The RATS Software Forum

Code: Select all

open data kor.xls
data(format=xls,org=columns) 1 284 lmr fxr mmr
*
*
* Estimation using MAXIMIZE
* The initial few lines of this set the estimation range, which needs to be done
* explicitly, and the number of variables. Then, vectors for the dependent
* variables, residuals and residuals formulas are set up. The SET instructions
* copy the dependent variables over into the slots in the vector of series.
*
compute gstart=2,gend=284
compute n=3
dec vect[series] y(n) u(n)
dec vect[frml] resid(n)
set y(1) = lmr
set y(2) = fxr
set y(3) = mmr

*
* This is specific to a mean-only model. It sets up the formulas (the &i are
* needed in the formula definitions when the FRML is defined in a loop), and
* estimates them using NLSYSTEM. This both initializes the mean parameters, and
* computes the unconditional covariance matrix. If you want more general mean
* equations, the simplest way to do that would be to define each FRML separately.
*
dec vect b(n) o(n) w(n) k(n) 
nonlin(parmset=meanparms) b o(1) o(2) w(1) w(2)  k   

frml lmreq lmr = b(1) + o(1)*lmr{1} + w(1)*fxr{1} + k(1)*mmr{1} + u(1)
frml  fxreq fxr = b(2) + o(2)*lmr{1} + w(2)*fxr{1} + k(2)*mmr{1} + u(2)
frml  mmreq mmr= b(3) + k(3)*mmr{1} + u(3)
frml resid(1) = (lmr-b(1)-o(1)*lmr{1}-w(1)*fxr{1}-k(1)*mmr{1})
frml resid(2) = (fxr-b(2)-o(2)*lmr{1}-w(2)*fxr{1}-k(2)*mmr{1})
frml resid(3) = (mmr-b(3)-k(3)*mmr{1})

* the third equation is an AR(1) BUT the first two a VAR(1)

nlsystem(parmset=meanparms,resids=u) gstart gend resid
compute rr=%sigma
*
* The paths of the covariance matrices and uu' are saved in the SERIES[SYMM] names
* H and UU. UX and HX are used to pull in residuals and H matrices.
*
declare series[symm] h uu
*
* ux is used when extracting a u vector
*
declare symm hx(n,n)
declare vect ux(n)
*
* These are used to initialize pre-sample variances.
*
gset h  * gend = rr
gset uu * gend = rr
*
* This is a standard (normal) log likelihood formula for any multivariate GARCH
* model. The difference among these will be in the definitions of HF and RESID.
* The function %XT pulls information out of a matrix of SERIES.
*
declare frml[symm] hf
*
frml logl = $
    hx = hf(t) , $
    %do(i,1,n,u(i)=resid(i)) , $
    ux = %xt(u,t), $
    h(t)=hx, uu(t)=%outerxx(ux), $
    %logdensity(hx,ux)
*****************************************************
*
* Positive definite parameterization (BEKK,EK)
* This enforces a positive definite covariance matrix by writing the covariance
* matrix evolution as
*
*   V(t) = C'C + A'u(t)u(t)'A + B'V(t-1)B
*
* Note that the parameters are not globally identified: changing the signs of all
* members of C, A or B will have no effect on the function value. Using
* PMETHOD=SIMPLEX to begin is quite important with this setup, to pull the
* estimates away from zero before starting the derivative-based methods.
*
dec rect   var(n,n) vbr(n,n)
dec packed vcr(n,n)
nonlin(parmset=garchparms) vcr var vbr
nonlin(parmset=restrictions) var(3,1)=var(3,2)=0.0 vbr(3,1)=vbr(3,2)=0.0

frml hf = $
  hx=h{1},uux=uu{1},$
  %ltouterxx(vcr)+%mqform(uux,var)+%mqform(hx,vbr)
*
*  Initialize c's from the decomp of the covariance matrix
*
compute vcr = %decomp(rr)
compute var = %mscalar(.05) , vbr = %mscalar(.05)
*
maximize(parmset=meanparms+garchparms+restrictions,pmethod=simplex,piters=100,method=bfgs,robust,iters=1500) logl gstart gend

Code: Select all

all 6237
open data g10xrate.xls
data(format=xls,org=columns) / usxjpn usxfra usxsui
*
set xjpn = 100.0*log(usxjpn/usxjpn{1})
set xfra = 100.0*log(usxfra/usxfra{1})
set xsui = 100.0*log(usxsui/usxsui{1})
*
compute n=3
compute gstart=3,gend=6237
*
dec series[vect] yv
dec frml[vect] residv
dec vect[series] u(n)
*
* The paths of the covariance matrices and uu' are saved in the
* SERIES[SYMM] named H and UU. UX and HX are used for the current values
* of the residual vector and H matrices
*
declare series[symm] h uu
*
* ux is used when extracting a u vector
*
declare symm hx(n,n)
declare vect ux(n)
*
* These will be the parameters for the mean equations. These are adjusted to add
* variance or covariance terms as needed.
*
dec vect b(n)
dec rect ar(n,n) ma(n,n) gm(n,n)
nonlin(parmset=meanparms) b ar ma gm
*
* Mean model = VARMA(1,1) with sqrt(h) "M" term
*
frml residv = yv-b-ar*yv{1}-ma*%xt(u,t-1)-gm*%sqrt(%xdiag(h))
*
gset yv = ||xjpn,xfra,xsui||
*
* Run preliminary VAR(4) to get estimates of residuals
*
linreg xjpn / u(1)
# constant xjpn{1 to 4} xfra{1 to 4} xsui{1 to 4}
linreg xfra / u(2)
# constant xjpn{1 to 4} xfra{1 to 4} xsui{1 to 4}
linreg xsui / u(3)
# constant xjpn{1 to 4} xfra{1 to 4} xsui{1 to 4}
*
linreg xjpn
# constant xjpn{1} xfra{1} xsui{1} u(1){1} u(2){1} u(3){1}
compute b(1)=%beta(1),ar(1,1)=%beta(2),ar(1,2)=%beta(3),ar(1,3)=%beta(4),$
                      ma(1,1)=%beta(5),ma(1,2)=%beta(6),ma(1,3)=%beta(7)
linreg xfra
# constant xjpn{1} xfra{1} xsui{1} u(1){1} u(2){1} u(3){1}
compute b(2)=%beta(1),ar(2,1)=%beta(2),ar(2,2)=%beta(3),ar(2,3)=%beta(4),$
                      ma(2,1)=%beta(5),ma(2,2)=%beta(6),ma(2,3)=%beta(7)
linreg xsui
# constant xjpn{1} xfra{1} xsui{1} u(1){1} u(2){1} u(3){1}
compute b(3)=%beta(1),ar(3,1)=%beta(2),ar(3,2)=%beta(3),ar(3,3)=%beta(4),$
                      ma(3,1)=%beta(5),ma(3,2)=%beta(6),ma(3,3)=%beta(7)

vcv(matrix=rr,noprint)
# u
*
* These are used to initialize pre-sample variances.
*
gset h  * gend = rr
gset uu * gend = rr
set u(1) = 0.0
set u(2) = 0.0
set u(3) = 0.0
*
declare frml[symm] hf
*
frml logl = $
    hx    = hf(t) , $
    h(t)  = hx, $
    ux    = residv , $
    uu(t) = %outerxx(ux), $
    %pt(u,t,ux),$
    %logdensity(hx,ux)
*
* This does a simple GARCH(1,1) model for the variance.
*
dec symm vcs(n,n) vas(n,n) vbs(n,n)
compute vcs=rr,vbs=%const(0.50),vas=%const(0.05)
nonlin(parmset=garchparms) vcs vas vbs
frml hf = vcs+vbs.*h{1}+vas.*uu{1}
maximize(trace,parmset=meanparms+garchparms,pmethod=simplex,piters=10,method=bfgs,iters=400) logl gstart gend
*
* This does a BEKK model for the variance
*
dec rect vab(n,n) vbb(n,n)
compute vab=.05*%identity(n),vbb=.50*%identity(n)
nonlin(parmset=garchparms) vcs vab vbb
compute vcs=%decomp(rr)
frml hf = vcs*tr(vcs)+vbb*h{1}*tr(vbb)+vab*uu{1}*tr(vab)
maximize(trace,parmset=meanparms+garchparms,pmethod=simplex,piters=10,method=bfgs,iters=400) logl gstart gend