976 163 1.000 0.060 0.200 2.807 0.067 0.000 2 372012 1810 1976 167 1.000 0.067 0.151 2.786 0.077 -0.002 3 372021 1705 1976 272 1.000 0.053 0.278 3.236 0.060 -0.016 4 372022 1726 1976 251 1.000 0.060 0.148 3.716 0.065 -0.010 5 372031 1701 1976 276 1.000 0.068 2.316 20.875 0.068 -0.051 6 372032 1709 1976 268 1.000 0.055 0.024 3.553 0.062 -0.074 7 372041 1769 1976 208 1.000 0.048 0.474 3.302 0.056 -0.015 8 372042 1748 1976 229 1.000 0.054 0.184 3.806 0.060 -0.006 9 372051 1734 1976 243 1.000 0.054 0.515 3.157 0.059 -0.020 10 372052 1755 1976 222 1.000 0.052 0.015 3.847 0.060 -0.008 11 372091 1813 1976 164 1.000 0.062 0.171 3.114 0.069 -0.014 12 372092 1788 1976 189 1.000 0.056 0.261 2.842 0.064 0.023 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 221 1.000 0.057 0.395 4.754 0.064 -0.016 STANDARD DEVIATION 42 0.000 0.006 0.623 5.091 0.006 0.025 MEDIAN (50TH QUANTILE) 225 1.000 0.055 0.192 3.269 0.063 -0.012 INTERQUARTILE RANGE 81 0.000 0.008 0.226 0.783 0.007 0.014 MINIMUM VALUE 163 1.000 0.048 0.015 2.786 0.056 -0.074 LOWER HINGE (25TH QUANTILE) 178 1.000 0.053 0.150 2.978 0.060 -0.018 UPPER HINGE (75TH QUANTILE) 259 1.000 0.061 0.376 3.761 0.067 -0.004 MAXIMUM VALUE 276 1.000 0.068 2.316 20.875 0.077 0.023 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.392 0.092 0.011 1.058 4.783 0.233 0.715 MINIMUM CORRELATION: 0.233 SERIES 372012 AND 372021 167 YEARS MAXIMUM CORRELATION: 0.715 SERIES 372011 AND 372012 163 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 70.89 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1760. 1785. 1810. 1835. 1860. 1885. 1910. 1935. CORR 10. 21. 28. 45. 66. 66. 66. 66. RBAR 0.410 0.364 0.438 0.413 0.430 0.451 0.474 0.426 SDEV 0.159 0.163 0.137 0.165 0.164 0.152 0.124 0.128 SERR 0.050 0.036 0.026 0.025 0.020 0.019 0.015 0.016 EPS 0.822 0.825 0.889 0.893 0.901 0.908 0.915 0.899 NSS 6.7 8.3 10.3 11.9 12.0 12.0 12.0 12.0 |======================== 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 1701 1976 276 0.999 0.043 0.238 3.768 0.048 -0.074 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.107 0.039 0.001 60 216 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.24 0.60 1.01 1.12 1.72 9.41 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.11 0.00 0.84 0.95 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 -0.074 -0.128 -0.051 -0.011 0.016 -0.012 0.051 0.158 -0.098 -0.018 PACF -0.074 -0.134 -0.073 -0.040 -0.006 -0.023 0.048 0.169 -0.057 0.019 95% C.L. 0.120 0.121 0.123 0.123 0.123 0.123 0.123 0.124 0.127 0.128 |------------------ 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 2 0.029 -0.085 -0.137 |---------- 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 -0.008 -0.076 -0.035 0.014 0.014 0.057 0.157 -0.078 -0.004 PACF -0.007 -0.008 -0.076 -0.036 0.012 0.008 0.053 0.161 -0.072 0.006 95% C.L. 0.120 0.120 0.120 0.121 0.121 0.121 0.121 0.122 0.125 0.125 |----------------- 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 0.006 -0.008 -0.008 |========================= 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 1701 1976 276 0.999 0.047 0.292 3.314 0.038 0.434 |------------ 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 0.433 0.263 0.101 0.071 0.083 0.095 0.129 0.168 0.020 0.025 PACF 0.433 0.094 -0.053 0.030 0.060 0.042 0.072 0.093 -0.133 0.022 95% C.L. 0.120 0.141 0.148 0.149 0.150 0.150 0.151 0.153 0.155 0.155 |------------------- 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 0.201 0.443 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.20 MINUTES