* G13FAF Example Program Text * Mark 22 Revised. NAG Copyright 2006. * .. Parameters .. INTEGER NOUT PARAMETER (NOUT=6) INTEGER NPARMX, LDCOVR, NUM, MSTATE, MSEED, NUM1, NREGMX, + LRVEC PARAMETER (NPARMX=10,LDCOVR=NPARMX,NUM=1500,MSTATE=200, + MSEED=1,NUM1=3000,NREGMX=10,LRVEC=40) DOUBLE PRECISION ZERO PARAMETER (ZERO=0.0D0) * .. Local Scalars .. DOUBLE PRECISION FAC1, GAMMA, HP, LGF, MEAN, TOL, XTERM INTEGER D, DF, GENID, I, IFAIL, IP, IQ, ISYM, J, K, LDX, + LSEED, LSTATE, LWORK, MAXIT, MN, NPAR, NPAR2, + NREG, NT, SUBID LOGICAL FCALL CHARACTER DIST * .. Local Arrays .. DOUBLE PRECISION BX(10), COVR(LDCOVR,NPARMX), CVAR(100), + ETM(NUM1), HT(NUM1+10), HTM(NUM1), PARAM(NPARMX), + RVEC(LRVEC), SC(NPARMX), SE(NPARMX), + THETA(NPARMX), WORK(NUM1*3+NPARMX+NREGMX*NUM1+20* + 20+1), X(NUM1,10), YT(NUM1+10) INTEGER SEED(MSEED), STATE(MSTATE) LOGICAL COPTS(2) * .. External Subroutines .. EXTERNAL G05KFF, G05PDF, G13FAF, G13FBF * .. Intrinsic Functions .. INTRINSIC DBLE, SIN * .. Executable Statements .. IFAIL = 0 WRITE (NOUT,*) 'G13FAF Example Program Results' WRITE (NOUT,*) * Initialize the seed SEED(1) = 111 * GENID and SUBID identify the base generator GENID = 1 SUBID = 1 * Initialize the generator to a repeatable sequence LSTATE = MSTATE LSEED = MSEED CALL G05KFF(GENID,SUBID,SEED,LSEED,STATE,LSTATE,IFAIL) * * Initialize the time dependent, exogenous, variables LDX = NUM1 BX(1) = 1.5D0 BX(2) = 2.5D0 BX(3) = 3.0D0 DO 20 I = 1, NUM FAC1 = DBLE(I)*0.01D0 X(I,1) = 0.01D0 + 0.7D0*SIN(FAC1) X(I,2) = 0.5D0 + FAC1*0.1D0 X(I,3) = 1.0D0 20 CONTINUE * * Show two examples, normally distributed errors, * and student t errors DO 180 D = 1, 2 IF (D.EQ.1) THEN * Errors distributed as a normal distribution WRITE (NOUT,*) WRITE (NOUT,*) 'Normal distribution' WRITE (NOUT,*) DIST = 'N' * Initialize the series parameters required * for generation of some test data MEAN = 3.0D0 MN = 1 NREG = 0 ISYM = 1 GAMMA = -0.4D0 IP = 0 IQ = 3 PARAM(1) = 0.8D0 PARAM(2) = 0.6D0 PARAM(3) = 0.2D0 PARAM(4) = 0.1D0 ELSE * Errors distributed as a students t distribution WRITE (NOUT,*) WRITE (NOUT,*) 'Students T distribution' WRITE (NOUT,*) DIST = 'T' * Initialize the series parameters required * for generation of some test data DF = 4 MEAN = 3.0D0 MN = 1 NREG = 2 IP = 1 IQ = 1 ISYM = 1 GAMMA = -0.2D0 PARAM(1) = 0.1D0 PARAM(2) = 0.2D0 PARAM(3) = 0.3D0 END IF * * Start of data generation * Generate the errors FCALL = .TRUE. CALL G05PDF(DIST,NUM,IP,IQ,PARAM,GAMMA,DF,HT,YT,FCALL,RVEC, + LRVEC,STATE,IFAIL) * Calculate the observed data DO 60 I = 1, NUM XTERM = ZERO DO 40 K = 1, NREG XTERM = XTERM + X(I,K)*BX(K) 40 CONTINUE IF (MN.EQ.1) THEN YT(I) = MEAN + XTERM + YT(I) ELSE YT(I) = XTERM + YT(I) END IF 60 CONTINUE * End of data generation * * Calculate the number of parameters and required workspace NPAR = 1 + IQ + IP NPAR2 = NPAR + ISYM + MN + NREG IF (DIST.EQ.'T') NPAR2 = NPAR2 + 1 LWORK = NREG*NUM + 3*NUM + NPAR2 + 403 * * Set the model fitting options COPTS(1) = .TRUE. COPTS(2) = .TRUE. MAXIT = 200 TOL = 1.0D-5 * * Generate initial values for the alpha_i and beta_j parameters DO 80 I = 1, NPAR THETA(I) = PARAM(I)*0.5D0 80 CONTINUE * Generate initial values for the asymmetry parameter, gamma J = NPAR + 1 IF (ISYM.EQ.1) THEN THETA(J) = GAMMA*0.5D0 J = J + 1 END IF * Generate initial values for DF estimate IF (DIST.EQ.'T') THEN THETA(J) = DF*0.65D0 J = J + 1 END IF * Generate the initial values for b_0 IF (MN.EQ.1) THEN THETA(J) = MEAN*0.5D0 J = J + 1 END IF * Generate the initial values for the linear regression * coefficients b_i, if required IF ( .NOT. COPTS(2)) THEN DO 100 I = 1, NREG THETA(I+J-1) = BX(I)*0.5D0 100 CONTINUE END IF * * Call the analysis routine IFAIL = -1 CALL G13FAF(DIST,YT,X,LDX,NUM,IP,IQ,NREG,MN,ISYM,NPAR2,THETA, + SE,SC,COVR,LDCOVR,HP,ETM,HTM,LGF,COPTS,MAXIT,TOL, + WORK,LWORK,IFAIL) IF (IFAIL.EQ.0 .OR. IFAIL.EQ.5 .OR. IFAIL.EQ.6) THEN * Output the results WRITE (NOUT,*) ' Parameter Standard ', + 'Correct' WRITE (NOUT,*) ' estimates errors ', + 'values' * Output the coefficient alpha_0 WRITE (NOUT,99999) THETA(1), SE(1), PARAM(1) * Output the coefficients alpha_i DO 120 I = 2, IQ WRITE (NOUT,99999) THETA(I), SE(I), PARAM(I) 120 CONTINUE * Output the coefficients beta_j DO 140 I = IQ + 1, NPAR WRITE (NOUT,99999) THETA(I), SE(I), PARAM(I) 140 CONTINUE * Output the estimated asymmetry parameter, gamma J = NPAR + 1 IF (ISYM.EQ.1) THEN WRITE (NOUT,99999) THETA(J), SE(J), GAMMA J = J + 1 END IF * Output the estimated degrees of freedom, df IF (DIST.EQ.'T') THEN WRITE (NOUT,99999) THETA(J), SE(J), DBLE(DF) J = J + 1 END IF * Output the estimated mean term, b_0 IF (MN.EQ.1) THEN WRITE (NOUT,99999) THETA(J), SE(J), MEAN J = J + 1 END IF * Output the estimated linear regression coefficients, b_i DO 160 I = 1, NREG WRITE (NOUT,99999) THETA(I+J-1), SE(I+J-1), BX(I) 160 CONTINUE * * Calculate the volatility forecast NT = 4 CALL G13FBF(NUM,NT,IP,IQ,THETA,GAMMA,CVAR,HTM,ETM,IFAIL) * Display the volatility forecast WRITE (NOUT,*) WRITE (NOUT,99998) 'Volatility forecast = ', CVAR(NT) WRITE (NOUT,*) END IF 180 CONTINUE * 99999 FORMAT (1X,3F16.4) 99998 FORMAT (1X,A,F12.4) END