The regcmpnt program fits and does signal extraction for time series models with regression terms and errors following ARIMA component models. It handles REGARIMA models as a special case, although the regarima and X-12-ARIMA programs are more flexible and efficient if only REGARIMA models are of interest. All three of these programs can be downloaded via ftp from the Census Bureau's Internet site at ftp.census.gov. The regcmpnt program, along with this file, the full input and output files given below, and additional example input and output files, are in the directory pub/ts/regcmpnt (in the unix, pc, and vax subdirectories). Instructions on downloading regcmpnt are contained in the Readme file of this directory. Since we do not have formal documentation available for regcmpnt, it is hoped that the examples below and the others available in /pub/ts/regcmpnt can guide people in using the program on their own applications. Below we list input and output files for four examples for the program regcmpnt. The input code can be split off and stored in the following four files for input to regcmpnt: bdptrs.nam: U.S. Retail Sales of Dept Stores, Fixed TD and Easter effects bsm.nam: Retail Sales of Department Stores - Basic Structural Model tvreg.nam: U.S. Retail Sales of Dept Stores, time varying TD effect teen.nam: U.S. Teen Unemployment, Jan 72 - Dec 83 The first three examples use the same data, though in bsm.nam the data are not included in the input file. They would need to be stored in file bdptrs.dat in the same directory that regcmpnt is run from. Alternatively, store the data anywhere and put the full filename with path in the file statement of bsm.nam. Some editing was done to shorten the output below for each example. The basic regcmpnt output (that which comes to the screen, if not redirected to a file) is shown nearly complete for the options given. The saved output files (of KF innovations, and of signal extraction estimates and variances) are brief excerpts, shown only to permit checking of results. The first example (bdptrs.nam) fits a model with fixed TD and Easter regression variables and errors following an ARIMA(0,1,1)(0,1,1)12 model (airline model). The second example (bsm.nam) replaces the airline model with the Basic Structural Model of Harvey. The third example (tvreg.nam) retains the airline model and fixed 10-day (default) Easter effect, but converts the trading-day coefficients to stochastic coefficients following independent random walk models. The fourth example (teen.nam) illustrates an application of regcmpnt to repeated survey estimation. In this example the second component represents sampling error, for which the model was developed outside regcmpnt using estimates of sampling error variances and autocorrelations. Hence, the second component model parameters are kept fixed (lfix = t) in this example. Also, the scale factors (rh) for the second component are the sampling error standard deviations, which vary over time. The second component innovation variance is specified at a value so that the variance of the unscaled second component (given the specified values of the ARMA parameters) is 1. ************************************************************************** * Example: U.S. Retail Sales of Dept Stores, Fixed TD and Easter effects * ************************************************************************** &series ibegdt=1967,1 ienddt=1993,12 isp=12 rlam=0 ctitle='U.S. Retail Sales of Dept Stores, Fixed TD and Easter effects', ry= 1746 1624 2195 2124 2308 2435 2109 2404 2439 2445 2935 4419 1915 1880 2290 2482 2561 2561 2466 2763 2527 2768 3321 4897 2114 1974 2540 2665 2831 2727 2643 2912 2737 2983 3359 5269 2281 2075 2644 2759 2879 2858 2733 2871 2818 3178 3487 5584 2385 2268 2834 3195 3138 3264 3075 3253 3316 3444 4081 6219 2580 2568 3268 3223 3546 3575 3335 3646 3666 3857 4468 6719 2929 2834 3685 3838 3990 4044 3689 4045 3897 4172 5037 7182 3156 2985 3886 4188 4355 4162 3988 4422 4084 4432 5085 7326 3161 3096 4036 4103 4729 4409 4227 4642 4502 4715 5544 8538 3564 3514 4382 4895 4691 4853 4693 4923 4933 5321 6218 9513 3743 3780 4937 5297 5259 5274 5251 5591 5547 5966 7050 11161 4158 4230 5646 5732 6121 6193 5684 6233 6172 6393 7642 11933 4552 4453 5948 6107 6505 6371 5992 6731 6451 6947 8526 12578 4954 5024 6103 6277 6949 6398 6320 7096 6626 7469 8779 13469 5408 5337 6778 7470 7716 7602 7188 7848 7528 8301 9521 14941 5635 5622 7216 7728 8160 7698 7654 7981 7693 8423 10005 16026 6067 5880 7893 8057 8667 8602 7993 8820 8555 9208 11194 17703 6777 6957 8589 9021 9970 9763 8636 9852 9393 9945 12615 18969 7138 7271 9346 9747 10464 9791 9114 10731 9536 10539 13078 19657 7524 7621 10201 10090 11369 10415 9993 11441 10335 11237 13539 20721 8066 8327 10320 11162 11930 11103 10565 11982 10947 12221 14451 22943 8467 8695 11314 11386 12093 11836 11003 12261 11635 12798 15565 24584 9035 9053 12093 12251 12820 12662 11791 13279 12465 13178 16629 25519 9489 9882 12946 12704 13341 13291 12143 13969 12553 13412 17068 25418 9782 10273 13425 13094 14276 13448 12844 14905 12932 14272 17978 26277 10870 11888 13623 14218 15120 14131 13869 15613 14095 15850 19152 28785 11898 12064 14287 15208 16177 15371 15398 16571 15578 17187 20494 30954 &end ®var ltd=t leastr=t neastr=10 &end &arima nd=1 nma=1 nsd=1 nsma=1 rvar=1 &end &opts lsmth=f lprint=t &end ----- Output File ----- REGCMPNT: Regression + ARIMA Component Model Estimation and Smoothing Program Version 1.6, 20 Sep 1995 by Time Series Staff Census Bureau Rm 3000-4 (SRD) WASH DC 20233-9100 Date Thu Aug 15 15:19:35 1996 Reading input namelist file from bdptrs.nam NOTICE: Trading day option, LTD, will adjust the series by length of month. U.S. Retail Sales of Dept Stores, Fixed TD and Easter effects JAN FEB MAR APR MAY JUN Year JUL AUG SEP OCT NOV DEC ------------------------------------------------------------------------------- 1967 1746.000 1624.000 2195.000 2124.000 2308.000 2435.000 2109.000 2404.000 2439.000 2445.000 2935.000 4419.000 1968 1915.000 1880.000 2290.000 2482.000 2561.000 2561.000 2466.000 2763.000 2527.000 2768.000 3321.000 4897.000 1969 2114.000 1974.000 2540.000 2665.000 2831.000 2727.000 2643.000 2912.000 2737.000 2983.000 3359.000 5269.000 1993 11898.000 12064.000 14287.000 15208.000 16177.000 15371.000 15398.000 16571.000 15578.000 17187.000 20494.000 30954.000 Transformation ln(y/lom) Regression Model Trading Day+Holiday ARIMA Model ( 0 1 1)( 0 1 1)12 MODEL ESTIMATION/EVALUATION Exact ARMA likelihood estimation Max total ARMA iterations 200 Max ARMA iter's w/in an IGLS iter. 40 Convergence tolerance 1.00E-05 First variance has been concentrated out. Iterations IGLS: Estimate regression parameters given last values of ARMA parameters. ARMA: Estimate ARMA parameters using residuals from last IGLS regression. Note: ARMA iteration counts are cumulative over IGLS iterations. IGLS Iteration 1 Function evaluations 9 Log Likelihood 7.151849339E+02 Regression parameters -0.004180161 0.002586540 -0.007151431 0.006972448 0.007393721 0.009407430 0.037291628 ARMA Iteration 0 Function evaluations 9 Log Likelihood 7.151849339E+02 Parameters 0.100000000 0.100000000 ARMA Iteration 1 Function evaluations 15 Log Likelihood 7.575478288E+02 Parameters 0.434735496 0.392880135 ARMA Iteration 2 Function evaluations 18 Log Likelihood 7.616591429E+02 Parameters 0.520730337 0.519280107 ARMA Iteration 3 Function evaluations 21 Log Likelihood 7.617065213E+02 Parameters 0.524295498 0.535148130 ARMA Iteration 4 Function evaluations 22 Log Likelihood 7.617067015E+02 Parameters 0.525049749 0.535730788 IGLS Iteration 2 Function evaluations 31 Log Likelihood 7.622387909E+02 Regression parameters -0.004418202 0.002208995 -0.007313847 0.006759393 0.007864897 0.009862125 0.034630374 ARMA Iteration 5 Function evaluations 37 Log Likelihood 7.622412036E+02 Parameters 0.525799817 0.539319600 ARMA Iteration 6 Function evaluations 38 Log Likelihood 7.622412086E+02 Parameters 0.525942435 0.539379636 IGLS Iteration 3 Function evaluations 47 Log Likelihood 7.622412343E+02 Regression parameters -0.004423562 0.002206244 -0.007311828 0.006758310 0.007864044 0.009869730 0.034622240 ARMA Iteration 7 Function evaluations 51 Log Likelihood 7.622412347E+02 Parameters 0.525951833 0.539424027 IGLS Iteration 4 Function evaluations 60 Log Likelihood 7.622412347E+02 Regression parameters -0.004423627 0.002206211 -0.007311802 0.006758296 0.007864035 0.009869824 0.034622149 Estimation converged in 7 ARMA iterations, 60 function evaluations Regression Model ------------------------------------------------------------------ Parameter Standard Variable Estimate Error t-value ------------------------------------------------------------------ Trading Day TD1 -0.0044 0.00209 -2.11 TD2 0.0022 0.00211 1.05 TD3 -0.0073 0.00207 -3.54 TD4 0.0068 0.00210 3.22 TD5 0.0079 0.00208 3.78 TD6 0.0099 0.00211 4.69 *Sun (derived) -0.0150 0.00206 -7.25 Holiday Easter 10 0.0346 0.00424 8.16 ------------------------------------------------------------------ *For trading-day and fixed seasonal effects, the derived parameter estimate is obtained indirectly as minus the sum of the directly estimated parameters that define the effect. Chi-squared Tests ------------------------------------------------------------------ Regression Effect df Chi-square p-value ------------------------------------------------------------------ Trading Day 6 243.78 0.00 ------------------------------------------------------------------ Correlation matrix Variable 1 2 3 4 5 6 7 ----------------------------------------------------------- TD1 1.00 TD2 -0.57 1.00 TD3 0.01 -0.53 1.00 TD4 0.06 -0.03 -0.54 1.00 TD5 0.03 0.05 0.00 -0.54 1.00 TD6 -0.01 0.05 0.06 -0.02 -0.55 1.00 Easter 10 -0.16 0.19 0.00 -0.12 -0.05 0.19 1.00 ARIMA Model: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Seasonal Difference (fixed) Lag 12 1.0000 Nonseasonal MA Lag 1 0.5260 0.04860 Seasonal MA Lag 12 0.5394 0.05294 Variance 0.42900E-03 0.45155E-04 log(Variance) -7.75406 0.10526 ----------------------------------------------------- Likelihood statistics ------------------------------------------------------------ Effective number of observations (nefobs) 311 Number of parameters estimated (np) 10 Log likelihood 762.2412 Transformation Adjustment -2751.0055 Adjusted Log likelihood (L) -1988.7643 AIC 3997.5286 F-corrected AIC 3998.2620 Hannan Quinn 4012.4771 BIC 4034.9265 ------------------------------------------------------------ nefobs = nobs-d, where d = 13 is the total differencing order Transformation Adjustment = (lam-1)*sum{log[y(i)]} (lam = Box-Cox power, sum is over last nefobs obervations) AIC = -2*L + 2*np F-corrected-AIC = -2*L + 2*np/[(1-(np+1)/nefobs)] Hannan Quinn = -2*L + 2*np*{log[log(nefobs)]} BIC = -2*L + [log(nefobs)]*np ARMA Parameter Correlation Matrix Parameter 1 2 3 ------------------------------ ARIMA Model ------------------------------ Nonseasonal MA Lag 1 1.00 Seasonal MA Lag 12 0.07 1.00 Var 1 -0.01 -0.03 1.00 Sample ACF of the KF Standardized Innovations If residuals are random, the Ljung Box Q should be distributed as chi-squared on df degrees of freedom Lag 1 2 3 4 5 6 7 8 9 10 11 12 ACF 0.01 -0.08 0.10 -0.01 -0.02 0.02 -0.06 0.00 -0.06 -0.05 -0.02 0.04 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Q 0.04 1.84 5.08 5.11 5.30 5.40 6.68 6.69 7.88 8.63 8.76 9.28 DF 0 0 0 1 2 3 4 5 6 7 8 9 ACF 0.03 -0.12 -0.06 0.00 0.03 0.03 -0.03 0.03 -0.08 -0.10 -0.03 -0.06 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Q 9.49 14.29 15.54 15.54 15.80 16.08 16.36 16.65 18.71 22.08 22.31 23.53 DF 10 11 12 13 14 15 16 17 18 19 20 21 Sample PACF of the KF Standardized Innovations Lag 1 2 3 4 5 6 7 8 9 10 11 12 PACF 0.01 -0.08 0.10 -0.02 -0.01 0.01 -0.06 0.01 -0.08 -0.03 -0.03 0.05 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 PACF 0.03 -0.12 -0.06 -0.03 0.05 0.03 -0.03 0.03 -0.11 -0.09 -0.06 -0.08 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Histogram of the KF Standardized Innovations Standard Deviations Frequency -3 +# |# -2 +########## |######################## -1 +######################################## |############################################### 0 +#################################################################### |############################################### 1 +########################################### |################## 2 +####### |### 3 +## One '#'= 1 observation[s] Summary Statistics for the KF Standardized Innovations Minimum -3.092 Maximum 3.098 Median -0.028 Robust Std Dev 1.076 FILE SAVE REQUESTS (* indicates file exists and will be overwritten) bdptrs.inn Model Innovations Performing Forward Filtering ----- File: bdptrs.inn (excerpts) ----- t Data Innovation Inn. Var Std. Inn. 14 1880.0 0.19791E-01 0.70703E-03 0.74430 15 2290.0 -0.14845E-01 0.58702E-03 -0.61270 16 2482.0 0.29368E-01 0.56249E-03 1.2383 17 2561.0 -0.15881E-01 0.55619E-03 -0.67338 18 2561.0 -0.25327E-01 0.55448E-03 -1.0756 19 2466.0 0.72924E-01 0.55401E-03 3.0982 20 2763.0 -0.17102E-02 0.55388E-03 -0.72669E-01 21 2527.0 -0.44678E-01 0.55384E-03 -1.8985 ************************************************************************** * Example: Retail Sales of Department Stores - Basic Structural Model * ************************************************************************** &series ibegdt = 1967,1 ienddt = 1993,12 isp=12 rlam=0 ctitle = 'Retail Sales of Department Stores - Basic Structural Model' cfile = 'bdptrs.dat' &end ®var lconst=f, lseff=f, ltd=t, leastr=t &end &arima nd=2 nma=1 rma= .8 rvar= 200.0 &end &arima rvar= 200.0 &end &arima ndiff=11 rdiff=11*-1. rvar=1.0 &end &opts lestim=t lsmth=t lprint=t &end ----- Output File ----- REGCMPNT: Regression + ARIMA Component Model Estimation and Smoothing Program Version 1.6, 20 Sep 1995 Reading input namelist file from bsm.nam Reading data from bdptrs.dat NOTICE: Trading day option, LTD, will adjust the series by length of month. Retail Sales of Department Stores - Basic Structural Model JAN FEB MAR APR MAY JUN Year JUL AUG SEP OCT NOV DEC ------------------------------------------------------------------------------- 1967 1746.000 1624.000 2195.000 2124.000 2308.000 2435.000 2109.000 2404.000 2439.000 2445.000 2935.000 4419.000 1993 11898.000 12064.000 14287.000 15208.000 16177.000 15371.000 15398.000 16571.000 15578.000 17187.000 20494.000 30954.000 Transformation ln(y/lom) Regression Model Trading Day+Holiday Component 1 ( 0 2 1)1 Component 2 ( 0 0 0) Component 3 ( 011 0)1 Smoothed signal will be produced MODEL ESTIMATION/EVALUATION Exact ARMA likelihood estimation Max total ARMA iterations 200 Max ARMA iter's w/in an IGLS iter. 40 Convergence tolerance 1.00E-05 First variance has been concentrated out. Iterations IGLS: Estimate regression parameters given last values of ARMA parameters. ARMA: Estimate ARMA parameters using residuals from last IGLS regression. Note: ARMA iteration counts are cumulative over IGLS iterations. IGLS Iteration 1 Function evaluations 9 Log Likelihood 6.798211132E+02 Regression parameters -0.003327991 0.001586013 -0.007463519 0.006870883 0.007608543 0.011203696 0.034700244 ARMA Iteration 0 Function evaluations 9 Log Likelihood 6.798211132E+02 Parameters 0.800000000 1.000000000 0.070710678 ARMA Iteration 1 Function evaluations 17 Log Likelihood 7.022373878E+02 Parameters 1.261921876 0.535433359 0.153727455 ARMA Iteration 2 Function evaluations 22 Log Likelihood 7.315884796E+02 Parameters 0.938596228 0.501138043 0.185181399 ARMA Iteration 29 Function evaluations 162 Log Likelihood 7.562595869E+02 Parameters 1.007671088 1.012455821 0.630134123 IGLS Iteration 5 Function evaluations 171 Log Likelihood 7.562595869E+02 Regression parameters -0.004644557 0.002629162 -0.007322879 0.006514370 0.007818126 0.009784219 0.034593828 Estimation converged in 29 ARMA iterations, 171 function evaluations Regression Model ------------------------------------------------------------------ Parameter Standard Variable Estimate Error t-value ------------------------------------------------------------------ Trading Day TD1 -0.0046 0.00212 -2.19 TD2 0.0026 0.00213 1.24 TD3 -0.0073 0.00209 -3.50 TD4 0.0065 0.00212 3.07 TD5 0.0078 0.00210 3.72 TD6 0.0098 0.00213 4.60 *Sun (derived) -0.0148 0.00208 -7.09 Holiday Easter 10 0.0346 0.00427 8.10 ------------------------------------------------------------------ *For trading-day and fixed seasonal effects, the derived parameter estimate is obtained indirectly as minus the sum of the directly estimated parameters that define the effect. Chi-squared Tests ------------------------------------------------------------------ Regression Effect df Chi-square p-value ------------------------------------------------------------------ Trading Day 6 210.93 0.00 ------------------------------------------------------------------ Correlation matrix Variable 1 2 3 4 5 6 7 ----------------------------------------------------------- TD1 1.00 TD2 -0.57 1.00 TD3 0.03 -0.53 1.00 TD4 0.04 -0.01 -0.54 1.00 TD5 0.01 0.03 0.01 -0.53 1.00 TD6 0.01 0.03 0.04 -0.01 -0.54 1.00 Easter 10 -0.16 0.20 -0.01 -0.11 -0.05 0.19 1.00 Component 1: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 2.0000 Lag 2 -1.0000 Nonseasonal MA Lag 1 1.0077 0.01334 Variance 0.88045E-04 0.19123E-04 log(Variance) -9.33766 0.21720 Component 2: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Variance 0.90252E-04 0.25798E-04 log(Variance) -9.31290 0.28584 Component 3: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- User Difference (fixed) Lag 1 -1.0000 Lag 2 -1.0000 Lag 3 -1.0000 Lag 4 -1.0000 Lag 5 -1.0000 Lag 6 -1.0000 Lag 7 -1.0000 Lag 8 -1.0000 Lag 9 -1.0000 Lag 10 -1.0000 Lag 11 -1.0000 Variance 0.34960E-04 0.91263E-05 log(Variance) -10.26131 0.26105 ----------------------------------------------------- Likelihood statistics ------------------------------------------------------------ Effective number of observations (nefobs) 311 Number of parameters estimated (np) 11 Log likelihood 756.2596 Transformation Adjustment -2751.0055 Adjusted Log likelihood (L) -1994.7460 AIC 4011.4919 F-corrected AIC 4012.3749 Hannan Quinn 4027.9352 BIC 4052.6296 ------------------------------------------------------------ nefobs = nobs-d, where d = 13 is the total differencing order Transformation Adjustment = (lam-1)*sum{log[y(i)]} (lam = Box-Cox power, sum is over last nefobs obervations) AIC = -2*L + 2*np F-corrected-AIC = -2*L + 2*np/[(1-(np+1)/nefobs)] Hannan Quinn = -2*L + 2*np*{log[log(nefobs)]} BIC = -2*L + [log(nefobs)]*np ARMA Parameter Correlation Matrix Parameter 1 2 3 4 ------------------------------------ Component 1 ------------------------------------ Nonseasonal MA Lag 1 1.00 Var 1 -0.29 1.00 Component 2 ------------------------------------ Var 2 0.11 -0.37 1.00 Component 3 ------------------------------------ Var 3 -0.03 0.19 -0.47 1.00 Sample ACF of the KF Standardized Innovations If residuals are random, the Ljung Box Q should be distributed as chi-squared on df degrees of freedom Lag 1 2 3 4 5 6 7 8 9 10 11 12 ACF 0.08 -0.10 0.03 -0.06 -0.05 -0.02 -0.08 -0.03 -0.09 -0.02 0.09 0.09 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Q 2.03 5.44 5.79 6.95 7.76 7.84 9.69 10.05 12.83 12.96 15.40 17.85 DF 0 0 0 0 1 2 3 4 5 6 7 8 ACF 0.14 -0.09 -0.09 -0.01 0.01 0.01 -0.05 0.00 -0.10 -0.08 0.04 -0.01 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Q 23.94 26.36 29.11 29.17 29.24 29.27 29.97 29.97 33.04 35.47 35.95 36.02 DF 9 10 11 12 13 14 15 16 17 18 19 20 Sample PACF of the KF Standardized Innovations Lag 1 2 3 4 5 6 7 8 9 10 11 12 PACF 0.08 -0.11 0.05 -0.08 -0.03 -0.03 -0.08 -0.03 -0.11 -0.01 0.06 0.07 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 PACF 0.13 -0.12 -0.05 -0.04 0.03 0.01 -0.05 0.04 -0.12 -0.05 -0.01 -0.07 SE 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 Histogram of the KF Standardized Innovations Standard Deviations Frequency -3 + |### -2 +########### |##################### -1 +################################### |################################################################## 0 +######################################################### |#################################################### 1 +########################################## |############ 2 +####### |## 3 +### One '#'= 1 observation[s] Summary Statistics for the KF Standardized Innovations Minimum -2.744 Maximum 3.011 Median -0.046 Robust Std Dev 0.997 FILE SAVE REQUESTS (* indicates file exists and will be overwritten) bsm.inn Model Innovations bsm.est Estimates of the Components bsm.var Signal Extraction Variances Performing Backward Smoothing Performing Forward Smoothing NOTICE: Logarithms are taken (rlam = 0). Signal extraction estimates are transformed back to the original scale, but signal extraction variances are left on the log (percentage) scale. NOTICE: Length-of-month (or length-of-quarter) factors will be incorporated into separate regression effects (component 0) for signal extraction estimates on the original scale. These factors have no effect on the signal extraction variances given in the log scale. ----- File: bsm.inn (excerpts) ----- t Data Innovation Inn. Var Std. Inn. 14 1880.0 0.19839E-01 0.74827E-03 0.72526 15 2290.0 -0.15133E-01 0.61118E-03 -0.61211 16 2482.0 0.28554E-01 0.59413E-03 1.1715 17 2561.0 -0.15104E-01 0.59195E-03 -0.62079 18 2561.0 -0.27291E-01 0.59169E-03 -1.1220 19 2466.0 0.73249E-01 0.59166E-03 3.0114 20 2763.0 -0.14477E-03 0.59166E-03 -0.59517E-02 21 2527.0 -0.48827E-01 0.59166E-03 -2.0074 ----- File: bsm.est (excerpts) ----- Signal Extraction Estimates Separate Regression Effects (including lom or loq factors): t Regression 1 1.0015 2 0.91992 3 1.0471 4 0.96062 5 1.0090 6 0.99985 Component 1: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 7.7310 1.0000 2277.9 1.0000 2277.9 2 7.7343 1.0000 2285.5 1.0000 2285.5 3 7.7404 1.0000 2299.5 1.0000 2299.5 4 7.7441 1.0000 2307.8 1.0000 2307.8 5 7.7558 1.0000 2335.1 1.0000 2335.1 6 7.7646 1.0000 2355.7 1.0000 2355.7 7 7.7636 1.0000 2353.3 1.0000 2353.3 Component 2: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 0.32829E-02 1.0000 1.0033 1.0000 1.0033 2 -0.28243E-02 1.0000 0.99718 1.0000 0.99718 3 0.25388E-02 1.0000 1.0025 1.0000 1.0025 4 -0.82648E-02 1.0000 0.99177 1.0000 0.99177 5 0.29742E-02 1.0000 1.0030 1.0000 1.0030 6 0.99998E-02 1.0000 1.0100 1.0000 1.0100 7 -0.13094E-01 1.0000 0.98699 1.0000 0.98699 Component 3: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 -0.27072 1.0000 0.76283 1.0000 0.76283 2 -0.25539 1.0000 0.77461 1.0000 0.77461 3 -0.95070E-01 1.0000 0.90931 1.0000 0.90931 4 -0.34557E-01 1.0000 0.96603 1.0000 0.96603 5 -0.23602E-01 1.0000 0.97667 1.0000 0.97667 6 0.23244E-01 1.0000 1.0235 1.0000 1.0235 7 -0.10520 1.0000 0.90015 1.0000 0.90015 ----- File: bsm.var (excerpts) ----- Signal Extraction Variances (on transformed scale) Component 1: Unscaled Scaled t Stochastic Stochastic Combined 1 0.86572E-04 0.86572E-04 0.87614E-04 2 0.59196E-04 0.59196E-04 0.59541E-04 3 0.52967E-04 0.52967E-04 0.53296E-04 4 0.51711E-04 0.51711E-04 0.52060E-04 5 0.51475E-04 0.51475E-04 0.51622E-04 Component 2: Unscaled Scaled t Stochastic Stochastic Combined 1 0.71815E-04 0.71815E-04 0.72232E-04 2 0.69305E-04 0.69305E-04 0.69455E-04 3 0.67388E-04 0.67388E-04 0.68615E-04 4 0.66822E-04 0.66822E-04 0.68264E-04 5 0.66693E-04 0.66693E-04 0.67261E-04 6 0.66667E-04 0.66667E-04 0.67333E-04 7 0.66663E-04 0.66663E-04 0.67223E-04 8 0.66662E-04 0.66662E-04 0.67142E-04 Component 3: Unscaled Scaled t Stochastic Stochastic Combined 1 0.76579E-04 0.76579E-04 0.77166E-04 2 0.63272E-04 0.63272E-04 0.63757E-04 3 0.62037E-04 0.62037E-04 0.64006E-04 4 0.61901E-04 0.61901E-04 0.64027E-04 5 0.61885E-04 0.61885E-04 0.63163E-04 6 0.61883E-04 0.61883E-04 0.63137E-04 7 0.61883E-04 0.61883E-04 0.63157E-04 8 0.61884E-04 0.61884E-04 0.63124E-04 ************************************************************************** * Example: U.S. Retail Sales of Dept Stores, time varying TD effect * ************************************************************************** &series ibegdt=1967,1 ienddt=1993,12 isp=12 rlam=0 lomadj=t ctitle='U.S. Retail Sales of Dept Stores, time varying TD effect', ry= 1746 1624 2195 2124 2308 2435 2109 2404 2439 2445 2935 4419 1915 1880 2290 2482 2561 2561 2466 2763 2527 2768 3321 4897 2114 1974 2540 2665 2831 2727 2643 2912 2737 2983 3359 5269 2281 2075 2644 2759 2879 2858 2733 2871 2818 3178 3487 5584 2385 2268 2834 3195 3138 3264 3075 3253 3316 3444 4081 6219 2580 2568 3268 3223 3546 3575 3335 3646 3666 3857 4468 6719 2929 2834 3685 3838 3990 4044 3689 4045 3897 4172 5037 7182 3156 2985 3886 4188 4355 4162 3988 4422 4084 4432 5085 7326 3161 3096 4036 4103 4729 4409 4227 4642 4502 4715 5544 8538 3564 3514 4382 4895 4691 4853 4693 4923 4933 5321 6218 9513 3743 3780 4937 5297 5259 5274 5251 5591 5547 5966 7050 11161 4158 4230 5646 5732 6121 6193 5684 6233 6172 6393 7642 11933 4552 4453 5948 6107 6505 6371 5992 6731 6451 6947 8526 12578 4954 5024 6103 6277 6949 6398 6320 7096 6626 7469 8779 13469 5408 5337 6778 7470 7716 7602 7188 7848 7528 8301 9521 14941 5635 5622 7216 7728 8160 7698 7654 7981 7693 8423 10005 16026 6067 5880 7893 8057 8667 8602 7993 8820 8555 9208 11194 17703 6777 6957 8589 9021 9970 9763 8636 9852 9393 9945 12615 18969 7138 7271 9346 9747 10464 9791 9114 10731 9536 10539 13078 19657 7524 7621 10201 10090 11369 10415 9993 11441 10335 11237 13539 20721 8066 8327 10320 11162 11930 11103 10565 11982 10947 12221 14451 22943 8467 8695 11314 11386 12093 11836 11003 12261 11635 12798 15565 24584 9035 9053 12093 12251 12820 12662 11791 13279 12465 13178 16629 25519 9489 9882 12946 12704 13341 13291 12143 13969 12553 13412 17068 25418 9782 10273 13425 13094 14276 13448 12844 14905 12932 14272 17978 26277 10870 11888 13623 14218 15120 14131 13869 15613 14095 15850 19152 28785 11898 12064 14287 15208 16177 15371 15398 16571 15578 17187 20494 30954 &end ®var ltd=t leastr=t neastr=10 icptrg= 2,3,4,5,6,7,0 &end &arima nd=1 nma=1 nsd=1 nsma=1 rvar=1 &end &arima nd=1 rvar=.1 ltvreg=t &end &arima nd=1 rvar=.1 ltvreg=t &end &arima nd=1 rvar=.1 ltvreg=t &end &arima nd=1 rvar=.1 ltvreg=t &end &arima nd=1 rvar=.1 ltvreg=t &end &arima nd=1 rvar=.1 ltvreg=t &end &opts lsmth=t lprint=f &end ----- Output File ----- REGCMPNT: Regression + ARIMA Component Model Estimation and Smoothing Program Version 1.6, 20 Sep 1995 Reading input namelist file from tvreg.nam NOTICE: Trading day option, LTD, will adjust the series by length of month. U.S. Retail Sales of Dept Stores, time varying TD effect Transformation ln(y/lom) Regression Model Trading Day+Holiday Component 1 ( 0 1 1)( 0 1 1)12 Component 2 Time varying regression of TD1 ( 0 1 0)1 Component 3 Time varying regression of TD2 ( 0 1 0)1 Component 4 Time varying regression of TD3 ( 0 1 0)1 Component 5 Time varying regression of TD4 ( 0 1 0)1 Component 6 Time varying regression of TD5 ( 0 1 0)1 Component 7 Time varying regression of TD6 ( 0 1 0)1 Smoothed signal will be produced MODEL ESTIMATION/EVALUATION Exact ARMA likelihood estimation Max total ARMA iterations 200 Max ARMA iter's w/in an IGLS iter. 40 Convergence tolerance 1.00E-05 Time Varying Component 2 Adjustment: TD1 Copied to Scale Factors Time Varying Component 3 Adjustment: TD2 Copied to Scale Factors Time Varying Component 4 Adjustment: TD3 Copied to Scale Factors Time Varying Component 5 Adjustment: TD4 Copied to Scale Factors Time Varying Component 6 Adjustment: TD5 Copied to Scale Factors Time Varying Component 7 Adjustment: TD6 Copied to Scale Factors Time Varying Component 2 Adjustment: TD1 Deleted from Regression Matrix Time Varying Component 3 Adjustment: TD2 Deleted from Regression Matrix Time Varying Component 4 Adjustment: TD3 Deleted from Regression Matrix Time Varying Component 5 Adjustment: TD4 Deleted from Regression Matrix Time Varying Component 6 Adjustment: TD5 Deleted from Regression Matrix Time Varying Component 7 Adjustment: TD6 Deleted from Regression Matrix First variance has been concentrated out. Estimation converged in 43 ARMA iterations, 452 function evaluations Regression Model ------------------------------------------------------------------ Parameter Standard Variable Estimate Error t-value ------------------------------------------------------------------ Holiday Easter 10 0.0317 0.00401 7.91 ------------------------------------------------------------------ Component 1: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Seasonal Difference (fixed) Lag 12 1.0000 Nonseasonal MA Lag 1 0.4879 0.05133 Seasonal MA Lag 12 0.5198 0.05426 Variance 0.38673E-03 0.42185E-04 log(Variance) -7.85778 0.10908 Component 2: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Variance 0.19594E-06 0.34860E-06 log(Variance) -15.44545 1.77910 Component 3: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Variance 0.14223E-06 0.23141E-06 log(Variance) -15.76584 1.62703 Component 4: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Variance 0.28872E-12 0.64949E-08 log(Variance) -28.87331 22495.28939 Component 5: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Variance 0.12674E-12 0.32944E-08 log(Variance) -29.69660 25992.62996 Component 6: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Variance 0.21169E-06 0.25806E-06 log(Variance) -15.36814 1.21903 Component 7: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Variance 0.63714E-07 0.25512E-06 log(Variance) -16.56886 4.00411 ----------------------------------------------------- Likelihood statistics ------------------------------------------------------------ Effective number of observations (nefobs) 305 Number of parameters estimated (np) 10 Log likelihood 744.1172 Transformation Adjustment -2704.4067 Adjusted Log likelihood (L) -1960.2896 AIC 3940.5791 F-corrected AIC 3941.3274 Hannan Quinn 3955.4596 BIC 3977.7823 ------------------------------------------------------------ nefobs = nobs-d, where d = 19 is the total differencing order Transformation Adjustment = (lam-1)*sum{log[y(i)]} (lam = Box-Cox power, sum is over last nefobs obervations) AIC = -2*L + 2*np F-corrected-AIC = -2*L + 2*np/[(1-(np+1)/nefobs)] Hannan Quinn = -2*L + 2*np*{log[log(nefobs)]} BIC = -2*L + [log(nefobs)]*np ARMA Parameter Correlation Matrix Parameter 1 2 3 4 5 6 7 8 9 ------------------------------------------------------------------ Component 1 ------------------------------------------------------------------ Nonseasonal MA Lag 1 1.00 Seasonal MA Lag 12 0.08 1.00 Var 1 0.05 -0.02 1.00 Component 2 ------------------------------------------------------------------ Var 2 -0.02 -0.08 -0.01 1.00 Component 3 ------------------------------------------------------------------ Var 3 -0.06 0.03 -0.05 -0.24 1.00 Component 4 ------------------------------------------------------------------ Var 4 -0.11 0.15 -0.08 -0.03 0.03 1.00 Component 5 ------------------------------------------------------------------ Var 5 0.05 -0.14 0.07 0.00 -0.05 -0.58 1.00 Component 6 ------------------------------------------------------------------ Var 6 -0.06 -0.01 -0.02 0.02 0.06 0.04 -0.01 1.00 Component 7 ------------------------------------------------------------------ Var 7 -0.06 -0.05 -0.04 0.01 -0.04 -0.01 -0.02 -0.23 1.00 FILE SAVE REQUESTS (* indicates file exists and will be overwritten) tvreg.est Estimates of the Components tvreg.var Signal Extraction Variances Performing Backward Smoothing Performing Forward Smoothing NOTICE: Logarithms are taken (rlam = 0). Signal extraction estimates are transformed back to the original scale, but signal extraction variances are left on the log (percentage) scale. NOTICE: Length-of-month (or length-of-quarter) factors will be incorporated into separate regression effects (component 0) for signal extraction estimates on the original scale. These factors have no effect on the signal extraction variances given in the log scale. ----- File: tvreg.est (excerpts) ----- Signal Extraction Estimates Separate Regression Effects (including lom or loq factors): t Regression 1 1.0185 2 0.91992 3 1.0380 4 0.96708 5 1.0185 6 0.98563 Component 1: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 7.4688 1.0000 1752.5 1.0000 1752.5 2 7.4761 1.0000 1765.4 1.0000 1765.4 3 7.6433 1.0000 2086.7 1.0000 2086.7 4 7.7130 1.0000 2237.3 1.0000 2237.3 5 7.7279 1.0000 2270.9 1.0000 2270.9 6 7.7916 1.0000 2420.1 1.0000 2420.1 7 7.6549 1.0000 2111.0 1.0000 2111.0 Component 2: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 -0.77170E-03 0. 1.0000 1.0000 1.0000 2 -0.77170E-03 0. 1.0000 1.0000 1.0000 3 -0.77170E-03 0. 1.0000 1.0000 1.0000 4 -0.77170E-03 -1.0000 1.0008 1.0000 1.0008 5 -0.78003E-03 1.0000 0.99922 1.0000 0.99922 6 -0.79218E-03 0. 1.0000 1.0000 1.0000 7 -0.80434E-03 0. 1.0000 1.0000 1.0000 8 -0.81650E-03 0. 1.0000 1.0000 1.0000 9 -0.82866E-03 0. 1.0000 1.0000 1.0000 10 -0.84082E-03 0. 1.0000 1.0000 1.0000 11 -0.85297E-03 0. 1.0000 1.0000 1.0000 12 -0.86513E-03 -1.0000 1.0009 1.0000 1.0009 13 -0.89096E-03 1.0000 0.99911 1.0000 0.99911 Component 3: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 0.59635E-02 0. 1.0000 1.0000 1.0000 2 0.59635E-02 0. 1.0000 1.0000 1.0000 3 0.59635E-02 0. 1.0000 1.0000 1.0000 4 0.59635E-02 -1.0000 0.99405 1.0000 0.99405 5 0.59574E-02 1.0000 1.0060 1.0000 1.0060 6 0.59486E-02 0. 1.0000 1.0000 1.0000 7 0.59398E-02 -1.0000 0.99408 1.0000 0.99408 Component 7: (Log Transformed Scale) | (Original Untransformed Scale) Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 0.87849E-02 -1.0000 0.99125 1.0000 0.99125 2 0.87897E-02 0. 1.0000 1.0000 1.0000 3 0.87946E-02 0. 1.0000 1.0000 1.0000 4 0.87995E-02 0. 1.0000 1.0000 1.0000 5 0.88043E-02 0. 1.0000 1.0000 1.0000 6 0.88092E-02 0. 1.0000 1.0000 1.0000 7 0.88141E-02 0. 1.0000 1.0000 1.0000 8 0.88189E-02 0. 1.0000 1.0000 1.0000 9 0.88238E-02 1.0000 1.0089 1.0000 1.0089 10 0.88224E-02 -1.0000 0.99122 1.0000 0.99122 11 0.88205E-02 0. 1.0000 1.0000 1.0000 ----- File: tvreg.var (excerpts) ----- Signal Extraction Variances (on transformed scale) Component 1: Unscaled Scaled t Stochastic Stochastic Combined 1 0.13628E-04 0.13628E-04 0.13631E-04 2 -0.10864E-39 -0.10864E-39 -0.10864E-39 3 0.10554E-04 0.10554E-04 0.14311E-04 4 0.18699E-04 0.18699E-04 0.21275E-04 5 0.13347E-04 0.13347E-04 0.13460E-04 Component 2: Unscaled Scaled t Stochastic Stochastic Combined 1 0.14413E-04 0. 0. 2 0.14217E-04 0. 0. 3 0.14021E-04 0. 0. 4 0.13825E-04 0.13825E-04 0.14165E-04 5 0.13647E-04 0.13647E-04 0.13984E-04 6 0.13482E-04 0. 0. 7 0.13317E-04 0. 0. 8 0.13151E-04 0. 0. 9 0.12984E-04 0. 0. 10 0.12817E-04 0. 0. 11 0.12649E-04 0. 0. 12 0.12481E-04 0.12481E-04 0.12804E-04 13 0.12324E-04 0.12324E-04 0.12647E-04 Component 3: Unscaled Scaled t Stochastic Stochastic Combined 1 0.11235E-04 0. 0. 2 0.11093E-04 0. 0. 3 0.10951E-04 0. 0. 4 0.10809E-04 0.10809E-04 0.10870E-04 5 0.10673E-04 0.10673E-04 0.10735E-04 6 0.10544E-04 0. 0. 7 0.10415E-04 0.10415E-04 0.10478E-04 8 0.10297E-04 0.10297E-04 0.10360E-04 9 0.10190E-04 0. 0. Component 7: Unscaled Scaled t Stochastic Stochastic Combined 1 0.90544E-05 0.90544E-05 0.92239E-05 2 0.89925E-05 0. 0. 3 0.89305E-05 0. 0. 4 0.88686E-05 0. 0. 5 0.88066E-05 0. 0. 6 0.87446E-05 0. 0. 7 0.86826E-05 0. 0. 8 0.86206E-05 0. 0. 9 0.85585E-05 0.85585E-05 0.87281E-05 10 0.85003E-05 0.85003E-05 0.86700E-05 ************************************************************************** * Example: U.S. Teen Unemployment, Jan 72 - Dec 83 * ************************************************************************** &series ctitle='Teen Unemployment Jan 72 - Dec 83' ibegdt=1972,1 ienddt=1983,12 ry= 1272 1361 1284 1140 959 1888 1631 1353 1266 1154 1237 1155 1058 1209 1112 1117 996 1804 1582 1184 1219 1129 1257 1152 1281 1271 1237 1040 1095 2067 1863 1306 1492 1412 1526 1473 1744 1667 1689 1535 1569 2451 2194 1839 1688 1617 1598 1615 1753 1670 1638 1568 1453 2268 2030 1810 1621 1587 1656 1576 1699 1655 1667 1456 1419 2391 1981 1676 1631 1501 1564 1315 1561 1592 1571 1380 1342 2065 1954 1567 1536 1454 1503 1470 1539 1539 1473 1381 1362 2065 1832 1567 1538 1471 1461 1427 1541 1547 1456 1314 1616 2307 2137 1750 1614 1616 1653 1472 1730 1747 1673 1565 1627 2258 1971 1682 1675 1703 1841 1679 1849 1918 1777 1778 1892 2415 2326 2015 1937 1924 2007 1883 1863 1805 1818 1718 1742 2527 2179 1907 1700 1627 1584 1474 &end ®var lconst=f,ltd=f,lseff=f &end &arima nd=1,nma=1,rma=.26, nsd=1,nsma=1,rsma=.78, rvar=3931,lfix=f &end &arima lar=1,rar=.6,nma=1,rma=.3,rvar=0.876712 lfix=t rh= 49.82326 51.51884 50.05537 47.19169 43.31417 60.55337 56.33827 51.36881 49.70677 47.47798 49.13975 47.49836 45.47737 48.58575 46.61365 46.71742 44.13545 59.21057 55.49621 48.08550 48.78436 46.96549 49.53152 47.43719 49.99744 49.80386 49.13975 45.09203 46.25905 63.31420 60.15705 50.47801 53.91357 52.46472 54.51713 53.57318 58.23133 56.94857 57.31817 54.67572 55.27055 68.84046 65.19759 59.77395 57.30142 56.09904 55.77264 56.06478 58.37932 56.99912 56.45748 55.25315 53.21242 66.26860 62.75412 59.30755 56.16750 55.58275 56.76282 55.39218 57.48534 56.74591 56.94857 53.26670 52.59317 68.00878 62.00410 57.10007 56.33827 54.07402 55.18350 50.64986 55.13120 55.66915 55.30533 51.87333 51.16178 63.28406 61.58666 55.23575 54.69332 53.23052 54.10961 53.51923 54.74605 54.74605 53.57318 51.89192 51.53756 63.28406 59.66172 55.23575 54.72848 53.53722 53.35703 52.73956 54.78119 54.88644 53.26670 50.63079 56.08191 66.82565 64.35958 58.33004 56.04763 56.08191 56.71205 53.55521 58.00033 58.28071 57.04962 55.20092 56.27003 66.12496 61.84984 57.20084 57.08326 57.55206 59.80598 57.15048 59.93389 61.02535 58.77205 58.78835 60.61652 68.34275 67.09523 62.52554 61.32228 61.11928 62.40327 60.47432 60.15705 59.22674 59.43660 57.80155 58.19839 69.87857 64.97818 60.85274 57.50202 56.27003 55.53085 53.59115 &end &opts lsmth=t,lprint=f &end ----- Output File ----- REGCMPNT: Regression + ARIMA Component Model Estimation and Smoothing Program Version 1.6, 20 Sep 1995 by Time Series Staff Census Bureau Rm 3000-4 (SRD) WASH DC 20233-9100 Date Thu Aug 15 15:30:54 1996 Reading input namelist file from teen.nam Teen Unemployment Jan 72 - Dec 83 JAN FEB MAR APR MAY JUN Year JUL AUG SEP OCT NOV DEC ------------------------------------------------------------------------------- 1972 1272.000 1361.000 1284.000 1140.000 959.000 1888.000 1631.000 1353.000 1266.000 1154.000 1237.000 1155.000 1973 1058.000 1209.000 1112.000 1117.000 996.000 1804.000 1582.000 1184.000 1219.000 1129.000 1257.000 1152.000 1974 1281.000 1271.000 1237.000 1040.000 1095.000 2067.000 1863.000 1306.000 1492.000 1412.000 1526.000 1473.000 1983 1863.000 1805.000 1818.000 1718.000 1742.000 2527.000 2179.000 1907.000 1700.000 1627.000 1584.000 1474.000 Transformation y Component 1 ( 0 1 1)( 0 1 1)12 Component 2 ( 1 0 1)1 Variance multipliers JAN FEB MAR APR MAY JUN Year JUL AUG SEP OCT NOV DEC ------------------------------------------------------------------------------- 1972 49.823 51.519 50.055 47.192 43.314 60.553 56.338 51.369 49.707 47.478 49.140 47.498 1973 45.477 48.586 46.614 46.717 44.135 59.211 55.496 48.086 48.784 46.965 49.532 47.437 1974 49.997 49.804 49.140 45.092 46.259 63.314 60.157 50.478 53.914 52.465 54.517 53.573 1983 60.157 59.227 59.437 57.802 58.198 69.879 64.978 60.853 57.502 56.270 55.531 53.591 Smoothed signal will be produced MODEL ESTIMATION/EVALUATION Exact ARMA likelihood estimation Max total ARMA iterations 200 Convergence tolerance 1.00E-05 Estimation converged in 6 ARMA iterations, 25 function evaluations Component 1: ----------------------------------------------------- Standard Parameter Estimate Errors ----------------------------------------------------- Nonseasonal Difference (fixed) Lag 1 1.0000 Seasonal Difference (fixed) Lag 12 1.0000 Nonseasonal MA Lag 1 0.2698 0.14636 Seasonal MA Lag 12 0.6781 0.13615 Variance 0.42277E+04 0.13471E+04 log(Variance) 8.34941 0.31864 Component 2: (fixed) ------------------------------------- Parameter Value ------------------------------------- Nonseasonal AR Lag 1 0.6000 Nonseasonal MA Lag 1 0.3000 Variance 0.87671E+00 log(Variance) -0.13158 ------------------------------------- Likelihood statistics ------------------------------------------------------------ Effective number of observations (nefobs) 131 Number of parameters estimated (np) 3 Log likelihood (L) -778.6210 AIC 1563.2419 F-corrected AIC 1563.4309 Hannan Quinn 1566.7469 BIC 1571.8675 ------------------------------------------------------------ nefobs = nobs-d, where d = 13 is the total differencing order AIC = -2*L + 2*np F-corrected-AIC = -2*L + 2*np/[(1-(np+1)/nefobs)] Hannan Quinn = -2*L + 2*np*{log[log(nefobs)]} BIC = -2*L + [log(nefobs)]*np ARMA Parameter Correlation Matrix Parameter 1 2 3 ------------------------------ Component 1 ------------------------------ Nonseasonal MA Lag 1 1.00 Seasonal MA Lag 12 0.31 1.00 Var 1 0.44 0.24 1.00 FILE SAVE REQUESTS (* indicates file exists and will be overwritten) teen.est Estimates of the Components teen.var Signal Extraction Variances Performing Backward Smoothing Performing Forward Smoothing ----- File: teen.est (excerpts) ----- Signal Extraction Estimates Component 1: Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 1271.7 1.0000 1271.7 0. 1271.7 2 1328.4 1.0000 1328.4 0. 1328.4 3 1260.4 1.0000 1260.4 0. 1260.4 4 1122.4 1.0000 1122.4 0. 1122.4 5 996.16 1.0000 996.16 0. 996.16 Component 2: Unscaled Scale Scaled Regression Combined t Stochastic Factors Stochastic Effects Estimate 1 0.63192E-02 49.823 0.31484 0. 0.31484 2 0.63291 51.519 32.607 0. 32.607 3 0.47166 50.055 23.609 0. 23.609 4 0.37260 47.192 17.584 0. 17.584 5 -0.85791 43.314 -37.160 0. -37.160 6 0.90161E-01 60.553 5.4596 0. 5.4596 7 -0.12875 56.338 -7.2535 0. -7.2535 8 0.74041 51.369 38.034 0. 38.034 ----- File: teen.var (excerpts) ----- Signal Extraction Variances Component 1: Unscaled Scaled t Stochastic Stochastic Combined 1 1992.1 1992.1 1992.1 2 1948.4 1948.4 1948.4 3 1818.7 1818.7 1818.7 4 1656.7 1656.7 1656.7 5 1472.0 1472.0 1472.0 Component 2: Unscaled Scaled t Stochastic Stochastic Combined 1 0.80250 1992.1 1992.1 2 0.73407 1948.4 1948.4 3 0.72587 1818.7 1818.7 4 0.74391 1656.7 1656.7 5 0.78458 1472.0 1472.0 6 0.61414 2251.9 2251.9 7 0.65663 2084.1 2084.1 8 0.70046 1848.3 1848.3