Shareware Grab Bag

home *** CD-ROM | disk | FTP | other *** search

/ Shareware Grab Bag / Shareware Grab Bag.iso / 090 / sampler4.arc / FORECAST.SAC < prev next >

Wrap

Text File | 1985-08-30 | 13.8 KB | 391 lines

!*******************************************************************! ! ! ! Forecasting the Single Equation Model ! ! (Section 9.4) ! ! ! !*******************************************************************! ON ECHO ! Forecasting with SORITEC SAMPLER is accomplished by RECOVERing ! the fitted equation from SORITEC's internal variables after ! estimation, changing the USE period to the forecast interval, and ! executing the FORECAST command. SAMPLER's forecasting capabilities ! are demonstrated with an example adapted from R.W. Kopcke, ! "Forecasting Investment Spending: The Performance of Statistical ! Models", New England Economic Review, November/December, 1982. ! ! In this example, we estimate two of the models evaluated in that ! study for forecasting investment in nonresidential structures: ! (1) The General Accelerator Model ! (2) The Time Series Model ! The General Accelerator Model relates gross private investment in ! nonresidential structures to gross domestic business product and ! net stocks of nonresidential structures. The Time Series Model ! relates the ratio of gross private investment and net stocks of ! residential structures lagged by one period to the ratio from the ! previous period. Independent variables in both equations are ! lagged several periods back. ! ! This example differs from the Kopcke study in both the data and ! estimator used to estimate the equations. Identical results ! should therefore not be expected. ! ! The equations are estimated from 1954q1 to 1977q4; forecasts are ! evaluated over the 1978q1 to 1980q4 period. Since independent ! variables are lagged several quarters back, data from 1951q1 are ! read into SORITEC SAMPLER. Data definitions are: ! ! qpi = gross private investment in nonresidential ! structures ! gdbp = gross domestic business product ! nonres_stocks = net stocks of nonresidential structures ! ! All data are expressed in 1972 dollars. ! USE 1951Q1 1981Q4 READ qpi gdbp nonres_stocks 20.4 290.37 212.285 21.1 293.18 214.449 21.0 297.06 216.341 20.1 299.83 218.194 20.2 301.93 219.826 20.4 299.83 221.699 20.6 301.60 223.370 21.4 317.93 225.434 22.0 325.07 227.386 22.5 328.88 229.658 22.6 326.74 231.688 23.1 314.62 234.039 23.5 312.10 236.217 23.7 311.91 238.645 23.7 315.90 241.038 23.7 325.03 243.397 24.5 339.87 245.919 25.0 349.06 248.528 25.9 353.77 251.319 26.4 360.03 254.194 27.3 360.79 257.508 28.4 362.50 260.792 28.8 360.41 264.128 28.8 367.20 267.685 28.5 370.94 270.855 28.5 369.76 274.255 28.4 368.58 277.312 28.3 361.67 280.301 27.9 347.20 283.434 26.9 346.27 285.997 26.2 357.20 288.349 26.4 372.40 290.718 26.3 385.87 293.028 27.2 399.29 295.824 28.0 391.06 298.487 27.9 393.59 301.390 29.3 409.83 304.301 29.0 406.35 307.404 29.2 400.68 310.212 30.6 396.69 313.639 30.6 398.89 316.711 30.1 408.79 319.935 30.1 415.73 322.800 29.9 428.45 325.900 30.4 438.04 328.901 31.6 441.13 332.159 32.7 446.08 335.980 31.9 448.65 339.221 30.6 454.69 342.094 32.1 465.28 345.299 32.3 471.39 348.509 32.8 476.69 351.799 32.8 488.96 355.044 34.3 495.49 358.615 35.1 503.30 362.336 35.6 507.50 366.129 37.6 525.09 370.736 40.7 532.16 375.689 40.9 539.42 380.623 43.4 553.87 386.110 43.8 566.45 391.620 43.2 571.17 396.507 44.1 576.32 401.937 42.7 580.54 406.942 42.8 581.53 411.490 41.7 584.79 416.103 41.9 591.29 420.701 41.5 599.63 425.136 43.0 608.77 429.881 42.4 620.19 434.411 42.1 631.16 438.803 43.6 639.04 443.507 44.1 645.39 448.269 44.5 648.75 453.064 45.9 653.08 458.140 45.4 650.00 463.021 44.2 643.46 467.535 44.3 644.90 472.012 43.9 650.64 476.327 43.3 640.70 480.433 43.2 660.25 484.456 42.9 662.96 488.349 43.0 670.16 491.721 42.3 680.18 495.353 43.5 698.07 499.232 43.9 711.45 503.156 44.0 720.35 507.051 45.2 739.28 511.188 45.9 759.64 515.442 47.3 757.51 520.504 48.3 758.00 525.235 47.9 763.59 529.801 46.6 755.51 533.973 45.2 756.38 538.278 41.8 751.28 541.691 40.8 739.88 544.278 38.6 720.60 546.828 37.6 733.36 548.556 38.3 755.08 550.984 38.5 766.15 552.889 39.2 790.39 555.494 39.4 793.51 557.014 39.8 800.75 559.159 39.5 805.49 561.198 38.9 823.77 563.059 40.2 849.78 565.219 41.3 870.62 567.622 41.2 873.84 570.535 41.9 877.78 572.455 44.7 903.70 575.605 45.7 909.09 578.960 46.2 920.95 582.393 46.6 924.03 585.295 48.2 918.39 588.539 50.4 922.38 592.268 51.2 919.65 596.127 50.9 928.33 600.218 48.4 908.49 603.854 47.5 910.13 607.217 48.3 923.83 610.731 50.4 940.97 614.867 52.3 942.98 619.351 55.0 948.08 624.448 55.1 928.47 629.499 ; END ! ! As the Time Series Model requires both the dependent and independent ! variables to be expressed as ratios, transform the variables before ! estimating the model. ! USE 1954q1 1981q4 lag_0 = qpi(0)/nonres_stocks(-1) lag_1 = qpi(-1)/nonres_stocks(-1) lag_2 = qpi(-2)/nonres_stocks(-1) lag_3 = qpi(-3)/nonres_stocks(-1) ! ! Define names for the transformed variables in a GROUP statement. ! GROUP tsm_vars lag_0 lag_1 lag_2 lag_3 ON GROUP ! ! Now estimate the Time Series Model using OLS. ! REGRESS tsm_vars OFF GROUP ! ! In order to forecast, we must recover the fitted equation which is ! stored as a SORITEC internal variable under the name, ^FOREQ. ! Also, we want to recover rho, which measures the autocorrelation ! between residual terms. Rho is stored as the first element of the ! internal SORITEC variable ^AUTOCOR and is used correct the ! raw forecast data as was done in the Kopcke article. ! RECOVER tsm_fitted FOREQ SET tsm_rho = ^AUTOCOR(1) ! ! Now estimate the General Accelerator Model over the 1954q1 to 1977q4 ! period. Note that in this specification, gross domestic business ! product is lagged from t=0 to t=-5. These can be specified quite ! simply in SORITEC as shown in the command line. Again, OLS is used ! to estimate the model ! REGRESS qpi gdbp(0 to -5) nonres_stocks(-1) ! ! Again, RECOVER the fitted equation and rho. ! RECOVER gam_fitted FOREQ SET gam_rho = ^AUTOCOR(1) ! ! The important thing to remember when FORECASTing a fitted equation is ! that the original dependent variable is replaced by forecast values of ! the dependent variable over the period being forecast. Because of this, ! it is advisable either to databank the original data series (remember, ! all observations will be saved regardless of the active USE period), or ! copy the original series into another via a transformation, i.e., ! USE 1951Q1 1981Q4 qpi_original = qpi ! ! Now adjust the USE period to the period over which forecasts are to ! be made. ! USE 1978q1 1981q4 ! ! Then simply forecast the dependent variable for each model. ! ! (1) For the Time Series Model: ! FORECAST tsm_fitted ! ! Transform the dependent variable for the Time Series Model back into ! gross private investment in nonresidential structures. ! qpi_tsm = lag_0 * nonres_stocks(-1) ! ! (2) For the General Accelerator Model: ! FORECAST gam_fitted ! ! Copy the forecast dependent variable into qpi_gam (for consistencey). ! qpi_gam = qpi ! ! Print out the original and two forecast values for gross private ! investment in nonresidential structures. ! PRINT qpi_original qpi_tsm qpi_gam ! ! Plot the original data and the two forecast estimates. ! Let qpi_original = O ! qpi_tsm = T ! qpi_gam = G ! PLOT qpi_original O qpi_tsm T qpi_gam G ! ! Correct the raw forecast error by subtracting the product of the ! raw forecast error from the previous quarter and the equations ! autocorrelation coefficient (rho) from the raw forecast error ! for the current quarter. (Set the 1977q4 values of qpi_tsm and ! qpi_gam to the actual values, first. Note that you must REVISE ! the series or the forecast values will be wiped out.) ! USE 1977q4 REVISE qpi_tsm = qpi_original REVISE qpi_gam = qpi_original USE 1978q1 1981q4 tsm_error = (qpi_original - qpi_tsm) & - tsm_rho * (qpi_original(-1) - qpi_tsm(-1)) gam_error = (qpi_original - qpi_gam) & - gam_rho * (qpi_original(-1) - qpi_gam(-1)) ! ! Now calculate error statistics similar to those in the Kopcke ! article: ! ! (1) mean error ! DOT tsm_error gam_error SUM error_sum : SET mean_: = error_sum/16 ENDDOT ! ! (2) mean absolute error ! DOT tsm_error gam_error abs_: = abs(:) SUM error_sum abs_: SET mean_abs_: = error_sum/16 ENDDOT ! ! (3) root mean square error. ! DOT tsm_error gam_error squared_: = : ** 2 SUM error_sum squared_: SET mean_squared_: = (error_sum/16)**0.5 ENDDOT ! ! Write out results in formatted form and compare to Kopcke results ! ! First enter Kopcke results, as vectors. ! VECTOR gam_vec .57 1.0 1.1 VECTOR tsm_vec .52 1.1 1.3 ! ! Set up the format statements ! 100 FORMAT(/////15x,& 'Error Statistics for Static Forecasts of Investment Models') 101 FORMAT(31x,'1978Q1 to 1981Q4') 102 FORMAT(11x,'Estimated Results',25x,'Kopcke Results') 103 FORMAT(2(17x,'Mean',7x,'Root Mean',2x),/,2(4x,'Mean',7x,'Absolute', & 6x,'Squared',3x)/6(4x,'Error',4x)/) 104 FORMAT(6(f9.2,4x)) 105 FORMAT(' General Accelerator Model') 106 FORMAT(' Time Series Model') ! ! Write out the results. Since we don't want the results written ! out after each command (the commands and output would be intermixed), ! disable the ECHO option with the OFF ECHO command. This simply turns ! off the printing of input lines to the output device. ! OFF ECHO WRITE(100) WRITE(101) WRITE(102) WRITE(103) WRITE(105) WRITE(104) mean_gam_error mean_abs_gam_error mean_squared_gam_error gam_vec WRITE(106) WRITE(104) mean_tsm_error mean_abs_tsm_error mean_squared_tsm_error tsm_vec ON ECHO QUIT