statespace {viking}

Design a State-Space Model

Description

The function statespace builds a state-space model, with known or unknown variances. By default, this function builds a state-space model in the static setting, with a constant state (zero state noise covariance matrix) and constant observation noise variance.

Usage

statespace(X, y, kalman_params = NULL, viking_params = NULL, ...)

Arguments

X

design matrix.

y

variable of interest.

kalman_params

(default NULL) list containing initial values for theta,P as well as the variances (Q,sig). If it is not specified, the state-space model is constructed in the static setting (theta=0, P=I, Q=0, sig=1).

viking_params

(default NULL) list of parameters for the Viking algorithm.

...

additional parameters

Value

a statespace object.

Examples

set.seed(1)
### Simulate data
n <- 1000
d <- 5
Q <- diag(c(0,0,0.25,0.25,0.25))
sig <- 1

X <- cbind(matrix(rnorm((d-1)*n,sd=1),n,d-1),1)
theta <- matrix(rnorm(d), d, 1)
theta_arr <- matrix(0, n, d)
for (t in 1:n) {
  theta_arr[t,] <- theta
  theta <- theta + matrix(mvtnorm::rmvnorm(1,matrix(0,d,1),Q),d,1)
}
y <- rowSums(X * theta_arr) + rnorm(n, sd=sig)

####################
### Kalman Filter
# Default Static Setting
ssm <- viking::statespace(X, y)
plot(ssm)

# Known variances
ssm <- viking::statespace(X, y, kalman_params = list(Q=Q, sig=sig))
plot(ssm)