THE SCA STATISTICAL SYSTEM ( RELEASE 8.0 ) SCA ADVANCED EDITION SOFTWARE IDENTIFICATION: RUEY TSAY ( 7032218 ) SOFTWARE RELEASE DATE: 2/ 1/2007 SOFTWARE RENEWAL DATE: 4/ 2/2010 COPYRIGHT (C), SCIENTIFIC COMPUTING ASSOCIATES CORP. ALL RIGHTS RESERVED SIZE OF WORKSPACE IS 20000000 SINGLE PRECISION WORDS DATE -- 4/17/2007 TIME -- 21:54:56 -- profile review. owidth 80. -- input z1,z2. file 'mtshw3.dat' Z1 , A 152 BY 1 VARIABLE, IS STORED IN THE WORKSPACE Z2 , A 152 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- miden z1,z2. maxl 12. arfits 1 to 9. TIME PERIOD ANALYZED . . . . . . . . . . . . 1 TO 152 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 152 SERIES NAME MEAN STD. ERROR 1 Z1 15.3439 4.7221 2 Z2 11.3377 4.9050 NOTE: THE APPROX. STD. ERROR FOR THE ESTIMATED CORRELATIONS BELOW IS (1/NOBE**.5) = 0.08111 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.46 1.00 SUMMARIES OF CROSS CORRELATION MATRICES USING +,-,., WHERE + DENOTES A VALUE GREATER THAN 2/SQRT(NOBE) - DENOTES A VALUE LESS THAN -2/SQRT(NOBE) . DENOTES A NON-SIGNIFICANT VALUE BASED ON THE ABOVE CRITERION BEHAVIOR OF VALUES IN (I,J)TH POSITION OF CROSS CORRELATION MATRIX OVER ALL OUTPUTTED LAGS WHEN SERIES J LEADS SERIES I 1 2 1 +++++++..... ++++.+++.... 2 +++++....... ++.+.+...... CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 + + + + + + + + + . + + + + + + + . + + + . . + LAGS 7 THROUGH 12 + + . + . . . . . . . . . . . . . . . . . . . . DETERMINANT OF S(0) = 0.453175E+03 NOTE: S(0) IS THE SAMPLE COVARIANCE MATRIX OF W(MAXLAG+1),...,W(NOBE) ========== STEPWISE AUTOREGRESSION SUMMARY ========== ---------------------------------------------------------------------- I RESIDUAL I EIGENVAL.I CHI-SQ I I SIGNIFICANCE LAG I VARIANCESI OF SIGMA I TEST I AIC I OF PARTIAL AR COEFF. ----+----------+----------+---------+----------+---------------------- 1 I .668E+01 I .552E+01 I 177.16 I 4.899 I + + I .219E+02 I .231E+02 I I I + . ----+----------+----------+---------+----------+---------------------- 2 I .155E+01 I .142E+01 I 216.16 I 3.380 I - + I .185E+02 I .186E+02 I I I . + ----+----------+----------+---------+----------+---------------------- 3 I .151E+01 I .138E+01 I 4.91 I 3.396 I . . I .184E+02 I .185E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 4 I .148E+01 I .133E+01 I 4.53 I 3.415 I . . I .183E+02 I .185E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 5 I .148E+01 I .133E+01 I 1.49 I 3.456 I . . I .181E+02 I .183E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 6 I .145E+01 I .130E+01 I 3.11 I 3.485 I . . I .181E+02 I .182E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 7 I .144E+01 I .129E+01 I 1.04 I 3.529 I . . I .181E+02 I .182E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 8 I .142E+01 I .128E+01 I 6.73 I 3.528 I . . I .173E+02 I .174E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 9 I .136E+01 I .124E+01 I 9.19 I 3.506 I . + I .166E+02 I .167E+02 I I I - . ---------------------------------------------------------------------- NOTE: CHI-SQUARED CRITICAL VALUES WITH 4 DEGREES OF FREEDOM ARE 5 PERCENT: 9.5 1 PERCENT: 13.3 -- mtsm m1. series z1,z2. model (i-p1*b-p2*b**2)series=c1+noise. SUMMARY FOR MULTIVARIATE ARMA MODEL -- M1 VARIABLE DIFFERENCING Z1 Z2 PARAMETER FACTOR ORDER CONSTRAINT 1 C1 CONSTANT 0 CC1 2 P1 REG AR 1 CP1 3 P2 REG AR 2 CP2 -- mestim m1. hold resi(r1,r2) (output edited) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 2.296 ( 0.381 ) 4.390 ( 1.313 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .536 .367 + + -.179 .134 . . STANDARD ERRORS .043 .024 .146 .081 ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE -.340 .518 - + .200 .450 . + STANDARD ERRORS .035 .027 .121 .093 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.560549 2 1.535073 18.501264 -- p1(2,1)=0 -- p2(2,1)=0 -- cp1(2,1)=1 -- cp2(2,1)=1 -- mestim m1. hold resi(r1,r2). SUMMARY FOR THE MULTIVARIATE ARMA MODEL PARAMETER PARAMETER PARAMETER NUMBER DESCRIPTION VALUE ---------- ----------------------------- ------------ 1 CONSTANT( 1) 2.295619 2 CONSTANT( 2) 4.389943 3 AUTOREGRESSIVE ( 1, 1, 1) 0.536253 4 AUTOREGRESSIVE ( 1, 1, 2) 0.367049 *FIXED* AUTOREGRESSIVE ( 1, 2, 1) 0.000000 5 AUTOREGRESSIVE ( 1, 2, 2) 0.133644 6 AUTOREGRESSIVE ( 2, 1, 1) -0.340409 7 AUTOREGRESSIVE ( 2, 1, 2) 0.517908 *FIXED* AUTOREGRESSIVE ( 2, 2, 1) 0.000000 8 AUTOREGRESSIVE ( 2, 2, 2) 0.450193 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.560549 2 1.535073 18.501264 FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 2.349 ( 0.377 ) 5.036 ( 1.107 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .551 .366 + + .000 .119 . . STANDARD ERRORS .041 .023 -- .074 ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE -.357 .517 - + .000 .435 . + STANDARD ERRORS .034 .026 -- .074 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.562837 2 1.562877 18.839167 -- p1(2,2)=0 -- cp1(2,2)=1 -- mestim m1. hold resi(r1,r2). FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 2.438 ( 0.373 ) 6.101 ( 0.899 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .551 .356 + + .000 .000 . . STANDARD ERRORS .041 .023 -- -- ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE -.357 .519 - + .000 .460 . + STANDARD ERRORS .034 .026 -- .073 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.565147 2 1.590520 19.169804 -- miden r1,r2. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 3 TO 152 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 150 SERIES NAME MEAN STD. ERROR 1 R1 0.0000 1.2511 2 R2 0.0000 4.3783 NOTE: THE APPROX. STD. ERROR FOR THE ESTIMATED CORRELATIONS BELOW IS (1/NOBE**.5) = 0.08165 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.29 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . + . . . . . . . . . . . . . LAGS 7 THROUGH 12 - . . . . . . . . . . . . . . . . . . . . . . . -- sele old r1,r2. new r1,r2. span (3,152). -- save r1,r2. file 'mtshw3res.txt'. form '(2f10.5)'. -- input y1,y2. file 'mtshw4.dat' Y1 , A 145 BY 1 VARIABLE, IS STORED IN THE WORKSPACE Y2 , A 145 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- miden y1,y2. maxl 12. arftis 1 to 9. TIME PERIOD ANALYZED . . . . . . . . . . . . 1 TO 145 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 145 SERIES NAME MEAN STD. ERROR 1 Y1 16.9369 4.3122 2 Y2 24.3935 5.4363 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 -0.52 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 + - + - + - + - + - + - - + - + - + - + - + - + LAGS 7 THROUGH 12 + - + - + - + - + - + - - + - + - + - + - + - + DETERMINANT OF S(0) = 0.322964E+03 NOTE: S(0) IS THE SAMPLE COVARIANCE MATRIX OF W(MAXLAG+1),...,W(NOBE) ========== STEPWISE AUTOREGRESSION SUMMARY ========== ---------------------------------------------------------------------- I RESIDUAL I EIGENVAL.I CHI-SQ I I SIGNIFICANCE LAG I VARIANCESI OF SIGMA I TEST I AIC I OF PARTIAL AR COEFF. ----+----------+----------+---------+----------+---------------------- 1 I .153E+01 I .146E+01 I 332.92 I 3.320 I + - I .179E+02 I .179E+02 I I I - . ----+----------+----------+---------+----------+---------------------- 2 I .152E+01 I .144E+01 I 3.45 I 3.349 I . . I .176E+02 I .177E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 3 I .147E+01 I .137E+01 I 8.38 I 3.339 I . . I .173E+02 I .174E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 4 I .147E+01 I .137E+01 I 1.43 I 3.383 I . . I .172E+02 I .173E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 5 I .145E+01 I .136E+01 I 1.44 I 3.426 I . . I .171E+02 I .172E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 6 I .143E+01 I .135E+01 I 2.44 I 3.461 I . . I .169E+02 I .170E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 7 I .137E+01 I .128E+01 I 6.81 I 3.460 I - . I .168E+02 I .169E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 8 I .136E+01 I .128E+01 I 1.24 I 3.505 I . . I .167E+02 I .168E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 9 I .134E+01 I .125E+01 I 3.48 I 3.530 I . . I .165E+02 I .166E+02 I I I . . ---------------------------------------------------------------------- NOTE: CHI-SQUARED CRITICAL VALUES WITH 4 DEGREES OF FREEDOM ARE 5 PERCENT: 9.5 1 PERCENT: 13.3 -- mtsm m2. series y1,y2. model (i-g1*b)series=c2+noise. SUMMARY FOR MULTIVARIATE ARMA MODEL -- M2 VARIABLE DIFFERENCING Y1 Y2 PARAMETER FACTOR ORDER CONSTRAINT 1 C2 CONSTANT 0 CC2 2 G1 REG AR 1 CG1 -- mestim m2. hold resi(r1,r2) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 10.897 ( 0.912 ) 35.839 ( 3.071 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .727 -.255 + - -.748 .049 - . STANDARD ERRORS .029 .023 .096 .076 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.605603 2 1.308133 18.196631 -- g1(2,2)=0 -- cg1(2,2)=1 -- mestim m2. hold resi(r1,r2) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 11.009 ( 0.891 ) 37.581 ( 1.438 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .725 -.258 + - -.780 .000 - . STANDARD ERRORS .028 .022 .082 -- ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.605855 2 1.311753 18.248299 -- miden r1,r2. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 2 TO 145 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 144 SERIES NAME MEAN STD. ERROR 1 R1 0.0000 1.2672 2 R2 0.0001 4.2718 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.24 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . + . . . . . . . . . . . . . LAGS 7 THROUGH 12 . . . . . . . . . . . . . . . . . . . . . . . . -- sele old r1,r2. new r1,r2. span (2,145) -- save r1,r2. file 'mtshw4res.txt'. form '(2f10.5)'. -- input x1,x2. file 'mtshw1.dat' X1 , A 158 BY 1 VARIABLE, IS STORED IN THE WORKSPACE X2 , A 158 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- miden x1,x2. maxl 12. arfits 1 to 9. TIME PERIOD ANALYZED . . . . . . . . . . . . 1 TO 158 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 158 SERIES NAME MEAN STD. ERROR 1 X1 17.0261 1.3921 2 X2 24.8093 6.6327 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.43 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 - - . . . . . . . . + + - - . . . . . . . . . . LAGS 7 THROUGH 12 - . . . . . . . . . . . . . . . . . . . . . . . DETERMINANT OF S(0) = 0.741187E+02 NOTE: S(0) IS THE SAMPLE COVARIANCE MATRIX OF W(MAXLAG+1),...,W(NOBE) ========== STEPWISE AUTOREGRESSION SUMMARY ========== ---------------------------------------------------------------------- I RESIDUAL I EIGENVAL.I CHI-SQ I I SIGNIFICANCE LAG I VARIANCESI OF SIGMA I TEST I AIC I OF PARTIAL AR COEFF. ----+----------+----------+---------+----------+---------------------- 1 I .174E+01 I .154E+01 I 79.84 I 3.808 I - . I .276E+02 I .278E+02 I I I - - ----+----------+----------+---------+----------+---------------------- 2 I .160E+01 I .149E+01 I 28.71 I 3.658 I - . I .233E+02 I .235E+02 I I I - . ----+----------+----------+---------+----------+---------------------- 3 I .157E+01 I .144E+01 I 14.93 I 3.603 I . . I .218E+02 I .219E+02 I I I - . ----+----------+----------+---------+----------+---------------------- 4 I .154E+01 I .143E+01 I 15.29 I 3.544 I . . I .197E+02 I .198E+02 I I I - . ----+----------+----------+---------+----------+---------------------- 5 I .153E+01 I .143E+01 I 7.28 I 3.542 I . . I .187E+02 I .188E+02 I I I - . ----+----------+----------+---------+----------+---------------------- 6 I .147E+01 I .135E+01 I 9.53 I 3.522 I . . I .184E+02 I .185E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 7 I .146E+01 I .134E+01 I 3.90 I 3.544 I . . I .180E+02 I .182E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 8 I .145E+01 I .133E+01 I 1.20 I 3.585 I . . I .180E+02 I .181E+02 I I I . . ----+----------+----------+---------+----------+---------------------- 9 I .141E+01 I .131E+01 I 10.02 I 3.558 I . . I .168E+02 I .169E+02 I I I - + ---------------------------------------------------------------------- NOTE: CHI-SQUARED CRITICAL VALUES WITH 4 DEGREES OF FREEDOM ARE 5 PERCENT: 9.5 1 PERCENT: 13.3 -- mtsm m3. series x1,x2. model series=c3+(i-t1*b)noise. SUMMARY FOR MULTIVARIATE ARMA MODEL -- M3 VARIABLE DIFFERENCING X1 X2 PARAMETER FACTOR ORDER CONSTRAINT 1 C3 CONSTANT 0 CC3 2 T1 REG MA 1 CT1 -- mestim m3. hold resi(r1,r2). method exact. FINAL MODEL SUMMARY WITH MAXIMUM LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 17.031 ( 0.056 ) 24.816 ( 0.184 ) ----- THETA MATRICES ----- ESTIMATES OF THETA( 1 ) MATRIX AND SIGNIFICANCE .456 -.009 + . 1.864 .775 + + STANDARD ERRORS .053 .016 .204 .057 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.598689 2 1.462735 18.834740 -2*(LOG LIKELIHOOD AT FINAL ESTIMATES) IS 0.84411884E+03 -- t1(1,2)=0 -- ct1(1,2)=1 -- mestim m3. hold resi(r1,r2). method exact. FINAL MODEL SUMMARY WITH MAXIMUM LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 17.031 ( 0.056 ) 24.815 ( 0.186 ) ----- THETA MATRICES ----- ESTIMATES OF THETA( 1 ) MATRIX AND SIGNIFICANCE .446 .000 + . 1.886 .758 + + STANDARD ERRORS .052 -- .208 .052 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 1.593957 2 1.472567 18.941634 -2*(LOG LIKELIHOOD AT FINAL ESTIMATES) IS 0.84437724E+03 -- miden r1,r2. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 1 TO 158 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 158 SERIES NAME MEAN STD. ERROR 1 R1 -0.0065 1.2598 2 R2 -0.0179 4.3461 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.27 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . . . . . . . . . . . . . . . LAGS 7 THROUGH 12 - . . . . . . . . . . . . . . . . . . . . . . . -- print r1. span 1,5 R1 IS A 158 BY 1 VARIABLE .219 -.351 .061 1.584 .183 -- save r1,r2. file 'mtshw1res.txt'. form '(2f10.5)'. -- mfore m1. nofs 6. nopsiweight 6 ---------------------------------------- 6 FORECASTS, BEGINNING AT ORIGIN = 152 ---------------------------------------- SERIES: Z1 Z2 TIME FORECAST STD ERR FORECAST STD ERR 153 10.763 1.251 9.237 4.378 154 12.612 2.257 11.550 4.378 155 14.449 3.844 10.347 4.819 156 15.573 4.254 11.411 4.819 157 15.291 4.356 10.857 4.907 158 15.089 4.360 11.346 4.907 PSI MATRICES USED IN THE COMPUTATION OF FORECAST ERROR MATRICES PSI 1 0.551 0.356 0.000 0.000 PSI 2 -0.053 0.715 0.000 0.460 PSI 3 -0.226 0.431 0.000 0.000 PSI 4 -0.106 0.221 0.000 0.211 PSI 5 0.023 0.043 0.000 0.000 -- stop