******************************** *** SCA output for Problem B *** ******************************** -- (Output edited to remove unnecessary part) input x. file 'mtsa.dat'. datset TX1. X , A 125 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- input y. file 'mtsa.dat'. dataset TY1. -- miden x,y. maxl 12. arfits 1 to 9. TIME PERIOD ANALYZED . . . . . . . . . . . . 1 TO 125 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 125 SERIES NAME MEAN STD. ERROR 1 X 10.1776 2.3533 2 Y 60.9120 8.5704 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 -0.02 1.00 SUMMARIES OF CROSS CORRELATION MATRICES USING +,-,. 1 2 1 ..........-. ............ 2 .+++........ ++........-. CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . . . . + + + + . + . . . . . LAGS 7 THROUGH 12 . . . . . . . . - . . . . . . . . . . . . - . . DETERMINANT OF S(0) = 0.433838E+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 .565E+01 I .565E+01 I 35.58 I 5.820 I . . I .560E+02 I .560E+02 I I I . + ----+----------+----------+---------+----------+---------------------- 2 I .555E+01 I .486E+01 I 272.14 I 3.422 I . . I .486E+01 I .555E+01 I I I + . ----+----------+----------+---------+----------+---------------------- 3 I .554E+01 I .393E+01 I 23.12 I 3.272 I . . I .393E+01 I .554E+01 I I I + . ----+----------+----------+---------+----------+---------------------- 4 I .546E+01 I .392E+01 I 1.66 I 3.321 I . . I .392E+01 I .546E+01 I I I . . ----+----------+----------+---------+----------+---------------------- 5 I .543E+01 I .389E+01 I 1.39 I 3.372 I . . I .389E+01 I .543E+01 I I I . . ----+----------+----------+---------+----------+---------------------- 6 I .529E+01 I .378E+01 I 5.41 I 3.383 I . . I .379E+01 I .530E+01 I I I . . ----+----------+----------+---------+----------+---------------------- 7 I .526E+01 I .373E+01 I 2.03 I 3.427 I . . I .374E+01 I .528E+01 I I I . . ----+----------+----------+---------+----------+---------------------- 8 I .504E+01 I .372E+01 I 4.43 I 3.446 I . - I .373E+01 I .505E+01 I I I . . ----+----------+----------+---------+----------+---------------------- 9 I .497E+01 I .358E+01 I 4.59 I 3.462 I . . I .361E+01 I .500E+01 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 x,y. model (i-p1*b-p2*b**2-p3*b**3)series@ = c1+noise. SUMMARY FOR MULTIVARIATE ARMA MODEL -- M1 VARIABLE DIFFERENCING X Y PARAMETER FACTOR ORDER CONSTRAINT 1 C1 CONSTANT 0 CC1 2 P1 REG AR 1 CP1 3 P2 REG AR 2 CP2 4 P3 REG AR 3 CP3 -- mestim m1. hold resi(r1,r2) SUMMARY FOR THE MULTIVARIATE ARMA MODEL SERIES NAME MEAN STD DEV DIFFERENCE ORDER(S) 1 X 10.1776 2.3533 2 Y 60.9120 8.5704 FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 11.359 ( 2.386 ) -0.574 ( 2.040 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .046 .039 . . -.030 .078 . . STANDARD ERRORS .090 .094 .077 .080 ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE -.007 -.048 . . 2.997 .206 + + STANDARD ERRORS .090 .053 .077 .045 ESTIMATES OF PHI( 3 ) MATRIX AND SIGNIFICANCE -.076 -.005 . . 1.299 .016 + . STANDARD ERRORS .296 .029 .253 .025 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 5.517766 2 .059481 4.034198 -- miden r1,r2. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 4 TO 125 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 122 SERIES NAME MEAN STD. ERROR 1 R1 0.0000 2.3490 2 R2 0.0000 2.0085 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.01 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . . . . . . . . . . . . . . . LAGS 7 THROUGH 12 . . . . . . . . - . . . . . . . . . . . . . . . -- input p1. nrow 2. ncol 2. <== Fix phi(1) = 0 -- input cp1. nrow 2. ncol 2. -- input p2. nrow 2. ncol 2. <== Set constriants on phi(2) -- input cp2. nrow 2. ncol 2. -- input p3. nrow 2. ncol 2. <== Set constriants on phi(3). -- input cp3. nrow 2. ncol 2. -- mestim m1. hold resi(r1,r2). ITERATIONS TERMINATED DUE TO: RELATIVE CHANGE IN DETERMINANT OF COVARIANCE MATRIX .LE. 0.100E-03 FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 10.154 ( 0.215 ) -0.292 ( 1.696 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .000 .000 . . .000 .000 . . STANDARD ERRORS -- -- -- -- ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE .000 .000 . . 2.993 .253 + + STANDARD ERRORS -- -- .077 .021 ESTIMATES OF PHI( 3 ) MATRIX AND SIGNIFICANCE .000 .000 . . 1.532 .000 + . STANDARD ERRORS -- -- .077 -- ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 5.623139 2 .062426 4.091208 -- miden r1,r2. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 4 TO 125 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 122 SERIES NAME MEAN STD. ERROR 1 R1 0.0000 2.3713 2 R2 0.0000 2.0227 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.01 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . . . . . . . . . . . . . . . LAGS 7 THROUGH 12 . . . . . . . . - . . . . . . . . . . . . . . . -- mfore m1. nofs 4. ---------------------------------------- 4 FORECASTS, BEGINNING AT ORIGIN = 125 ---------------------------------------- SERIES: X Y TIME FORECAST STD ERR FORECAST STD ERR 126 10.154 2.371 68.463 2.023 127 10.154 2.371 65.901 2.023 128 10.154 2.371 63.525 7.404 129 10.154 2.371 62.346 8.248 ************************************ ** Problem C ** ************************************ input jp. file 'm-jpus.txt' JP , A 412 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- input uk. file 'm-usuk.txt' UK , A 412 BY 1 VARIABLE, IS STORED IN THE WORKSPACE -- jp=ln(jp) -- uk=ln(uk) -- miden jp,uk. arfits 1 to 8. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 1 TO 412 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 412 SERIES NAME MEAN STD. ERROR 1 JP 5.1306 0.4003 2 UK 0.5629 0.1796 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 0.53 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 + + + + + + + + + + + + + + + + + + + + + + + + LAGS 7 THROUGH 12 + + + + + + + + + + + + + + + + + + + + + + + + DETERMINANT OF S(0) = 0.351514E-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 .753E-03 I .363E-03 I 3687.18 I -14.838 I + . I .582E-03 I .971E-03 I I I . + ----+----------+----------+---------+----------+---------------------- 2 I .663E-03 I .330E-03 I 96.47 I -15.060 I - . I .506E-03 I .839E-03 I I I . - ----+----------+----------+---------+----------+---------------------- 3 I .659E-03 I .327E-03 I 8.69 I -15.063 I . . I .496E-03 I .828E-03 I I I . + ----+----------+----------+---------+----------+---------------------- 4 I .653E-03 I .323E-03 I 9.19 I -15.067 I . . I .490E-03 I .819E-03 I I I . - ----+----------+----------+---------+----------+---------------------- 5 I .651E-03 I .323E-03 I 1.00 I -15.050 I . . I .490E-03 I .818E-03 I I I . . ----+----------+----------+---------+----------+---------------------- 6 I .648E-03 I .323E-03 I 3.08 I -15.038 I . . I .487E-03 I .812E-03 I I I . . ----+----------+----------+---------+----------+---------------------- 7 I .642E-03 I .322E-03 I 3.55 I -15.028 I . . I .486E-03 I .807E-03 I I I . . ----+----------+----------+---------+----------+---------------------- 8 I .641E-03 I .320E-03 I 2.49 I -15.015 I . . I .485E-03 I .806E-03 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 jp,uk. model (i-p1*b-p2*b**2)series=c1+noise. SUMMARY FOR MULTIVARIATE ARMA MODEL -- M1 VARIABLE DIFFERENCING JP UK 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) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 0.038 ( 0.017 ) -0.004 ( 0.015 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE 1.296 -.065 + . .003 1.345 . + STANDARD ERRORS .052 .059 .045 .051 ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE -.305 .084 - . -.30E-03 -.363 . - STANDARD ERRORS .051 .059 .045 .051 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 .000653 2 -.000238 .000499 -- p1(1,2)=0 -- p1(2,1)=0 -- cp1(1,2)=1 -- cp1(2,1)=1 -- p2(2,1)=0 -- p2(1,2)=0 -- cp2(1,2)=1 -- cp2(2,1)=1 -- mestim m1. hold resi(r1,r2). ITERATIONS TERMINATED DUE TO: RELATIVE CHANGE IN DETERMINANT OF COVARIANCE MATRIX .LE. 0.100E-03 FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 0.022 ( 0.015 ) 0.005 ( 0.003 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE 1.326 .000 + . .000 1.325 . + STANDARD ERRORS .043 -- -- .043 ESTIMATES OF PHI( 2 ) MATRIX AND SIGNIFICANCE -.331 .000 - . .000 -.335 . - STANDARD ERRORS .043 -- -- .042 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 .000663 2 -.000242 .000501 -- miden r1,r2. maxl 12. output level(deta) TIME PERIOD ANALYZED . . . . . . . . . . . . 3 TO 412 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 410 SERIES NAME MEAN STD. ERROR 1 R1 0.0000 0.0258 2 R2 0.0000 0.0224 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 -0.42 1.00 SAMPLE CROSS CORRELATION MATRICES: LAG = 1 0.03 -0.07 -0.04 0.07 LAG = 2 -0.10 0.05 0.09 -0.15 LAG = 3 0.06 0.00 0.00 0.04 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . . . . . . - . . . . . . . . LAGS 7 THROUGH 12 . . . . . . . . + . . . . . . . . . . . - . . . -- mtsm m2. series jp,uk. model (i-h1*b)series=c3+(i-t1*b)noise. SUMMARY FOR MULTIVARIATE ARMA MODEL -- M2 VARIABLE DIFFERENCING JP UK PARAMETER FACTOR ORDER CONSTRAINT 1 C3 CONSTANT 0 CC3 2 H1 REG AR 1 CH1 3 T1 REG MA 1 CT1 -- mestim m2. hold resi(s1,s2) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 0.047 ( 0.023 ) -0.002 ( 0.021 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .988 .023 + + .003 .978 . + STANDARD ERRORS .005 .011 .005 .010 ----- THETA MATRICES ----- ESTIMATES OF THETA( 1 ) MATRIX AND SIGNIFICANCE -.341 .092 - . .019 -.421 . - STANDARD ERRORS .050 .058 .042 .049 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 .000645 2 -.000229 .000485 -- h1(2,1)=0 -- ch1(2,1)=1 -- t1(1,2)=0 -- t1(2,1)=0 -- ct1(1,2)=1 -- ct1(2,1)=1 -- mestim m2. hold resi(s1,s2) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 0.041 ( 0.021 ) 0.010 ( 0.005 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .989 .020 + . .000 .982 . + STANDARD ERRORS .005 .011 -- .008 ----- THETA MATRICES ----- ESTIMATES OF THETA( 1 ) MATRIX AND SIGNIFICANCE -.361 .000 - . .000 -.402 . - STANDARD ERRORS .043 -- -- .042 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 .000649 2 -.000231 .000486 -- h1(1,2)=0 -- ch1(1,2)=1 -- mestim m2. hold resi(s1,s2) FINAL MODEL SUMMARY WITH CONDITIONAL LIKELIHOOD PARAMETER ESTIMATES ----- CONSTANT VECTOR (STD ERROR) ----- 0.032 ( 0.021 ) 0.006 ( 0.005 ) ----- PHI MATRICES ----- ESTIMATES OF PHI( 1 ) MATRIX AND SIGNIFICANCE .993 .000 + . .000 .987 . + STANDARD ERRORS .004 -- -- .008 ----- THETA MATRICES ----- ESTIMATES OF THETA( 1 ) MATRIX AND SIGNIFICANCE -.359 .000 - . .000 -.403 . - STANDARD ERRORS .043 -- -- .042 ----------------------- ERROR COVARIANCE MATRIX ----------------------- 1 2 1 .000655 2 -.000233 .000486 -- miden s1,s2. maxl 12. TIME PERIOD ANALYZED . . . . . . . . . . . . 2 TO 412 EFFECTIVE NUMBER OF OBSERVATIONS (NOBE). . . 411 SERIES NAME MEAN STD. ERROR 1 S1 0.0000 0.0256 2 S2 0.0000 0.0220 SAMPLE CORRELATION MATRIX OF THE SERIES 1.00 -0.41 1.00 CROSS CORRELATION MATRICES IN TERMS OF +,-,. LAGS 1 THROUGH 6 . . . . . . . . . . . . . . . . . . . . . . . . LAGS 7 THROUGH 12 . . . . . . . . + . . . . . . . . . . . . . . .