profile review. owidth 80. <== Store output into the file "scaoutp.otp". -- input x,y. file 'data1.txt' <== Input data -- iarima x. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 THE CRITICAL VALUE FOR SIGNIFICANCE TESTS OF ACF AND ESTIMATES IS 1.960 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- UTSMODEL ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 X D-AR 1 1 NONE 1.5154 .0397 38.13 2 X D-AR 1 2 NONE -.6129 .0398 -15.39 TOTAL NUMBER OF OBSERVATIONS . . . . 400 EFFECTIVE NUMBER OF OBSERVATIONS . . 398 RESIDUAL STANDARD ERROR. . . . . . . 0.962827E+00 -- tsm mx. model (1,2)x=c1+noise. <== Include a constant term. -- estim mx. hold resi(rx) SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- MX ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 C1 CNST 1 0 NONE .0041 .0483 .08 2 X AR 1 1 NONE 1.5154 .0397 38.12 3 X AR 1 2 NONE -.6129 .0398 -15.39 EFFECTIVE NUMBER OF OBSERVATIONS . . 398 R-SQUARE . . . . . . . . . . . . . . 0.926 RESIDUAL STANDARD ERROR. . . . . . . 0.962818E+00 -- tsm mx. model (1,2)x=noise. <== Drop the constant term based on estimation result. -- estim mx. hold resi(rx). THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- MX ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 X AR 1 1 NONE 1.5154 .0397 38.13 2 X AR 1 2 NONE -.6129 .0398 -15.39 EFFECTIVE NUMBER OF OBSERVATIONS . . 398 R-SQUARE . . . . . . . . . . . . . . 0.926 RESIDUAL STANDARD ERROR. . . . . . . 0.962827E+00 -- acf rx. maxl 12. NAME OF THE SERIES . . . . . . . . . . RX TIME PERIOD ANALYZED . . . . . . . . . 3 TO 400 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0041 STANDARD DEVIATION OF THE SERIES . . . 0.9628 T-VALUE OF MEAN (AGAINST ZERO) . . . . 0.0842 AUTOCORRELATIONS 1- 12 .03 -.04 .00 -.03 .08 -.03 .00 -.03 .03 -.01 .01 .09 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 Q .5 1.1 1.1 1.4 4.0 4.3 4.3 4.7 5.0 5.0 5.1 8.7 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.03 + IX+ 2 -0.04 +XI + 3 0.00 + I + 4 -0.03 +XI + 5 0.08 + IXX 6 -0.03 +XI + 7 0.00 + I + 8 -0.03 +XI + 9 0.03 + IX+ 10 -0.01 + I + 11 0.01 + I + 12 0.09 + IXX -- iarima y. SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- UTSMODEL ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 Y D-AR 1 1 NONE 1.5693 .0485 32.38 2 Y D-AR 1 2 NONE -.3118 .0879 -3.55 3 Y D-AR 1 3 NONE -.5826 .0879 -6.63 4 Y D-AR 1 4 NONE .2700 .0487 5.54 TOTAL NUMBER OF OBSERVATIONS . . . . 400 EFFECTIVE NUMBER OF OBSERVATIONS . . 396 RESIDUAL STANDARD ERROR. . . . . . . 0.845427E+01 -- tsm my. model (1,2,3,4)y=c2+noise. -- estim my. hold resi(ry). SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- MY ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 C2 CNST 1 0 NONE .0699 .4249 .16 2 Y AR 1 1 NONE 1.5691 .0485 32.38 3 Y AR 1 2 NONE -.3116 .0879 -3.55 4 Y AR 1 3 NONE -.5827 .0879 -6.63 5 Y AR 1 4 NONE .2701 .0487 5.54 EFFECTIVE NUMBER OF OBSERVATIONS . . 396 R-SQUARE . . . . . . . . . . . . . . 0.966 RESIDUAL STANDARD ERROR. . . . . . . 0.845398E+01 -- tsm my. model (1,2,3,4)y=noise. -- estim my. hold resi(ry) THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- MY ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 Y AR 1 1 NONE 1.5692 .0485 32.38 2 Y AR 1 2 NONE -.3116 .0879 -3.55 3 Y AR 1 3 NONE -.5826 .0879 -6.63 4 Y AR 1 4 NONE .2700 .0487 5.54 EFFECTIVE NUMBER OF OBSERVATIONS . . 396 R-SQUARE . . . . . . . . . . . . . . 0.966 RESIDUAL STANDARD ERROR. . . . . . . 0.845427E+01 -- acf ry. maxl 12. NAME OF THE SERIES . . . . . . . . . . RY TIME PERIOD ANALYZED . . . . . . . . . 5 TO 400 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0699 STANDARD DEVIATION OF THE SERIES . . . 8.4540 T-VALUE OF MEAN (AGAINST ZERO) . . . . 0.1645 AUTOCORRELATIONS 1- 12 -.01 .01 .01 -.03 .01 .04 .01 -.05 -.02 .02 -.00 .08 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 Q .0 .0 .1 .5 .5 1.0 1.1 2.3 2.4 2.5 2.5 5.4 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 -0.01 + I + 2 0.01 + I + 3 0.01 + I + 4 -0.03 +XI + 5 0.01 + I + 6 0.04 + IX+ 7 0.01 + I + 8 -0.05 +XI + 9 -0.02 + I + 10 0.02 + I + 11 0.00 + I + 12 0.08 + IXX -- tsm tstx. model x=(0 to 5)y+1/(1,2)noise. <== Test the exogeneity of x. -- estim tstx. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- TSTX ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED X RANDOM ORIGINAL NONE Y RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 Y NUM. 1 0 NONE .0020 .0072 .28 2 Y NUM. 1 1 NONE .0094 .0073 1.29 3 Y NUM. 1 2 NONE .0139 .0069 2.02 4 Y NUM. 1 3 NONE .0049 .0065 .76 5 Y NUM. 1 4 NONE .0067 .0061 1.11 6 Y NUM. 1 5 NONE -.0054 .0063 -.86 7 X D-AR 1 1 NONE 1.5522 .0415 37.37 8 X D-AR 1 2 NONE -.7023 .0458 -15.34 EFFECTIVE NUMBER OF OBSERVATIONS . . 393 R-SQUARE . . . . . . . . . . . . . . 0.927 RESIDUAL STANDARD ERROR. . . . . . . 0.957614E+00 -- tsm tsty. model y=(0 to 5)x+1/(1,2,3,4)noise. <== Test exogeneity of y. -- estim tsty. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- TSTY ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 X NUM. 1 0 NONE -.2410 .1562 -1.54 2 X NUM. 1 1 NONE .1672 .2891 .58 3 X NUM. 1 2 NONE 2.9271 .3300 8.87 4 X NUM. 1 3 NONE 6.1798 .3294 18.76 5 X NUM. 1 4 NONE .8313 .2882 2.88 6 X NUM. 1 5 NONE 3.4219 .1559 21.94 7 Y D-AR 1 1 NONE -.0265 .0507 -.52 8 Y D-AR 1 2 NONE .2801 .0501 5.59 9 Y D-AR 1 3 NONE .1650 .0501 3.29 10 Y D-AR 1 4 NONE .0981 .0507 1.93 EFFECTIVE NUMBER OF OBSERVATIONS . . 391 R-SQUARE . . . . . . . . . . . . . . 0.996 RESIDUAL STANDARD ERROR. . . . . . . 0.298457E+01 -- filter mx. old x,y. new fx,fy. <== Filtering using the model of x series. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 SERIES X IS FILTERED USING MODEL MX , THE RESULT IS IN FX SERIES Y IS FILTERED USING MODEL MX , THE RESULT IS IN FY -- ccf fx,fy. maxl 12. hold ccf(vb) TIME PERIOD ANALYZED . . . . . . . . . 3 TO 400 NAMES OF THE SERIES . . . . . . . . . FX FY EFFECTIVE NUMBER OF OBSERVATIONS . . . 398 398 STANDARD DEVIATION OF THE SERIES . . . 0.9628 9.1273 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0041 0.0986 STANDARD DEVIATION OF THE MEAN . . . . 0.0483 0.4575 T-VALUE OF MEAN (AGAINST ZERO) . . . . 0.0842 0.2156 CORRELATION BETWEEN FY AND FX IS -0.02 CROSS CORRELATION BETWEEN FX(T) AND FY(T-L) 1- 12 -.01 .05 -.03 .05 -.06 .03 .01 .03 .07 -.04 .09 -.02 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 CROSS CORRELATION BETWEEN FY(T) AND FX(T-L) 1- 12 .00 .33 .62 .22 .19 .04 .06 .01 .08 -.04 .01 -.02 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I -12 -0.02 +XI + -11 0.01 + I + -10 -0.04 +XI + -9 0.08 + IXX -8 0.01 + I + -7 0.06 + IX+ -6 0.04 + IX+ -5 0.19 + IX+XXX -4 0.22 + IX+XXXX -3 0.62 + IX+XXXXXXXXXXXXXX -2 0.33 + IX+XXXXXX -1 0.00 + I + 0 -0.02 +XI + 1 -0.01 + I + 2 0.05 + IX+ 3 -0.03 +XI + 4 0.05 + IX+ 5 -0.06 +XI + 6 0.03 + IX+ 7 0.01 + I + 8 0.03 + IX+ 9 0.07 + IXX 10 -0.04 +XI + 11 0.09 + IXX 12 -0.02 + I + -- ff=sqrt(var(fy))/sqrt(var(fx)) -- ccf fy,fx. maxl 12. hold ccf(vb) TIME PERIOD ANALYZED . . . . . . . . . 3 TO 400 NAMES OF THE SERIES . . . . . . . . . FY FX EFFECTIVE NUMBER OF OBSERVATIONS . . . 398 398 STANDARD DEVIATION OF THE SERIES . . . 9.1273 0.9628 MEAN OF THE (DIFFERENCED) SERIES . . . 0.0986 0.0041 STANDARD DEVIATION OF THE MEAN . . . . 0.4575 0.0483 T-VALUE OF MEAN (AGAINST ZERO) . . . . 0.2156 0.0842 CORRELATION BETWEEN FX AND FY IS -0.02 CROSS CORRELATION BETWEEN FY(T) AND FX(T-L) 1- 12 .00 .33 .62 .22 .19 .04 .06 .01 .08 -.04 .01 -.02 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 CROSS CORRELATION BETWEEN FX(T) AND FY(T-L) 1- 12 -.01 .05 -.03 .05 -.06 .03 .01 .03 .07 -.04 .09 -.02 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I -12 -0.02 + I + -11 0.09 + IXX -10 -0.04 +XI + -9 0.07 + IXX -8 0.03 + IX+ -7 0.01 + I + -6 0.03 + IX+ -5 -0.06 +XI + -4 0.05 + IX+ -3 -0.03 +XI + -2 0.05 + IX+ -1 -0.01 + I + 0 -0.02 +XI + 1 0.00 + I + 2 0.33 + IX+XXXXXX 3 0.62 + IX+XXXXXXXXXXXXXX 4 0.22 + IX+XXXX 5 0.19 + IX+XXX 6 0.04 + IX+ 7 0.06 + IX+ 8 0.01 + I + 9 0.08 + IXX 10 -0.04 +XI + 11 0.01 + I + 12 -0.02 +XI + -- vhat=vb*ff -- sele old vhat. new xx. span (13,25). VARIABLE VHAT IS EDITED, THE RESULT IS STORED IN VARIABLE XX VARIABLE XX IS A 13 BY 1 MATRIX -- corner xx. size nrows(8), ncolx(6). CORNER TABLE FOR THE TRANSFER FUNCTION WEIGHTS IN XX 1 2 3 4 5 6 0 -0.04 0.00 0.00 0.00 0.00 0.00 1 0.00 0.02 0.00 0.00 0.00 0.00 2 0.53 0.28 0.11 0.04 0.01 0.00 <=== b = 2 3 1.00 0.81 0.71 0.63 0.56 0.49 <=== b+s = 3, implying s = 1. 4 0.36 -0.18 -0.07 -0.02 0.00 -0.05 <== From the first two columns, r = 1. 5 0.31 0.07 0.00 0.00 0.00 0.01 6 0.07 -0.02 0.00 0.00 0.00 0.00 7 0.09 0.01 0.00 0.00 0.00 0.00 -- tsm m1. model y=(0 to 12)x+1/(1,2,3,4)noise. <== Model used to estimate Nt series -- estim m1. hold disturb(nt). THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M1 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 X NUM. 1 0 NONE -.0648 .1048 -.62 2 X NUM. 1 1 NONE .0514 .2577 .20 3 X NUM. 1 2 NONE 3.0414 .3222 9.44 4 X NUM. 1 3 NONE 5.8339 .3310 17.63 5 X NUM. 1 4 NONE 1.9206 .3329 5.77 6 X NUM. 1 5 NONE 2.0572 .3368 6.11 7 X NUM. 1 6 NONE .3805 .3395 1.12 8 X NUM. 1 7 NONE .5712 .3385 1.69 9 X NUM. 1 8 NONE -.2942 .3359 -.88 10 X NUM. 1 9 NONE .8009 .3345 2.39 11 X NUM. 1 10 NONE -.3525 .3252 -1.08 12 X NUM. 1 11 NONE -.0733 .2587 -.28 13 X NUM. 1 12 NONE .1179 .1052 1.12 14 Y D-AR 1 1 NONE -.6858 .0508 -13.49 15 Y D-AR 1 2 NONE -.4202 .0598 -7.03 16 Y D-AR 1 3 NONE -.3058 .0597 -5.12 17 Y D-AR 1 4 NONE -.1133 .0508 -2.23 EFFECTIVE NUMBER OF OBSERVATIONS . . 384 R-SQUARE . . . . . . . . . . . . . . 0.998 RESIDUAL STANDARD ERROR. . . . . . . 0.195769E+01 -- iarima nt. <= Identify a model for the disturbance term. THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 THE CRITICAL VALUE FOR SIGNIFICANCE TESTS OF ACF AND ESTIMATES IS 1.960 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- UTSMODEL ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED NT RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 NT MA 1 1 NONE .7182 .0349 20.58 TOTAL NUMBER OF OBSERVATIONS . . . . 388 EFFECTIVE NUMBER OF OBSERVATIONS . . 388 RESIDUAL STANDARD ERROR. . . . . . . 0.193858E+01 -- tsm m1. model y=(w0*b**2+w1*b**3+w2*b**4)x+(1)noise. <== Start with a simple model. -- estim m1. hold resi(r1) THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M1 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 W0 X NUM. 1 2 NONE 2.7074 .2407 11.25 2 W1 X NUM. 1 3 NONE 4.5724 .3889 11.76 3 W2 X NUM. 1 4 NONE 5.9779 .2415 24.76 4 Y MA 1 1 NONE -.2598 .0491 -5.29 EFFECTIVE NUMBER OF OBSERVATIONS . . 396 R-SQUARE . . . . . . . . . . . . . . 0.990 RESIDUAL STANDARD ERROR. . . . . . . 0.462872E+01 -- tsm m1. model y=(w0*b**2+w1*b**3)/(1-d1*b)x+(1)noise. <== Go to the identified model -- d1=0.4 <== Specify an initial estimate. -- estim m1. hold resi(r1) THE FOLLOWING ANALYSIS IS BASED ON TIME SPAN 1 THRU 400 NONLINEAR ESTIMATION TERMINATED DUE TO: RELATIVE CHANGE IN (OBJECTIVE FUNCTION)**0.5 LESS THAN 0.1000D-02 SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M1 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 W0 X NUM. 1 2 NONE 3.0515 .0447 68.24 2 W1 X NUM. 1 3 NONE 3.9331 .0715 55.03 3 D1 X DENM 1 1 NONE .5013 .0024 213.04 4 Y MA 1 1 NONE .7253 .0357 20.33 EFFECTIVE NUMBER OF OBSERVATIONS . . 391 R-SQUARE . . . . . . . . . . . . . . 0.998 RESIDUAL STANDARD ERROR. . . . . . . 0.198347E+01 -- acf r1. maxl 12. NAME OF THE SERIES . . . . . . . . . . R1 TIME PERIOD ANALYZED . . . . . . . . . 10 TO 400 MEAN OF THE (DIFFERENCED) SERIES . . . -0.0009 STANDARD DEVIATION OF THE SERIES . . . 1.9835 T-VALUE OF MEAN (AGAINST ZERO) . . . . -0.0087 AUTOCORRELATIONS 1- 12 .01 .03 -.07 .04 -.04 -.03 -.02 .02 .00 .02 -.02 .13 ST.E. .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 .05 Q .1 .4 2.5 3.0 3.6 3.9 4.1 4.3 4.3 4.4 4.5 11.1 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0 +----+----+----+----+----+----+----+----+----+----+ I 1 0.01 + I + 2 0.03 + IX+ 3 -0.07 XXI + 4 0.04 + IX+ 5 -0.04 +XI + 6 -0.03 + XI + 7 -0.02 + XI + 8 0.02 + IX + 9 0.00 + I + 10 0.02 + I + 11 -0.02 + I + 12 0.13 + IXXX Finally for forecasting comparison, use the following analysis. -- workspace novar-req 500. <== To increase the number of variables allowed. -- tsm m1. model (1,2,3,4)y=noise. -- estim m1. span 1,350. <== Re-estimate the model using the first 350 data points. SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- M1 ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 Y AR 1 1 NONE 1.5542 .0520 29.91 2 Y AR 1 2 NONE -.2731 .0932 -2.93 3 Y AR 1 3 NONE -.6079 .0935 -6.50 4 Y AR 1 4 NONE .2689 .0525 5.12 EFFECTIVE NUMBER OF OBSERVATIONS . . 346 R-SQUARE . . . . . . . . . . . . . . 0.965 RESIDUAL STANDARD ERROR. . . . . . . 0.852262E+01 -- fore m1. orig 350 to 399. nofs 1. hold forecasts(v1 to v50). (Output edited to simplify the handout.) -- join old v1 to v50. new fy. THE JOIN OPERATION HAS BEEN COMPLETED, RESULT IS STORED IN VARIABLE FY VARIABLE FY IS A 50 BY 1 MATRIX -- sele old y. new yy. span (351,400). VARIABLE Y IS EDITED, THE RESULT IS STORED IN VARIABLE YY VARIABLE YY IS A 50 BY 1 MATRIX -- err=yy-fy. <== Compute forecast errors. -- msqe=sum(err*err)/50 <== Compute the sum of squares of forecast errors. -- print msqe MSQE IS A 1 BY 1 VARIABLE 63.937 -- tsm mt. model y=(2,3;w0,w1)x+(1)noise. <== Use a two-step procedure to estimate the transfer function model. This is due to numerical issues. -- estim mt. span 1,350. -- tsm mt. change (2,3;w0,w1)/(1;d1)x <== Specify the identified transfer function model. -- estim mt. span 1,350. <== Use the first 350 data points to estimate the transfer function model SUMMARY FOR UNIVARIATE TIME SERIES MODEL -- MT ----------------------------------------------------------------------- VARIABLE TYPE OF ORIGINAL DIFFERENCING VARIABLE OR CENTERED Y RANDOM ORIGINAL NONE X RANDOM ORIGINAL NONE ----------------------------------------------------------------------- PARAMETER VARIABLE NUM./ FACTOR ORDER CONS- VALUE STD T LABEL NAME DENOM. TRAINT ERROR VALUE 1 W0 X NUM. 1 2 NONE 3.0490 .0497 61.36 2 W1 X NUM. 1 3 NONE 3.9486 .0800 49.39 3 D1 X DENM 1 1 NONE .5004 .0026 189.20 4 Y MA 1 1 NONE .7222 .0391 18.49 EFFECTIVE NUMBER OF OBSERVATIONS . . 341 R-SQUARE . . . . . . . . . . . . . . 0.998 RESIDUAL STANDARD ERROR. . . . . . . 0.201737E+01 -- fore mt. orig 350 to 399. nofs 1. hold forecast(u1 to u50). ** NO ARIMA MODEL IS SPECIFIED FOR THE STOCHASTIC INPUT VARIABLE X ; IT IS TREATED AS A NON-STOCHASTIC VARIABLE -- join old u1 to u50. new tf. THE JOIN OPERATION HAS BEEN COMPLETED, RESULT IS STORED IN VARIABLE TF VARIABLE TF IS A 50 BY 1 MATRIX -- er=yy-tf -- msqtf=sum(er*er)/50 -- print msqtf MSQTF IS A 1 BY 1 VARIABLE 3.040