Handle intercepts in the model about kfas

[helske]

Yes, there are no separate intercept terms in KFAS. What you can do is to add an extra time-invariant (Q=0) state variables C and D to the state vector a, using SSMcustom. Then C and D will be estimated "automatically" via Kalman filter.

Another option is to use bssm package which directly supports intercepts (see ?ssm_ulg for an example).

[zjph602xtc]

"What you can do is to add an extra time-invariant (Q=0) state variables C and D to the state vector a, using SSMcustom. Then C and D will be estimated "automatically" via Kalman filter."
But in this way, C and D will be different for the two series, since there are two models.

I will try the bssm package. Thank you!

[helske]

Ah, yes, but you can also build a bivariate model with common C, D etc and estimate that directly instead of two separate models.

[zjph602xtc]

The length of two series is different, and the Z_t is time-dependent (but is known and different for each series) in my case. Not sure whether it is possible to build one bivariate model. If I build one model, I have to assign many NA's in Z_t for the shorter series. Is it an appropriate way? Can you give some hints?
Thank you.

[helske]

Yes if you add NA to the end of shorter y_t then the corresponding value in Z is also ignored. Here is a quick sketch:

set.seed(1)
n1 <- 50
n2 <- 30
z1 <- sin(1:n1)
z2 <- cos(1:n2)

C <- 0.6
D <- -0.4
# random walk with drift D
x1 <- cumsum(rnorm(n1) + D)
x2 <- cumsum(rnorm(n2) + D)

y1 <- rnorm(n1, z1 * x1 + C * 1)
y2 <- rnorm(n2, z2 * x2 + C * 2)


library(KFAS)
n <- max(n1, n2)
Y <- matrix(NA, n, 2)
Y[1:n1, 1] <- y1
Y[1:n2, 2] <- y2

Z <- array(0, c(2, 4, n))
Z[1, 1, 1:n1] <- z1
Z[2, 2, 1:n2] <- z2 # trailing zeros are ok, as corresponding y is NA
Z[1, 3, ] <- 1 # x = 1
Z[2, 3, ] <- 2 # x = 2
# last state is only used in state equation so zeros in Z

T <- diag(4) # a1_t for y1, a2_t for y2, C, D
T[1, 4] <- 1 # D affects a_t
T[2, 4] <- 1 # D affects a_t
Q <- diag(c(NA, NA, 0, 0))
P1inf <- diag(4)
model <- SSModel(Y ~ -1 + SSMcustom(Z = Z, T = T, Q = Q, P1inf = P1inf,
  state_names = c("a1", "a2", "C", "D")), H = diag(NA, 2))

updatefn <- function(pars, model) {
  model$Q[] <- diag(c(exp(pars[1]), exp(pars[1]), 0, 0))
  model$H[] <- diag(exp(pars[2]), 2)
  model
}

fit <- fitSSM(model, inits = rep(-1, 2), updatefn = updatefn)

fit$model$Q[1] #0.2542451
KFS(fit$model)
Smoothed values of states and standard errors at time n = 50:
    Estimate   Std. Error
a1  -15.27620    0.86116 
a2  -12.35175    2.81083 
C     0.55220    0.08223 
D    -0.27226    0.06152 

[zjph602xtc]

I see. That is helpful!