Dear all,
I am currently trying to use the "dlm" package for Kalman filtering.
My model is very simple:
Y_t = F'_t Theta_t + v_t
Theta_t = G_t Theta_t-1 + w_t
v_t ~ N(0,V_t) = N(0,V)
w_t ~ N(0,W_t) = N(0,W)
Y_ t is a univariate time series (1x1)
F_t is a vector of factor returns (Kx1)
Theta_t is the state vector (Kx1)
G_t is the identity matrix
My first challenge is to get the Maximum Likelihood estimators of V and W
assuming they are time-invariant (homoscedastic) through the dlmMLE
function.
In the example provided in the user guide, F is the Identity matrix
(diag(2)) and I would like to know how to adapt the coding such that F can
vary over time and matches my case study described above.
data(NelPlo)
### multivariate local level -- seemingly unrelated time series
buildSu <- function(x) {
Vsd <- exp(x[1:2])
Vcorr <- tanh(x[3])
V <- Vsd %o% Vsd
V[1,2] <- V[2,1] <- V[1,2] * Vcorr
Wsd <- exp(x[4:5])
Wcorr <- tanh(x[6])
W <- Wsd %o% Wsd
W[1,2] <- W[2,1] <- W[1,2] * Wcorr
return(list(
m0 = rep(0,2),
C0 = 1e7 * diag(2),
FF = diag(2),
GG = diag(2),
V = V,
W = W))
}
suMLE <- dlmMLE(NelPlo, rep(0,6), buildSu); suMLE
buildSu(suMLE$par)[c("V","W")]
Thanking you in advance for your help,
Gerardo Amo
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