I have a question on how I should enter time-varying coefficient matrices in a DLM using functions. What I want to estimate are the states in a multivariate SSM with a vector of observables, a vector of states and time-varying coefficient matrices (that I estimate previous to running the KF).
In the code shown below, I get an error message as RATS doesn't seem to like the function expressions in the DLM-command (allthough they seem to work fine when just printing the matrices for a specific time period).
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function afunc A reset beta_q time
type vec[rec] A
type series reset
type vector beta_q
type integer time
type rect afunc
local integer k i j
local rec temp
*
dim afunc(%rows(A)*%rows(A(1))+2,%rows(A)*%rows(A(1))+2)
comp afunc = %const(0.0)
do k=1,%rows(A)
do i=1,%rows(A(1))
do j=1,%cols(A(1))
comp afunc(i,(k-1)*%rows(A(1))+j) = A(k)(i,j)
end do j
end do i
if k>1 {
do i=1,%rows(A(1))
do j=1,%cols(A(1))
comp afunc((k-1)*%rows(A(1))+i,(k-2)*%rows(A(1))+j) = i==j
end do j
end do i
}
do i=1,%cols(A(1))
comp temp = tr(beta_q)*%xsubmat(A(k),1,%rows(A(k)),i,i)
comp afunc(%rows(afunc)-1,(k-1)*%rows(A(1))+i) = temp(1,1)
comp afunc(%rows(afunc),(k-1)*%rows(A(1))+i) = temp(1,1)
end do i
end do k
comp afunc(%rows(afunc),%cols(afunc)) = reset(time)
end function afunc
*
function yfunc monthly quarterly time
type vec[int] monthly
type series quarterly
type integer time
type vec yfunc
local integer k
*
dim yfunc(%rows(monthly)+1)
do k=1,%rows(monthly)
comp yfunc(k) = ([series] monthly(k))(time)
end do k
comp yfunc(%rows(yfunc)) = quarterly(time)
end function yfunc
*
function cfunc Lambda p
type rec Lambda
type integer p
type rec cfunc
local integer i j
*
dim cfunc(%rows(Lambda)+1,%cols(Lambda)*p+2)
comp cfunc = %const(0.0)
do i=1,%rows(Lambda)
do j=1,%cols(Lambda)
comp cfunc(i,j) = Lambda(i,j)
end do j
end do i
comp cfunc(%rows(cfunc),%cols(cfunc)) = 1
comp cfunc = tr(cfunc)
end function cfunc
*
function zfunc mu_q r p
type real mu_q
type int r
type int p
type vect zfunc
*
comp zfunc = %zeros(r*p+2,1)
comp zfunc(%rows(zfunc)-1) = (1./3)*mu_q
comp zfunc(%rows(zfunc)) = (1./3)*mu_q
end function zfunc
*
function ffunc B p
type rect B
type int p
type rec ffunc
*
comp ffunc = B~~%zeros(%rows(B)*(p-1)+2,%cols(B))
end function ffunc
PROCEDURE NOWCAST QUARTERLY START END
*
type series quarterly
type int start end
*
option choice method 1 factor
option switch print 0
option switch intres 0
option switch graph 0
option integer fsteps 0
option integer ftime
option integer p 1; * lag order for factor VAR
option integer r 3; * number of factors
option integer q 2; * number of shocks
*
local integer nind lstart lend i time
local vec[int] monthly
local real mu_q Sigma_q
local vec[rea] mu beta_q
local rec[rea] z x D V F Lambda Psi Sigma B
local vec[rec] A
local vec[ser] F_q F_m
local series reset
local vec[str] F_lab
local ser[vec] st_vec
local ser[sym] st_var
*
if method==1 {
*
* Here follows some other code...
*
*----------------------------------------------------------------------------------------------
* Implementation of Kalman filter
if intres; disp "ESTIMATES OF THE VARIOUS MATRICES SUCCESSFULLY ESTIMATED! GOING ON WITH KALMAN FILTER..."
*
* The state vector, kf_X_t, includes the following [f_t f_t-1 ... f_t-p+1 y_hat y_hat_q]'
* The vector of observables, kf_Y_t, includes the following [z1_t z2_t ... zn_t y_q]'
* The matrix that relates the state vector to the observables, kf_c, is constant and includes the factor loadings
* The transition matrix for the state vector, kf_A_t, includes the coefficients from the factor VAR, beta_q, and an indicator to "re-set" the quarterly series (y_hat_q)
* The shift vector for the state, kf_z, includes the unconditional mean of y_q
set reset lstart lend = %mod(t,3)<>1
*disp yfunc(monthly,quarterly,lend)
disp afunc(A,reset,beta_q,lend)
*disp cfunc(Lambda,p)
*disp zfunc(mu_q,r,p)
*disp ffunc(B,p)
* Checking dimensions of the matrices
if intres; disp "kf_Y:" @10 %rows(yfunc(monthly,quarterly,lend)) "by" %cols(yfunc(monthly,quarterly,lend))
if intres; disp "kf_A:" @10 %rows(afunc(A,reset,beta_q,lend)) "by" %cols(afunc(A,reset,beta_q,lend))
if intres; disp "kf_c:" @10 %rows(cfunc(Lambda,p)) "by" %cols(cfunc(Lambda,p))
if intres; disp "kf_Z:" @10 %rows(zfunc(mu_q,r,p)) "by" %cols(zfunc(mu_q,r,p))
if intres; disp "kf_F:" @10 %rows(ffunc(B,p)) "by" %cols(ffunc(B,p))
* Estimation of states (factors and monthly GDP) by Kalman filter
dlm(var=known,presample=ergodic,method=bfgs,a=afunc(A,reset,beta_q,t),y=yfunc(monthly,quarterly,t),c=cfunc(Lambda,p),z=zfunc(mu_q,r,p),f=ffunc(B,p), $
sw=%identity(q),sv=Sigma~\%zeros(1,1)~\Sigma_q,type=filter) lstart lend st_vec st_var
}
*
end procedure
Note that all inputs (like A,Lambda,etc...) are properly defined in the code that I skipped to make this post more readable. afunc is properly displayed, but for the dlm-command I get the following error message, when sourcing the procedure:
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## SX22. Expected Type SERIES, Got REAL Instead
>>>>gs,a=afunc(A,reset,<<<<
Does anybody have an example of a similar multivariate SSM?