SIGNAL EXTRACTION IN 'ARIMA' TIME SERIES (BETA VERSION) (*) BY V. GOMEZ & A. MARAVALL, with the programming assistance of G. CAPORELLO Thanks are due to G. FIORENTINI and C. PLANAS for their research assistance (Based on an original program developed by J.P.BURMAN at the Bank of England, version 1982) (*) Copyright : V. GOMEZ, A. MARAVALL (1996) FIRST PART: ARIMA ESTIMATION SERIES TITLE: lg PREADJUSTED WITH TRAMO : YES METHOD: MAXIMUM LIKELIHOOD NO OF OBSERVATIONS =144 ORIGINAL UNCORRECTED SERIES (from TRAMO) YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.718 4.771 4.883 4.860 4.796 4.905 4.997 4.997 4.913 4.779 4.644 4.771 1950 4.745 4.836 4.949 4.905 4.828 5.004 5.136 5.136 5.063 4.890 4.736 4.942 1951 4.977 5.011 5.182 5.094 5.147 5.182 5.293 5.293 5.215 5.088 4.984 5.112 1952 5.142 5.193 5.263 5.199 5.209 5.385 5.438 5.489 5.342 5.252 5.147 5.268 1953 5.278 5.278 5.464 5.460 5.434 5.493 5.576 5.606 5.468 5.352 5.193 5.303 1954 5.318 5.236 5.460 5.425 5.455 5.576 5.710 5.680 5.557 5.434 5.313 5.434 1955 5.489 5.451 5.587 5.595 5.598 5.753 5.897 5.849 5.743 5.613 5.468 5.628 1956 5.649 5.624 5.759 5.746 5.762 5.924 6.023 6.004 5.872 5.724 5.602 5.724 1957 5.753 5.707 5.875 5.852 5.872 6.045 6.142 6.146 6.001 5.849 5.720 5.817 1958 5.829 5.762 5.892 5.852 5.894 6.075 6.196 6.225 6.001 5.883 5.737 5.820 1959 5.886 5.835 6.006 5.981 6.040 6.157 6.306 6.326 6.138 6.009 5.892 6.004 1960 6.033 5.969 6.038 6.133 6.157 6.282 6.433 6.407 6.230 6.133 5.966 6.068 PREADJUSTMENT COMPONENT Outliers and Other Deterministic Effects (from TRAMO) YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1951 0.000 0.000 0.000 0.000 0.096 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1952 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1953 0.000 0.000 0.000 0.000 0.000 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1954 -0.097 -0.177 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1955 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1956 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1957 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1958 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1959 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1960 -0.097 -0.097 -0.200 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 ORIGINAL SERIES (Corrected by TRAMO) YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.718 4.771 4.883 4.860 4.796 4.905 4.997 4.997 4.913 4.779 4.644 4.771 1950 4.745 4.836 4.949 4.905 4.828 5.004 5.136 5.136 5.063 4.890 4.736 4.942 1951 4.977 5.011 5.182 5.094 5.052 5.182 5.293 5.293 5.215 5.088 4.984 5.112 1952 5.142 5.193 5.263 5.199 5.209 5.385 5.438 5.489 5.342 5.252 5.147 5.268 1953 5.278 5.278 5.464 5.460 5.434 5.590 5.673 5.703 5.565 5.449 5.290 5.400 1954 5.415 5.413 5.556 5.522 5.552 5.673 5.807 5.777 5.654 5.530 5.410 5.530 1955 5.586 5.548 5.684 5.691 5.695 5.849 5.994 5.946 5.840 5.710 5.565 5.724 1956 5.746 5.721 5.856 5.843 5.859 6.021 6.120 6.101 5.969 5.820 5.699 5.820 1957 5.849 5.804 5.972 5.949 5.969 6.142 6.239 6.243 6.098 5.946 5.817 5.914 1958 5.926 5.859 5.988 5.949 5.991 6.172 6.293 6.321 6.098 5.980 5.833 5.917 1959 5.983 5.932 6.103 6.078 6.137 6.254 6.403 6.423 6.234 6.106 5.988 6.101 1960 6.130 6.065 6.238 6.230 6.254 6.379 6.530 6.504 6.327 6.230 6.063 6.165 INPUT PARAMETERS ---------------- LAM= 1 IMEAN= 0 RSA= 0 MQ=12 P= 0 BP= 0 Q= 1 BQ= 1 D= 1 BD= 1 NOADMISS= 1 RMOD= 0.500 M=36 QMAX=50 BIAS= 1 SMTR= 0 THTR= -0.400 MAXBIAS= 0.500 IQM= 24 OUT= 1 EPSPHI= 2.000 MAXIT= 20 XL= 0.990 SEK= 3.000 TRANSFORMATION: Z -> Z NONSEASONAL DIFFERENCING D= 1 SEASONAL DIFFERENCING BD= 1 DIFFERENCED SERIES YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1950 0.039 0.000 -0.021 -0.013 0.066 0.040 0.000 0.011 -0.039 -0.019 0.079 1951 0.061 -0.057 0.059 -0.045 0.035 -0.045 -0.020 0.000 -0.005 0.045 0.050 -0.077 1952 -0.005 0.017 -0.101 0.024 0.053 0.045 -0.058 0.051 -0.068 0.037 -0.001 -0.008 1953 -0.019 -0.051 0.116 0.060 -0.037 -0.019 0.029 -0.021 0.009 -0.026 -0.054 -0.010 1954 0.005 -0.001 -0.043 -0.030 0.056 -0.035 0.052 -0.060 0.014 -0.007 0.038 0.010 1955 0.040 -0.037 -0.007 0.042 -0.027 0.034 0.010 -0.018 0.017 -0.007 -0.025 0.039 1956 -0.034 0.013 -0.001 -0.020 0.012 0.008 -0.045 0.028 -0.025 -0.019 0.024 -0.038 1957 0.008 -0.021 0.033 -0.010 0.004 0.011 -0.002 0.024 -0.013 -0.004 -0.008 -0.025 1958 -0.017 -0.021 -0.038 -0.017 0.022 0.008 0.024 0.024 -0.078 0.034 -0.018 -0.013 1959 0.054 0.016 0.042 0.014 0.017 -0.064 0.028 -0.008 0.035 -0.011 0.030 0.029 1960 -0.037 -0.013 0.001 0.017 -0.035 0.009 0.001 -0.046 0.012 0.032 -0.050 -0.010 MEAN OF DIFFERENCED SERIES 0.2909E-03 MEAN SET EQUAL TO ZERO VARIANCE OF Z SERIES = 0.2302E+00 VARIANCE OF DIFFERENCED SERIES = 0.1284E-02 AUTOCORRELATIONS OF STATIONARY SERIES ------------------------------------- -0.2627 -0.0437 -0.0049 -0.0590 -0.0168 0.1180 -0.0315 -0.0767 0.0886 0.0326 0.1422 -0.3625 SE 0.0874 0.0932 0.0934 0.0934 0.0936 0.0937 0.0948 0.0949 0.0954 0.0960 0.0961 0.0977 0.0107 0.0830 -0.1044 -0.0291 0.1764 -0.1565 0.0302 -0.0071 0.0134 -0.1076 0.1260 -0.0046 SE 0.1074 0.1074 0.1079 0.1087 0.1088 0.1109 0.1126 0.1127 0.1127 0.1127 0.1135 0.1145 -0.0853 0.0143 0.1217 0.0195 -0.0547 0.0400 -0.0942 0.1388 -0.0034 -0.0381 -0.0081 -0.1044 SE 0.1145 0.1150 0.1150 0.1160 0.1160 0.1162 0.1163 0.1169 0.1182 0.1182 0.1183 0.1183 PARTIAL AUTOCORRELATIONS ------------------------ -0.2627 -0.1211 -0.0540 -0.0882 -0.0686 0.0890 0.0205 -0.0747 0.0528 0.0830 0.2100 -0.3155 SE 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 -0.1731 0.0470 -0.1113 -0.2093 0.0903 0.0203 -0.0070 -0.1657 0.0956 -0.0089 0.1293 -0.0867 SE 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 -0.1267 0.0220 0.1142 -0.0706 0.0479 0.0387 -0.0480 0.0658 0.0736 -0.1452 0.0981 -0.1143 SE 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 0.0874 MODEL FITTED NONSEASONAL P= 0 D= 1 Q= 1 SEASONAL BP= 0 BD= 1 BQ= 1 PERIODICITY MQ= 12 MEAN = 0.00000 SE = ******* ARIMA PARAMETERS TH = -0.3318 SE = ***** BTH = -0.4968 SE = ***** RESIDUALS X 10.0D-1 YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.018 -0.031 -0.090 0.121 -0.039 -0.268 -0.198 -0.098 -0.001 0.055 0.016 -0.187 1950 -0.364 0.252 0.048 -0.114 -0.206 0.466 0.500 0.150 0.179 -0.300 -0.295 0.598 1951 0.657 -0.171 0.512 -0.340 0.151 -0.139 -0.078 -0.034 0.001 0.271 0.494 -0.261 1952 0.087 0.010 -0.728 -0.257 0.578 0.546 -0.414 0.367 -0.554 0.323 0.300 -0.192 1953 -0.172 -0.580 0.604 0.793 0.224 0.061 0.018 0.046 -0.232 -0.086 -0.474 -0.402 1954 -0.141 -0.320 -0.139 -0.056 0.524 -0.187 0.453 -0.431 -0.122 -0.114 0.125 0.021 1955 0.407 -0.366 -0.204 0.348 0.119 0.195 0.421 -0.324 0.073 -0.080 -0.191 0.317 1956 -0.035 -0.131 -0.098 -0.027 0.114 0.196 -0.212 -0.018 -0.171 -0.295 0.056 -0.173 1957 -0.051 -0.281 0.209 -0.028 0.092 0.216 -0.087 0.235 -0.135 -0.199 -0.065 -0.364 1958 -0.289 -0.442 -0.379 -0.341 0.160 0.226 0.236 0.448 -0.740 0.018 -0.171 -0.359 1959 0.339 0.097 0.336 0.149 0.352 -0.440 0.216 0.173 -0.037 0.010 0.211 0.207 1960 -0.072 -0.163 0.106 0.226 -0.127 -0.233 0.116 -0.370 -0.049 0.313 -0.294 -0.129 TEST-STATISTICS ON RESIDUALS ---------------------------- MEAN= -0.3299E-03 ST.DEV.= 0.2415E-02 OF MEAN T-VALUE= -0.1366 NORMALITY TEST= 1.142 ( CHI-SQUARED(2) ) SKEWNESS= 0.2068 ( SE = 0.2041 ) KURTOSIS= 2.8611 ( SE = 0.4082 ) SUM OF SQUARES= 0.1210E+00 DURBIN-WATSON= 1.9723 STANDARD DEVI.= 0.3063E-01 OF RESID. VARIANCE= 0.9379E-03 OF RESID. AUTOCORRELATIONS OF RESIDUAL ---------------------------- 0.0131 -0.0172 -0.0502 -0.1464 0.0106 0.0763 -0.0401 -0.1172 0.0742 0.0444 0.1000 -0.0548 SE 0.0833 0.0833 0.0834 0.0836 0.0853 0.0854 0.0858 0.0860 0.0871 0.0875 0.0877 0.0884 -0.1270 0.0686 -0.1081 -0.0801 0.1197 -0.1088 -0.0544 -0.0003 -0.0018 -0.1051 0.1633 -0.0160 SE 0.0887 0.0899 0.0903 0.0912 0.0917 0.0928 0.0936 0.0939 0.0939 0.0939 0.0947 0.0966 -0.0421 0.0953 0.0395 -0.0015 -0.0633 -0.0141 -0.0286 0.1305 -0.0271 -0.0503 -0.0045 -0.0631 SE 0.0966 0.0968 0.0974 0.0975 0.0975 0.0978 0.0978 0.0979 0.0991 0.0991 0.0993 0.0993 THE LJUNG-BOX Q VALUE IS 25.70 AND IF RESIDUALS ARE RANDOM IT SHOULD BE DISTRIBUTED AS CHI-SQUARED (22) APPROXIMATE TEST OF RUNS ON RESIDUALS ------------------------------------- NUM.DATA= 144 NUM.(+)= 72 NUM.(-)= 72 T-VALUE= -1.17 AUTOCORRELATIONS OF SQUARED RESIDUAL ------------------------------------ 0.2777 0.1351 0.0624 -0.0157 0.0543 0.1979 0.1192 0.1039 0.0923 0.0389 0.0830 -0.0374 SE 0.0833 0.0895 0.0909 0.0912 0.0913 0.0915 0.0944 0.0954 0.0962 0.0968 0.0969 0.0974 -0.0109 0.0169 0.0819 0.0391 0.1069 -0.0251 -0.1430 -0.0236 -0.0197 -0.0571 0.0447 -0.0074 SE 0.0975 0.0975 0.0976 0.0980 0.0982 0.0990 0.0990 0.1004 0.1005 0.1005 0.1007 0.1009 0.0245 0.1323 0.0974 0.0691 -0.0583 -0.1472 -0.1124 0.0172 0.0054 -0.0130 -0.0803 -0.1731 SE 0.1009 0.1009 0.1021 0.1027 0.1031 0.1033 0.1047 0.1056 0.1056 0.1056 0.1056 0.1060 THE LJUNG-BOX Q VALUE IS 32.72 AND IF RESIDUALS ARE RANDOM IT SHOULD BE DISTRIBUTED AS CHI-SQUARED (24) BACKWARD RESIDUALS YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.011 0.010 -0.019 0.035 0.059 0.023 0.004 -0.008 -0.005 0.017 0.051 0.038 1950 -0.054 0.030 -0.005 0.044 -0.041 -0.034 0.008 -0.016 0.059 0.011 -0.088 -0.019 1951 -0.024 -0.032 0.068 0.054 0.022 -0.029 0.007 -0.057 0.013 -0.025 -0.015 -0.019 1952 -0.025 0.110 0.046 -0.018 -0.015 0.036 -0.050 -0.001 -0.046 -0.039 0.000 0.006 1953 -0.034 -0.044 -0.001 0.046 -0.007 0.029 -0.055 0.011 -0.001 0.038 0.022 0.014 1954 -0.035 0.008 0.027 -0.005 0.035 -0.009 0.000 -0.012 -0.018 -0.015 0.004 -0.030 1955 0.000 0.004 -0.020 0.019 -0.001 -0.029 0.026 -0.050 -0.012 0.000 -0.050 0.002 1956 -0.021 0.022 -0.007 0.018 0.008 0.022 0.016 -0.040 0.006 -0.023 -0.027 -0.005 1957 -0.022 -0.018 0.000 0.020 -0.009 0.036 -0.005 -0.048 0.032 -0.008 0.014 0.047 1958 0.026 0.046 0.016 -0.015 -0.050 0.022 -0.012 0.042 0.005 0.014 0.013 -0.035 1959 -0.010 -0.002 0.003 -0.027 0.009 -0.014 -0.031 0.013 0.010 -0.042 -0.005 0.011 1960 0.004 -0.010 -0.005 0.013 0.008 -0.004 0.018 -0.007 -0.010 0.020 0.001 -0.002 SECOND PART: DERIVATION OF THE MODELS FOR THE COMPONENTS SERIES TITLE: lg MODEL PARAMETERS (0,1,1)(0,1,1) PARAMETER VALUES PASSED FROM ARIMA ESTIMATION (TRUE SIGNS) THETA PARAMETERS 1.00 -0.33 BTHETA PARAMETERS 1.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 -0.50 PHI PARAMETERS 1.00 BPHI PARAMETERS 1.00 NUMERATOR OF THE MODEL ---------------------- 1.0000 -0.3318 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -0.4968 0.1648 STATIONARY AUTOREGRESSIVE TREND-CYCLE 1.0000 NON-STATIONARY AUTOREGRESSIVE TREND-CYCLE 1.0000 -2.0000 1.0000 AUTOREGRESSIVE TREND-CYCLE -------------------------- 1.0000 -2.0000 1.0000 STATIONARY AUTOREGRESSIVE TRANSITORY COMP. 1.0000 NON-STATIONARY AUTOREGRESSIVE TRANSITORY COMP. 1.0000 AUTOREGRESSIVE TRANSITORY COMP. ------------------------------ 1.0000 STATIONARY AUTOREGRESSIVE SEASONAL COMPONENT 1.0000 NON-STATIONARY AUTOREGRESSIVE SEASONAL COMPONENT 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 AUTOREGRESSIVE SEASONAL COMPONENT --------------------------------- 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 STATIONARY AUTOREGRESSIVE SEASONALLY ADJUSTED COMPONENT 1.0000 NON-STATIONARY AUTOREGRESSIVE SEASONALLY ADJUSTED COMPONENT 1.0000 -2.0000 1.0000 AUTOREGRESSIVE SEASONALLY ADJUSTED COMPONENT -------------------------------------------- 1.0000 -2.0000 1.0000 TOTAL DENOMINATOR ----------------- 1.0000 -1.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 -1.0000 1.0000 MA ROOTS OF TREND-CYCLE ----------------------- REAL PART IMAGINARY PART MODULUS ARGUMENT PERIOD (DEG.) 0.943 0.000 0.943 0.000 - -1.000 0.000 1.000 180.000 2.0 TOTAL SQUARED ERROR= 0.2562401E-32 MA ROOTS OF SEAS. ----------------- REAL PART IMAGINARY PART MODULUS ARGUMENT PERIOD (DEG.) 0.626 0.637 0.893 45.488 7.914 -0.690 0.688 0.975 135.058 2.666 0.236 0.896 0.927 75.274 4.783 -0.249 0.920 0.953 105.129 3.424 0.589 0.000 0.589 0.000 - -0.966 0.259 1.000 165.017 2.182 TOTAL SQUARED ERROR= 0.4873125E-24 MA ROOTS OF SEASONALLY ADJUSTED SERIES -------------------------------------- REAL PART IMAGINARY PART MODULUS ARGUMENT PERIOD (DEG.) 0.349 0.000 0.349 0.000 - 0.943 0.000 0.943 0.000 - TOTAL SQUARED ERROR= 0.0000000E+00 MODELS FOR THE COMPONENTS ------------------------- TREND-CYCLE NUMERATOR 1.0000 0.0565 -0.9435 TREND-CYCLE DENOMINATOR 1.0000 -2.0000 1.0000 INNOV. VAR. (*) 0.06147 SEAS. NUMERATOR 1.0000 1.4977 1.6260 1.5869 1.4038 1.1548 0.8754 0.5905 0.3449 0.1108 -0.0397 -0.3476 SEAS. DENOMINATOR 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 INNOV. VAR. (*) 0.07366 IRREGULAR VAR. 0.24845 SEASONALLY ADJUSTED NUMERATOR 1.0000 -1.2925 0.3293 SEASONALLY ADJUSTED DENOMINATOR 1.0000 -2.0000 1.0000 INNOV. VAR. (*) 0.57829 (*) IN UNITS OF VAR(A) MOVING AVERAGE REPRESENTATION OF ESTIMATORS (NONSTATIONARY) The last column (the sum of the Psi-Weights) should be zero for negative lags, 1 for lag=0, and equal to the Box-Jenkins Psi-Weights for positive lags. PSIEP(LAG), for example, represents the effect of the overall innovation a(t-lag) on the estimator of the trend for period t. Similarly for the other components. LAG PSIEP PSIES PSIEC PSIEA PSIUE PSIEP + PSIES + PSIUE -24 -0.0271 0.0892 0.0000 -0.0892 -0.0621 0.0000 -23 -0.0338 0.0338 0.0000 -0.0338 0.0000 0.0000 -22 -0.0254 0.0254 0.0000 -0.0254 0.0000 0.0000 -21 -0.0165 0.0164 0.0000 -0.0164 0.0000 0.0000 -20 -0.0069 0.0069 0.0000 -0.0069 0.0000 0.0000 -19 0.0031 -0.0032 0.0000 0.0032 0.0001 0.0000 -18 0.0136 -0.0140 0.0000 0.0140 0.0003 0.0000 -17 0.0243 -0.0253 0.0000 0.0253 0.0010 0.0000 -16 0.0343 -0.0373 0.0000 0.0373 0.0031 0.0000 -15 0.0411 -0.0503 0.0000 0.0503 0.0092 0.0000 -14 0.0370 -0.0647 0.0000 0.0647 0.0277 0.0000 -13 -0.0010 -0.0825 0.0000 0.0825 0.0835 0.0000 -12 -0.0545 0.1795 0.0000 -0.1795 -0.1250 0.0000 -11 -0.0680 0.0680 0.0000 -0.0680 0.0000 0.0000 -10 -0.0511 0.0511 0.0000 -0.0511 0.0000 0.0000 -9 -0.0331 0.0331 0.0000 -0.0331 0.0000 0.0000 -8 -0.0138 0.0139 0.0000 -0.0139 -0.0001 0.0000 -7 0.0067 -0.0065 0.0000 0.0065 -0.0002 0.0000 -6 0.0287 -0.0280 0.0000 0.0280 -0.0007 0.0000 -5 0.0526 -0.0506 0.0000 0.0506 -0.0020 0.0000 -4 0.0803 -0.0742 0.0000 0.0742 -0.0061 0.0000 -3 0.1167 -0.0984 0.0000 0.0984 -0.0183 0.0000 -2 0.1769 -0.1219 0.0000 0.1219 -0.0551 0.0000 -1 0.3070 -0.1410 0.0000 0.1410 -0.1660 0.0000 0 0.4700 0.2815 0.0000 0.7185 0.2484 1.0000 1 0.5560 0.1122 0.0000 0.5560 0.0000 0.6682 2 0.5841 0.0842 0.0000 0.5841 0.0000 0.6682 3 0.6121 0.0561 0.0000 0.6121 0.0000 0.6682 4 0.6401 0.0281 0.0000 0.6401 0.0000 0.6682 5 0.6681 0.0001 0.0000 0.6681 0.0000 0.6682 6 0.6961 -0.0279 0.0000 0.6961 0.0000 0.6682 7 0.7242 -0.0559 0.0000 0.7242 0.0000 0.6682 8 0.7522 -0.0840 0.0000 0.7522 0.0000 0.6682 9 0.7802 -0.1120 0.0000 0.7802 0.0000 0.6682 10 0.8082 -0.1400 0.0000 0.8082 0.0000 0.6682 11 0.8362 -0.1680 0.0000 0.8362 0.0000 0.6682 12 0.8642 0.3071 0.0000 0.8642 0.0000 1.1714 13 0.8923 0.1122 0.0000 0.8923 0.0000 1.0044 14 0.9203 0.0842 0.0000 0.9203 0.0000 1.0044 15 0.9483 0.0561 0.0000 0.9483 0.0000 1.0044 16 0.9763 0.0281 0.0000 0.9763 0.0000 1.0044 17 1.0043 0.0001 0.0000 1.0043 0.0000 1.0044 18 1.0324 -0.0279 0.0000 1.0324 0.0000 1.0044 19 1.0604 -0.0559 0.0000 1.0604 0.0000 1.0044 20 1.0884 -0.0840 0.0000 1.0884 0.0000 1.0044 21 1.1164 -0.1120 0.0000 1.1164 0.0000 1.0044 22 1.1444 -0.1400 0.0000 1.1444 0.0000 1.0044 23 1.1724 -0.1680 0.0000 1.1724 0.0000 1.0044 24 1.2005 0.3071 0.0000 1.2005 0.0000 1.5076 WIENER-KOLMOGOROV FILTERS (ONE SIDE) TREND-CYCLE COMPONENT 0.2588 0.1809 0.0768 0.0414 0.0289 0.0240 0.0214 0.0195 0.0173 0.0132 0.0034 -0.0237 -0.0441 -0.0254 -0.0001 0.0079 0.0102 0.0105 0.0102 0.0095 0.0085 0.0065 0.0017 -0.0118 -0.0219 -0.0126 -0.0001 0.0039 0.0050 0.0052 0.0051 0.0047 0.0042 0.0032 0.0008 -0.0058 -0.0109 -0.0063 0.0000 0.0019 0.0025 0.0026 0.0025 0.0024 0.0021 0.0016 0.0004 -0.0029 -0.0054 -0.0031 0.0000 0.0010 0.0012 0.0013 0.0012 0.0012 0.0010 0.0008 0.0002 -0.0014 SA SERIES COMPONENT 0.7573 0.0143 0.0215 0.0231 0.0229 0.0220 0.0209 0.0198 0.0187 0.0178 0.0173 0.0182 -0.1696 0.0165 0.0138 0.0125 0.0117 0.0110 0.0104 0.0099 0.0093 0.0088 0.0086 0.0091 -0.0842 0.0082 0.0069 0.0062 0.0058 0.0055 0.0052 0.0049 0.0046 0.0044 0.0043 0.0045 -0.0419 0.0041 0.0034 0.0031 0.0029 0.0027 0.0026 0.0024 0.0023 0.0022 0.0021 0.0022 -0.0208 0.0020 0.0017 0.0015 0.0014 0.0014 0.0013 0.0012 0.0011 0.0011 0.0011 0.0011 SEASONAL COMPONENT 0.2427 -0.0143 -0.0215 -0.0231 -0.0229 -0.0220 -0.0209 -0.0198 -0.0187 -0.0178 -0.0173 -0.0182 0.1696 -0.0165 -0.0138 -0.0125 -0.0117 -0.0110 -0.0104 -0.0099 -0.0093 -0.0088 -0.0086 -0.0091 0.0842 -0.0082 -0.0069 -0.0062 -0.0058 -0.0055 -0.0052 -0.0049 -0.0046 -0.0044 -0.0043 -0.0045 0.0419 -0.0041 -0.0034 -0.0031 -0.0029 -0.0027 -0.0026 -0.0024 -0.0023 -0.0022 -0.0021 -0.0022 0.0208 -0.0020 -0.0017 -0.0015 -0.0014 -0.0014 -0.0013 -0.0012 -0.0011 -0.0011 -0.0011 -0.0011 IRREGULAR COMPONENT 0.4985 -0.1666 -0.0553 -0.0183 -0.0061 -0.0020 -0.0005 0.0003 0.0015 0.0046 0.0139 0.0419 -0.1254 0.0419 0.0139 0.0046 0.0015 0.0005 0.0003 0.0003 0.0008 0.0023 0.0069 0.0208 -0.0623 0.0208 0.0069 0.0023 0.0008 0.0003 0.0001 0.0002 0.0004 0.0011 0.0034 0.0103 -0.0310 0.0103 0.0034 0.0011 0.0004 0.0001 0.0001 0.0001 0.0002 0.0006 0.0017 0.0051 -0.0154 0.0051 0.0017 0.0006 0.0002 0.0001 0.0000 0.0000 0.0001 0.0003 0.0008 0.0026 DISTRIBUTION OF COMPONENT, THEORETICAL ESTIMATOR AND EMPIRICAL ESTIMATE ----------------------------------------------------------------------- AUTOCORRELATION FUNCTION OF COMPONENTS (STATIONARY TRANSFORMATION) TREND-CYCLE LAG COMPONENT ESTIMATOR ESTIMATE 1 0.002 0.386 0.400 2 -0.498 -0.362 -0.364 3 0.000 -0.331 -0.423 4 0.000 -0.109 -0.211 5 0.000 -0.035 0.029 6 0.000 -0.008 0.116 7 0.000 0.006 -0.042 8 0.000 0.027 -0.074 9 0.000 0.084 0.159 10 0.000 0.092 0.285 11 0.000 -0.096 0.018 12 0.000 -0.251 -0.325 VAR.(*) 0.116 0.021 0.021 SEASONAL ADJUSTED LAG COMPONENT ESTIMATOR ESTIMATE 1 -0.618 -0.621 -0.607 2 0.119 0.122 0.091 3 0.000 0.000 0.055 4 0.000 0.000 -0.081 5 0.000 0.000 0.007 6 0.000 0.000 0.091 7 0.000 0.000 -0.033 8 0.000 0.000 -0.105 9 0.000 0.000 0.126 10 0.000 -0.031 -0.100 11 0.000 0.156 0.207 12 0.000 -0.252 -0.216 VAR.(*) 1.607 1.197 1.115 SEASONAL LAG COMPONENT ESTIMATOR ESTIMATE 1 0.928 0.791 0.808 2 0.791 0.442 0.432 3 0.622 0.054 -0.020 4 0.449 -0.295 -0.412 5 0.289 -0.550 -0.640 6 0.156 -0.678 -0.727 7 0.056 -0.666 -0.670 8 -0.008 -0.521 -0.472 9 -0.039 -0.270 -0.132 10 -0.043 0.043 0.254 11 -0.027 0.356 0.585 12 0.000 0.589 0.746 VAR.(*) 0.963 0.111 0.129 IRREGULAR LAG COMPONENT ESTIMATOR ESTIMATE 1 0.000 -0.334 -0.309 2 0.000 -0.111 -0.131 3 0.000 -0.037 -0.025 4 0.000 -0.012 -0.106 5 0.000 -0.004 0.019 6 0.000 -0.001 0.121 7 0.000 0.001 -0.052 8 0.000 0.003 -0.116 9 0.000 0.009 0.119 10 0.000 0.028 0.043 11 0.000 0.084 0.151 12 0.000 -0.252 -0.263 VAR.(*) 0.248 0.124 0.116 (*) IN UNITS OF VAR(A) For all components it should happen that : - Var(Component) > Var(Estimator) - Var(Estimator) close to Var(Estimate) CROSSCORRELATION BETWEEN STATIONARY TRANSFORMATION OF ESTIMATORS ESTIMATOR ESTIMATE TREND-CYCLE/SEASONAL -0.136 -0.151 SEASONAL/IRREGULAR 0.055 0.097 TREND-CYCLE/IRREGULAR -0.127 -0.140 THIRD PART: ERROR ANALYSIS FINAL ESTIMATION ERROR REVISION IN CONCURRENT ESTIMATOR ACF (LAG) TREND-CYCLE ADJUSTED TREND-CYCLE ADJUSTED 1 0.735 0.352 0.631 0.478 2 0.324 0.130 0.390 0.265 3 0.090 -0.041 0.202 0.081 4 -0.055 -0.165 0.052 -0.069 5 -0.142 -0.243 -0.065 -0.181 6 -0.182 -0.277 -0.149 -0.253 7 -0.181 -0.269 -0.199 -0.283 8 -0.142 -0.222 -0.213 -0.269 9 -0.071 -0.138 -0.189 -0.209 10 0.023 -0.020 -0.119 -0.101 11 0.115 0.130 0.012 0.057 12 0.165 0.616 0.154 0.516 VAR.(*) 0.123 0.119 0.171 0.128 TOTAL ESTIMATION ERROR (CONCURRENT ESTIMATOR) ---------------------- ACF (LAG) TREND-CYCLE ADJUSTED 1 0.674 0.418 2 0.362 0.200 3 0.155 0.022 4 0.007 -0.115 5 -0.097 -0.211 6 -0.163 -0.265 7 -0.191 -0.276 8 -0.183 -0.246 9 -0.140 -0.175 10 -0.060 -0.062 11 0.055 0.092 12 0.158 0.564 VAR.(*) 0.294 0.247 (*) IN UNITS OF VAR(A) VARIANCE OF THE REVISION ERROR (*) ------------------------------ ADDITIONAL TREND-CYCLE ADJUSTED PERIODS 0 0.1711 0.1283 12 0.1042E-01 0.3427E-01 24 0.2573E-02 0.8460E-02 36 0.6352E-03 0.2088E-02 48 0.1568E-03 0.5155E-03 60 0.3871E-04 0.1273E-03 PERCENTAGE REDUCTION IN THE STANDARD ERROR OF THE REVISION AFTER ADDITIONAL YEARS (COMPARISON WITH CONCURRENT ESTIMATORS) AFTER 1 YEAR 75.32 48.32 AFTER 2 YEAR 87.74 74.32 AFTER 3 YEAR 93.91 87.24 AFTER 4 YEAR 96.97 93.66 AFTER 5 YEAR 98.50 96.85 VARIANCE OF THE REVISION ERROR FOR THE SEASONAL COMPONENT (ONE YEAR AHEAD ADJUSTMENT) ------------------------------------------------------------------------------------- PERIODS AHEAD VARIANCE (*) 0 0.1283 1 0.2076 2 0.2201 3 0.2272 4 0.2304 5 0.2312 6 0.2312 7 0.2319 8 0.2351 9 0.2421 10 0.2547 11 0.2743 12 0.3025 AVERAGE PERCENTAGE REDUCTION IN RMSE FROM CONCURRENT ADJUSTMENT 24.68 (*) IN UNITS OF VAR(A) DECOMPOSITION OF THE SERIES: RECENT ESTIMATES --------------------------------------------- PERIOD SERIES TREND-CYCLE ADJUSTED ESTIMATE STANDARD ERROR ESTIMATE STANDARD ERROR TOTAL OF REVISION TOTAL OF REVISION -24 5.917 6.056 0.1086E-01 0.1554E-02 6.038 0.1094E-01 0.2817E-02 -23 5.983 6.070 0.1089E-01 0.1761E-02 6.075 0.1128E-01 0.3923E-02 -22 5.932 6.087 0.1094E-01 0.2042E-02 6.086 0.1132E-01 0.4057E-02 -21 6.103 6.102 0.1097E-01 0.2185E-02 6.106 0.1135E-01 0.4131E-02 -20 6.078 6.116 0.1098E-01 0.2243E-02 6.111 0.1136E-01 0.4162E-02 -19 6.137 6.128 0.1098E-01 0.2253E-02 6.142 0.1136E-01 0.4167E-02 -18 6.254 6.137 0.1098E-01 0.2255E-02 6.125 0.1136E-01 0.4168E-02 -17 6.403 6.150 0.1099E-01 0.2293E-02 6.148 0.1137E-01 0.4190E-02 -16 6.423 6.164 0.1102E-01 0.2411E-02 6.173 0.1140E-01 0.4261E-02 -15 6.234 6.175 0.1107E-01 0.2629E-02 6.174 0.1146E-01 0.4412E-02 -14 6.106 6.186 0.1114E-01 0.2914E-02 6.175 0.1156E-01 0.4673E-02 -13 5.988 6.201 0.1119E-01 0.3127E-02 6.206 0.1173E-01 0.5075E-02 -12 6.101 6.214 0.1119E-01 0.3127E-02 6.222 0.1200E-01 0.5669E-02 -11 6.130 6.222 0.1132E-01 0.3544E-02 6.222 0.1320E-01 0.7897E-02 -10 6.065 6.229 0.1151E-01 0.4110E-02 6.222 0.1336E-01 0.8166E-02 -9 6.238 6.239 0.1161E-01 0.4398E-02 6.239 0.1345E-01 0.8315E-02 -8 6.230 6.249 0.1166E-01 0.4513E-02 6.258 0.1349E-01 0.8377E-02 -7 6.254 6.254 0.1166E-01 0.4533E-02 6.255 0.1350E-01 0.8387E-02 -6 6.379 6.259 0.1167E-01 0.4538E-02 6.253 0.1350E-01 0.8390E-02 -5 6.530 6.263 0.1170E-01 0.4622E-02 6.272 0.1352E-01 0.8433E-02 -4 6.504 6.267 0.1181E-01 0.4895E-02 6.257 0.1361E-01 0.8575E-02 -3 6.327 6.274 0.1206E-01 0.5478E-02 6.270 0.1380E-01 0.8871E-02 -2 6.230 6.283 0.1258E-01 0.6540E-02 6.296 0.1413E-01 0.9369E-02 -1 6.063 6.287 0.1370E-01 0.8493E-02 6.282 0.1461E-01 0.1008E-01 0 6.165 6.291 0.1661E-01 0.1267E-01 6.288 0.1524E-01 0.1097E-01 STANDARD ERROR OF 0.1075E-01 0.1057E-01 FINAL ESTIMATOR PERIOD SEASONAL ESTIMATE STANDARD ERROR TOTAL OF REVISION -24 -0.1211 0.1094E-01 0.2817E-02 -23 -0.9202E-01 0.1128E-01 0.3923E-02 -22 -0.1541 0.1132E-01 0.4057E-02 -21 -0.3120E-02 0.1135E-01 0.4131E-02 -20 -0.3289E-01 0.1136E-01 0.4162E-02 -19 -0.4991E-02 0.1136E-01 0.4167E-02 -18 0.1290 0.1136E-01 0.4168E-02 -17 0.2552 0.1137E-01 0.4190E-02 -16 0.2497 0.1140E-01 0.4261E-02 -15 0.6015E-01 0.1146E-01 0.4412E-02 -14 -0.6912E-01 0.1156E-01 0.4673E-02 -13 -0.2172 0.1173E-01 0.5075E-02 -12 -0.1216 0.1200E-01 0.5669E-02 -11 -0.9180E-01 0.1320E-01 0.7897E-02 -10 -0.1568 0.1336E-01 0.8166E-02 -9 -0.1515E-02 0.1345E-01 0.8315E-02 -8 -0.2802E-01 0.1349E-01 0.8377E-02 -7 -0.1465E-02 0.1350E-01 0.8387E-02 -6 0.1261 0.1350E-01 0.8390E-02 -5 0.2576 0.1352E-01 0.8433E-02 -4 0.2462 0.1361E-01 0.8575E-02 -3 0.5767E-01 0.1380E-01 0.8871E-02 -2 -0.6578E-01 0.1413E-01 0.9369E-02 -1 -0.2189 0.1461E-01 0.1008E-01 0 -0.1230 0.1524E-01 0.1097E-01 STANDARD ERROR OF 0.1057E-01 FINAL ESTIMATOR DECOMPOSITION OF THE SERIES: FORECAST ------------------------------------- PERIOD SERIES TREND-CYCLE ADJUSTED FORECAST S.E. FORECAST STANDARD ERROR FORECAST STANDARD ERROR TOTAL OF REVISION TOTAL OF REVISION 1 6.206 0.3063E-01 6.299 0.2198E-01 0.1918E-01 6.299 0.2676E-01 0.2459E-01 2 6.148 0.3683E-01 6.306 0.2781E-01 0.2565E-01 6.306 0.3172E-01 0.2991E-01 3 6.313 0.4214E-01 6.314 0.3306E-01 0.3127E-01 6.314 0.3642E-01 0.3485E-01 4 6.295 0.4684E-01 6.322 0.3801E-01 0.3646E-01 6.322 0.4096E-01 0.3957E-01 5 6.329 0.5112E-01 6.330 0.4277E-01 0.4139E-01 6.330 0.4541E-01 0.4416E-01 6 6.464 0.5506E-01 6.338 0.4741E-01 0.4617E-01 6.338 0.4981E-01 0.4867E-01 7 6.605 0.5874E-01 6.346 0.5198E-01 0.5086E-01 6.346 0.5418E-01 0.5314E-01 8 6.599 0.6221E-01 6.354 0.5652E-01 0.5548E-01 6.354 0.5854E-01 0.5758E-01 9 6.419 0.6549E-01 6.362 0.6103E-01 0.6008E-01 6.362 0.6291E-01 0.6202E-01 10 6.306 0.6861E-01 6.370 0.6554E-01 0.6465E-01 6.370 0.6729E-01 0.6646E-01 11 6.158 0.7160E-01 6.377 0.7006E-01 0.6923E-01 6.377 0.7170E-01 0.7092E-01 12 6.262 0.7446E-01 6.385 0.7459E-01 0.7381E-01 6.385 0.7614E-01 0.7540E-01 13 6.300 0.8265E-01 6.393 0.7915E-01 0.7842E-01 6.393 0.8061E-01 0.7991E-01 14 6.243 0.8819E-01 6.401 0.8373E-01 0.8304E-01 6.401 0.8511E-01 0.8446E-01 15 6.407 0.9340E-01 6.409 0.8835E-01 0.8769E-01 6.409 0.8966E-01 0.8903E-01 16 6.390 0.9834E-01 6.417 0.9300E-01 0.9238E-01 6.417 0.9425E-01 0.9365E-01 17 6.424 0.1030 6.425 0.9769E-01 0.9710E-01 6.425 0.9888E-01 0.9831E-01 18 6.558 0.1075 6.433 0.1024 0.1019 6.433 0.1035 0.1030 19 6.700 0.1118 6.441 0.1072 0.1066 6.441 0.1083 0.1078 20 6.694 0.1160 6.448 0.1120 0.1115 6.448 0.1130 0.1125 21 6.514 0.1200 6.456 0.1169 0.1164 6.456 0.1178 0.1174 22 6.400 0.1239 6.464 0.1218 0.1213 6.464 0.1227 0.1222 23 6.253 0.1276 6.472 0.1267 0.1262 6.472 0.1276 0.1272 24 6.357 0.1313 6.480 0.1317 0.1312 6.480 0.1326 0.1321 PERIOD SEASONAL FORECAST STANDARD ERROR TOTAL OF REVISION 1 -0.9293E-01 0.1751E-01 0.1395E-01 2 -0.1583 0.1784E-01 0.1437E-01 3 -0.1734E-02 0.1802E-01 0.1460E-01 4 -0.2682E-01 0.1811E-01 0.1470E-01 5 -0.1073E-02 0.1813E-01 0.1472E-01 6 0.1258 0.1813E-01 0.1472E-01 7 0.2590 0.1815E-01 0.1475E-01 8 0.2453 0.1823E-01 0.1485E-01 9 0.5740E-01 0.1841E-01 0.1507E-01 10 -0.6395E-01 0.1872E-01 0.1545E-01 11 -0.2193 0.1921E-01 0.1604E-01 12 -0.1234 0.1989E-01 0.1684E-01 13 -0.9293E-01 0.2200E-01 0.1929E-01 14 -0.1583 0.2227E-01 0.1960E-01 15 -0.1734E-02 0.2241E-01 0.1976E-01 16 -0.2682E-01 0.2248E-01 0.1984E-01 17 -0.1073E-02 0.2250E-01 0.1986E-01 18 0.1258 0.2250E-01 0.1986E-01 19 0.2590 0.2251E-01 0.1988E-01 20 0.2453 0.2258E-01 0.1995E-01 21 0.5740E-01 0.2272E-01 0.2011E-01 22 -0.6395E-01 0.2298E-01 0.2040E-01 23 -0.2193 0.2338E-01 0.2085E-01 24 -0.1234 0.2394E-01 0.2148E-01 CONFIDENCE INTERVAL AROUND A SEASONAL COMPONENT OF 0 ---------------------------------------------------- FINAL ESTIMATOR CONCURRENT ESTIMATOR 95% CONFIDENCE -0.2072E-01 0.2072E-01 -0.2986E-01 0.2986E-01 INTERVAL 70% CONFIDENCE -0.1096E-01 0.1096E-01 -0.1580E-01 0.1580E-01 INTERVAL SAMPLE MEANS ------------ COMPLETE PERIOD LAST THREE YEARS SERIES 5.604 6.144 TREND-CYCLE 5.603 6.145 ADJUSTED 5.603 6.144 SEASONAL 0.4428E-03 -0.1145E-03 STANDARD ERROR OF ALTERNATIVE MEASURES OF GROWTH (NONANNUALIZED GROWTH) 1. PERIOD TO PERIOD GROWTH OF THE SERIES TREND-CYCLE SEASONALLY ADJ. SERIES CONCURRENT ESTIMATOR 0.010 0.016 1 - PERIOD REVISION 0.009 0.016 2 - PERIOD REVISION 0.008 0.016 3 - PERIOD REVISION 0.008 0.016 4 - PERIOD REVISION 0.008 0.016 5 - PERIOD REVISION 0.008 0.016 6 - PERIOD REVISION 0.008 0.016 7 - PERIOD REVISION 0.008 0.016 8 - PERIOD REVISION 0.008 0.016 9 - PERIOD REVISION 0.008 0.016 10 - PERIOD REVISION 0.008 0.016 11 - PERIOD REVISION 0.008 0.015 12 - PERIOD REVISION 0.008 0.013 FINAL ESTIMATOR 0.008 0.012 2. GROWTH OF A 3 - PERIOD (CENTERED) MOVING AVERAGE TREND-CYCLE SEASONALLY ADJ. SERIES CONCURRENT ESTIMATOR 0.021 0.028 1 - PERIOD REVISION 0.018 0.020 2 - PERIOD REVISION 0.017 0.020 3 - PERIOD REVISION 0.017 0.020 4 - PERIOD REVISION 0.016 0.020 5 - PERIOD REVISION 0.016 0.020 6 - PERIOD REVISION 0.016 0.020 7 - PERIOD REVISION 0.016 0.020 8 - PERIOD REVISION 0.016 0.020 9 - PERIOD REVISION 0.016 0.020 10 - PERIOD REVISION 0.016 0.019 11 - PERIOD REVISION 0.016 0.019 12 - PERIOD REVISION 0.015 0.018 FINAL ESTIMATOR 0.014 0.015 3. ACCUMULATED GROWTH OVER THE LAST DECEMBER CONCURRENT ESTIMATOR FINAL ESTIMATOR TREND-CYCLE SEASONALLY ADJ. SERIES TREND-CYCLE SEASONALLY ADJ. SERIES JANUARY 0.115 0.190 0.094 0.144 FEBRUARY 0.092 0.110 0.075 0.084 MARCH 0.073 0.081 0.058 0.061 APRIL 0.061 0.065 0.047 0.048 MAY 0.052 0.054 0.039 0.040 JUNE 0.045 0.046 0.033 0.034 JULY 0.039 0.040 0.028 0.029 AUGUST 0.034 0.034 0.024 0.025 SEPTEMBER 0.029 0.030 0.021 0.021 OCTOBER 0.025 0.025 0.018 0.018 NOVEMBER 0.021 0.021 0.016 0.015 DECEMBER 0.018 0.011 0.014 0.009 (CENTERED) ESTIMATOR OF THE PRESENT ANNUAL GROWTH STANDARD TREND-CYCLE SEAS. ADJ. ORIGINAL ERROR SERIES SERIES CONCURRENT 0.054 0.057 0.059 ESTIMATOR FINAL ESTI- 0.014 0.009 0.000 MATOR FOURTH PART: ESTIMATES OF THE COMPONENTS (LEVELS) PREADJUSTMENT COMPONENT Outliers and Other Deterministic Effects (from TRAMO) YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1951 0.000 0.000 0.000 0.000 0.096 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1952 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1953 0.000 0.000 0.000 0.000 0.000 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1954 -0.097 -0.177 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1955 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1956 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1957 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1958 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1959 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 1960 -0.097 -0.097 -0.200 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 -0.097 ORIGINAL SERIES --------------- (Corrected by TRAMO) YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.718 4.771 4.883 4.860 4.796 4.905 4.997 4.997 4.913 4.779 4.644 4.771 1950 4.745 4.836 4.949 4.905 4.828 5.004 5.136 5.136 5.063 4.890 4.736 4.942 1951 4.977 5.011 5.182 5.094 5.052 5.182 5.293 5.293 5.215 5.088 4.984 5.112 1952 5.142 5.193 5.263 5.199 5.209 5.385 5.438 5.489 5.342 5.252 5.147 5.268 1953 5.278 5.278 5.464 5.460 5.434 5.590 5.673 5.703 5.565 5.449 5.290 5.400 1954 5.415 5.413 5.556 5.522 5.552 5.673 5.807 5.777 5.654 5.530 5.410 5.530 1955 5.586 5.548 5.684 5.691 5.695 5.849 5.994 5.946 5.840 5.710 5.565 5.724 1956 5.746 5.721 5.856 5.843 5.859 6.021 6.120 6.101 5.969 5.820 5.699 5.820 1957 5.849 5.804 5.972 5.949 5.969 6.142 6.239 6.243 6.098 5.946 5.817 5.914 1958 5.926 5.859 5.988 5.949 5.991 6.172 6.293 6.321 6.098 5.980 5.833 5.917 1959 5.983 5.932 6.103 6.078 6.137 6.254 6.403 6.423 6.234 6.106 5.988 6.101 1960 6.130 6.065 6.238 6.230 6.254 6.379 6.530 6.504 6.327 6.230 6.063 6.165 SEASONAL COMPONENT YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 -0.092 -0.045 0.067 0.017 -0.048 0.080 0.174 0.168 0.070 -0.079 -0.224 -0.087 1950 -0.091 -0.048 0.067 0.010 -0.051 0.083 0.178 0.173 0.069 -0.081 -0.225 -0.087 1951 -0.084 -0.052 0.065 0.002 -0.046 0.090 0.179 0.176 0.063 -0.079 -0.218 -0.089 1952 -0.082 -0.066 0.053 -0.005 -0.036 0.103 0.186 0.186 0.058 -0.076 -0.214 -0.096 1953 -0.089 -0.089 0.039 -0.005 -0.024 0.114 0.203 0.197 0.061 -0.072 -0.216 -0.103 1954 -0.090 -0.107 0.025 -0.010 -0.018 0.119 0.219 0.200 0.062 -0.075 -0.219 -0.104 1955 -0.086 -0.117 0.015 -0.015 -0.015 0.125 0.231 0.206 0.064 -0.077 -0.221 -0.105 1956 -0.085 -0.127 0.008 -0.020 -0.013 0.133 0.238 0.218 0.066 -0.078 -0.220 -0.110 1957 -0.089 -0.140 0.001 -0.029 -0.013 0.137 0.245 0.236 0.069 -0.073 -0.215 -0.114 1958 -0.091 -0.149 -0.005 -0.037 -0.012 0.134 0.252 0.248 0.065 -0.072 -0.217 -0.121 1959 -0.092 -0.154 -0.003 -0.033 -0.005 0.129 0.255 0.250 0.060 -0.069 -0.217 -0.122 1960 -0.092 -0.157 -0.002 -0.028 -0.001 0.126 0.258 0.246 0.058 -0.066 -0.219 -0.123 STANDARD ERROR OF SEASONAL X 10.0D-1 YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.152 0.146 0.141 0.138 0.136 0.135 0.135 0.135 0.135 0.135 0.134 0.132 1950 0.120 0.117 0.116 0.115 0.114 0.114 0.114 0.114 0.114 0.114 0.113 0.113 1951 0.109 0.109 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1952 0.107 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1953 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1954 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1955 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1956 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1957 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.107 1958 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.109 0.109 1959 0.113 0.113 0.114 0.114 0.114 0.114 0.114 0.114 0.115 0.116 0.117 0.120 1960 0.132 0.134 0.135 0.135 0.135 0.135 0.135 0.136 0.138 0.141 0.146 0.152 TREND-CYCLE YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.808 4.815 4.823 4.831 4.834 4.831 4.830 4.834 4.843 4.853 4.858 4.858 1950 4.860 4.872 4.883 4.890 4.901 4.922 4.945 4.964 4.975 4.980 4.993 5.020 1951 5.049 5.071 5.088 5.095 5.097 5.103 5.113 5.129 5.148 5.170 5.190 5.206 1952 5.221 5.229 5.225 5.228 5.244 5.261 5.274 5.287 5.304 5.326 5.348 5.362 1953 5.372 5.390 5.418 5.444 5.460 5.470 5.482 5.494 5.504 5.509 5.509 5.508 1954 5.512 5.520 5.530 5.542 5.555 5.566 5.576 5.584 5.595 5.609 5.625 5.641 1955 5.657 5.668 5.681 5.697 5.713 5.729 5.745 5.756 5.770 5.784 5.799 5.817 1956 5.832 5.843 5.852 5.862 5.872 5.880 5.884 5.890 5.897 5.906 5.917 5.928 1957 5.939 5.951 5.964 5.976 5.986 5.995 6.001 6.010 6.018 6.023 6.025 6.023 1958 6.016 6.008 6.001 6.001 6.012 6.028 6.042 6.049 6.048 6.048 6.050 6.056 1959 6.070 6.087 6.102 6.116 6.128 6.137 6.150 6.164 6.175 6.186 6.201 6.214 1960 6.222 6.229 6.239 6.249 6.254 6.259 6.263 6.267 6.274 6.283 6.287 6.291 STANDARD ERROR OF TREND-CYCLE X 10.0D-1 YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.166 0.137 0.126 0.121 0.118 0.117 0.117 0.117 0.117 0.116 0.115 0.113 1950 0.112 0.112 0.111 0.111 0.110 0.110 0.110 0.110 0.110 0.110 0.109 0.109 1951 0.109 0.109 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1952 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1953 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1954 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 1955 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 0.107 1956 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1957 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1958 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.109 0.109 1959 0.109 0.109 0.110 0.110 0.110 0.110 0.110 0.110 0.111 0.111 0.112 0.112 1960 0.113 0.115 0.116 0.117 0.117 0.117 0.117 0.118 0.121 0.126 0.137 0.166 SEASONALLY ADJUSTED SERIES YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.811 4.816 4.816 4.842 4.843 4.825 4.823 4.829 4.842 4.858 4.868 4.858 1950 4.836 4.885 4.882 4.896 4.879 4.921 4.958 4.963 4.993 4.971 4.961 5.029 1951 5.061 5.063 5.116 5.092 5.097 5.091 5.115 5.117 5.152 5.166 5.201 5.201 1952 5.224 5.259 5.210 5.204 5.246 5.281 5.252 5.303 5.284 5.328 5.362 5.364 1953 5.367 5.367 5.425 5.465 5.457 5.476 5.470 5.506 5.504 5.521 5.506 5.503 1954 5.505 5.520 5.531 5.532 5.570 5.554 5.588 5.577 5.592 5.605 5.629 5.634 1955 5.671 5.665 5.669 5.706 5.710 5.724 5.762 5.740 5.776 5.787 5.785 5.829 1956 5.831 5.848 5.848 5.863 5.872 5.888 5.882 5.883 5.902 5.898 5.918 5.930 1957 5.939 5.944 5.970 5.978 5.982 6.005 5.993 6.007 6.029 6.019 6.032 6.028 1958 6.016 6.008 5.993 5.986 6.003 6.038 6.041 6.073 6.033 6.052 6.050 6.038 1959 6.075 6.086 6.106 6.111 6.142 6.125 6.148 6.173 6.174 6.175 6.206 6.222 1960 6.222 6.222 6.239 6.258 6.255 6.253 6.272 6.257 6.270 6.296 6.282 6.288 STANDARD ERROR OF SEASONALLY ADJUSTED SERIES X 10.0D-1 YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.152 0.146 0.141 0.138 0.136 0.135 0.135 0.135 0.135 0.135 0.134 0.132 1950 0.120 0.117 0.116 0.115 0.114 0.114 0.114 0.114 0.114 0.114 0.113 0.113 1951 0.109 0.109 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 1952 0.107 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1953 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1954 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1955 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1956 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 1957 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.106 0.107 1958 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.108 0.109 0.109 1959 0.113 0.113 0.114 0.114 0.114 0.114 0.114 0.114 0.115 0.116 0.117 0.120 1960 0.132 0.134 0.135 0.135 0.135 0.135 0.135 0.136 0.138 0.141 0.146 0.152 IRREGULAR COMPONENT X 10.0D-1 YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.027 0.007 -0.069 0.112 0.096 -0.057 -0.067 -0.052 -0.011 0.053 0.101 0.000 1950 -0.241 0.129 -0.008 0.053 -0.224 -0.011 0.123 -0.003 0.182 -0.087 -0.316 0.083 1951 0.123 -0.085 0.281 -0.036 0.000 -0.114 0.014 -0.118 0.038 -0.036 0.116 -0.049 1952 0.029 0.302 -0.152 -0.240 0.014 0.202 -0.213 0.151 -0.196 0.022 0.143 0.027 1953 -0.054 -0.230 0.063 0.202 -0.025 0.052 -0.115 0.112 -0.003 0.121 -0.029 -0.052 1954 -0.070 0.000 0.011 -0.103 0.151 -0.118 0.124 -0.077 -0.030 -0.038 0.039 -0.073 1955 0.145 -0.036 -0.115 0.088 -0.030 -0.054 0.179 -0.160 0.054 0.027 -0.137 0.124 1956 -0.005 0.054 -0.045 0.012 0.000 0.081 -0.026 -0.067 0.050 -0.080 0.015 0.015 1957 -0.003 -0.070 0.063 0.021 -0.041 0.102 -0.079 -0.022 0.112 -0.039 0.074 0.057 1958 0.004 0.006 -0.075 -0.151 -0.089 0.098 -0.009 0.239 -0.149 0.033 -0.005 -0.185 1959 0.045 -0.011 0.046 -0.047 0.142 -0.126 -0.020 0.091 -0.003 -0.109 0.050 0.086 1960 0.000 -0.067 0.000 0.090 0.007 -0.057 0.089 -0.095 -0.046 0.134 -0.052 -0.032 DETERMINISTIC COMPONENT (from TRAMO) ------------------------------------ LEVEL SHIFT X 10.0D-1 YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1951 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1952 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1953 0.000 0.000 0.000 0.000 0.000 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1954 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1955 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1956 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1957 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1958 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1959 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 1960 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 -0.967 TRANSITORY OUTLIERS YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1950 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1951 0.000 0.000 0.000 0.000 0.096 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1952 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1953 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1954 0.000 -0.080 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1955 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1956 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1957 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1958 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1959 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1960 0.000 0.000 -0.103 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 FINAL DECOMPOSITION ------------------- ORIGINAL UNCORRECTED SERIES (from TRAMO) YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.718 4.771 4.883 4.860 4.796 4.905 4.997 4.997 4.913 4.779 4.644 4.771 1950 4.745 4.836 4.949 4.905 4.828 5.004 5.136 5.136 5.063 4.890 4.736 4.942 1951 4.977 5.011 5.182 5.094 5.147 5.182 5.293 5.293 5.215 5.088 4.984 5.112 1952 5.142 5.193 5.263 5.199 5.209 5.385 5.438 5.489 5.342 5.252 5.147 5.268 1953 5.278 5.278 5.464 5.460 5.434 5.493 5.576 5.606 5.468 5.352 5.193 5.303 1954 5.318 5.236 5.460 5.425 5.455 5.576 5.710 5.680 5.557 5.434 5.313 5.434 1955 5.489 5.451 5.587 5.595 5.598 5.753 5.897 5.849 5.743 5.613 5.468 5.628 1956 5.649 5.624 5.759 5.746 5.762 5.924 6.023 6.004 5.872 5.724 5.602 5.724 1957 5.753 5.707 5.875 5.852 5.872 6.045 6.142 6.146 6.001 5.849 5.720 5.817 1958 5.829 5.762 5.892 5.852 5.894 6.075 6.196 6.225 6.001 5.883 5.737 5.820 1959 5.886 5.835 6.006 5.981 6.040 6.157 6.306 6.326 6.138 6.009 5.892 6.004 1960 6.033 5.969 6.038 6.133 6.157 6.282 6.433 6.407 6.230 6.133 5.966 6.068 FINAL COMPONENT --------------- FINAL SEASONALLY ADJUSTED SERIES YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.811 4.816 4.816 4.842 4.843 4.825 4.823 4.829 4.842 4.858 4.868 4.858 1950 4.836 4.885 4.882 4.896 4.879 4.921 4.958 4.963 4.993 4.971 4.961 5.029 1951 5.061 5.063 5.116 5.092 5.193 5.091 5.115 5.117 5.152 5.166 5.201 5.201 1952 5.224 5.259 5.210 5.204 5.246 5.281 5.252 5.303 5.284 5.328 5.362 5.364 1953 5.367 5.367 5.425 5.465 5.457 5.379 5.373 5.409 5.407 5.424 5.409 5.406 1954 5.408 5.343 5.435 5.435 5.473 5.457 5.491 5.480 5.495 5.508 5.532 5.537 1955 5.575 5.568 5.573 5.609 5.613 5.627 5.666 5.644 5.679 5.690 5.689 5.732 1956 5.734 5.751 5.751 5.766 5.775 5.791 5.785 5.786 5.806 5.801 5.822 5.833 1957 5.842 5.847 5.874 5.881 5.885 5.908 5.897 5.911 5.933 5.922 5.935 5.932 1958 5.920 5.911 5.896 5.889 5.906 5.941 5.945 5.976 5.937 5.955 5.953 5.941 1959 5.978 5.989 6.009 6.014 6.045 6.028 6.051 6.076 6.078 6.078 6.109 6.126 1960 6.125 6.126 6.039 6.161 6.158 6.156 6.175 6.161 6.173 6.199 6.185 6.191 FINAL TREND-CYCLE YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 4.808 4.815 4.823 4.831 4.834 4.831 4.830 4.834 4.843 4.853 4.858 4.858 1950 4.860 4.872 4.883 4.890 4.901 4.922 4.945 4.964 4.975 4.980 4.993 5.020 1951 5.049 5.071 5.088 5.095 5.097 5.103 5.113 5.129 5.148 5.170 5.190 5.206 1952 5.221 5.229 5.225 5.228 5.244 5.261 5.274 5.287 5.304 5.326 5.348 5.362 1953 5.372 5.390 5.418 5.444 5.460 5.374 5.385 5.398 5.408 5.412 5.412 5.411 1954 5.415 5.424 5.434 5.445 5.458 5.469 5.479 5.488 5.498 5.512 5.528 5.545 1955 5.560 5.572 5.584 5.601 5.616 5.633 5.648 5.660 5.673 5.688 5.702 5.720 1956 5.735 5.746 5.755 5.765 5.775 5.783 5.788 5.793 5.801 5.809 5.820 5.832 1957 5.842 5.854 5.867 5.879 5.889 5.898 5.905 5.913 5.922 5.926 5.928 5.926 1958 5.919 5.911 5.904 5.904 5.915 5.931 5.946 5.952 5.952 5.952 5.954 5.960 1959 5.974 5.990 6.005 6.019 6.031 6.041 6.053 6.067 6.078 6.089 6.104 6.117 1960 6.125 6.132 6.143 6.152 6.158 6.162 6.166 6.170 6.177 6.186 6.190 6.195 FINAL SEASONAL YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 -0.092 -0.045 0.067 0.017 -0.048 0.080 0.174 0.168 0.070 -0.079 -0.224 -0.087 1950 -0.091 -0.048 0.067 0.010 -0.051 0.083 0.178 0.173 0.069 -0.081 -0.225 -0.087 1951 -0.084 -0.052 0.065 0.002 -0.046 0.090 0.179 0.176 0.063 -0.079 -0.218 -0.089 1952 -0.082 -0.066 0.053 -0.005 -0.036 0.103 0.186 0.186 0.058 -0.076 -0.214 -0.096 1953 -0.089 -0.089 0.039 -0.005 -0.024 0.114 0.203 0.197 0.061 -0.072 -0.216 -0.103 1954 -0.090 -0.107 0.025 -0.010 -0.018 0.119 0.219 0.200 0.062 -0.075 -0.219 -0.104 1955 -0.086 -0.117 0.015 -0.015 -0.015 0.125 0.231 0.206 0.064 -0.077 -0.221 -0.105 1956 -0.085 -0.127 0.008 -0.020 -0.013 0.133 0.238 0.218 0.066 -0.078 -0.220 -0.110 1957 -0.089 -0.140 0.001 -0.029 -0.013 0.137 0.245 0.236 0.069 -0.073 -0.215 -0.114 1958 -0.091 -0.149 -0.005 -0.037 -0.012 0.134 0.252 0.248 0.065 -0.072 -0.217 -0.121 1959 -0.092 -0.154 -0.003 -0.033 -0.005 0.129 0.255 0.250 0.060 -0.069 -0.217 -0.122 1960 -0.092 -0.157 -0.002 -0.028 -0.001 0.126 0.258 0.246 0.058 -0.066 -0.219 -0.123 FINAL IRREGULAR YEAR JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC 1949 0.003 0.001 -0.007 0.011 0.010 -0.006 -0.007 -0.005 -0.001 0.005 0.010 0.000 1950 -0.024 0.013 -0.001 0.005 -0.022 -0.001 0.012 0.000 0.018 -0.009 -0.032 0.008 1951 0.012 -0.008 0.028 -0.004 0.096 -0.011 0.001 -0.012 0.004 -0.004 0.012 -0.005 1952 0.003 0.030 -0.015 -0.024 0.001 0.020 -0.021 0.015 -0.020 0.002 0.014 0.003 1953 -0.005 -0.023 0.006 0.020 -0.002 0.005 -0.012 0.011 0.000 0.012 -0.003 -0.005 1954 -0.007 -0.080 0.001 -0.010 0.015 -0.012 0.012 -0.008 -0.003 -0.004 0.004 -0.007 1955 0.014 -0.004 -0.011 0.009 -0.003 -0.005 0.018 -0.016 0.005 0.003 -0.014 0.012 1956 -0.001 0.005 -0.004 0.001 0.000 0.008 -0.003 -0.007 0.005 -0.008 0.002 0.001 1957 0.000 -0.007 0.006 0.002 -0.004 0.010 -0.008 -0.002 0.011 -0.004 0.007 0.006 1958 0.000 0.001 -0.008 -0.015 -0.009 0.010 -0.001 0.024 -0.015 0.003 0.000 -0.019 1959 0.005 -0.001 0.005 -0.005 0.014 -0.013 -0.002 0.009 0.000 -0.011 0.005 0.009 1960 0.000 -0.007 -0.103 0.009 0.001 -0.006 0.009 -0.009 -0.005 0.013 -0.005 -0.003 FORECAST OF FINAL COMPONENT ORIGINAL SEASONALLY TREND-CYCLE SEASONAL IRREGULAR (UNCORRECTED) ADJUSTED COMPONENT SERIES SERIES 6.109 6.202 6.202 -0.9293E-01 0.000 6.051 6.210 6.210 -0.1583 0.000 6.216 6.218 6.218 -0.1734E-02 0.000 6.199 6.225 6.225 -0.2682E-01 0.000 6.232 6.233 6.233 -0.1073E-02 0.000 6.367 6.241 6.241 0.1258 0.000 6.508 6.249 6.249 0.2590 0.000 6.502 6.257 6.257 0.2453 0.000 6.322 6.265 6.265 0.5740E-01 0.000 6.209 6.273 6.273 -0.6395E-01 0.000 6.061 6.281 6.281 -0.2193 0.000 6.165 6.289 6.289 -0.1234 0.000 6.204 6.296 6.296 -0.9293E-01 0.000 6.146 6.304 6.304 -0.1583 0.000 6.311 6.312 6.312 -0.1734E-02 0.000 6.293 6.320 6.320 -0.2682E-01 0.000 6.327 6.328 6.328 -0.1073E-02 0.000 6.462 6.336 6.336 0.1258 0.000 6.603 6.344 6.344 0.2590 0.000 6.597 6.352 6.352 0.2453 0.000 6.417 6.360 6.360 0.5740E-01 0.000 6.304 6.367 6.367 -0.6395E-01 0.000 6.156 6.375 6.375 -0.2193 0.000 6.260 6.383 6.383 -0.1234 0.000 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * PROCESSING COMPLETED* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *