SSModelSSModel creates a state space object
object of class SSModel which can be used as an
input object for various functions of KFAS
package.SSModel(y, Z = NULL, H = NULL, T = NULL, R = NULL,
Q = NULL, a1 = NULL, P1 = NULL, P1inf = NULL, u = NULL,
distribution = c("Gaussian", "Poisson", "Binomial"),
transform = c("none", "ldl", "augment"),
tolF = .Machine$double.eps^0.5,
tol0 = .Machine$double.eps^0.5)ts, or a
object that can be coerced to such.KFAS require
diagonal covariance matrix $H_t$. If
$H_t$ is not diagonal, model can be transformed
using one of the two options. Option "ldl"
performs LDL decomposition for covariance matrix
$H_t$, and mSSModel with elementsZ, H, T,
R, Q, a1, P1 and
P1inf. Matrix or scalar Z (array in case of
time-varying Z) is used to determine the number of
states $m$. If some of the other elements of the
object are missing, SSModel uses default values
which are identity matrix for T, R (or
$k$ first columns of identity matrix) and
P1inf, and zero matrix for H, Q,
P1 and , a1. If P1 is given and
P1inf is not, the it is assumed to be zero matrix.
If Q is given, it is used to define $r$, the
dimensions of Q, which can be smaller than $m$
(defaults to $m$).The linear Gaussian state space model is given by
$$y_t = Z_t \alpha_t + \epsilon_t,$$
$$\alpha_{t+1} = T_t \alpha_t + R_t \eta_t,$$
where $\epsilon_t ~ N(0,H_t)$, $\eta_t ~ N(0,Q_t)$ and $\alpha_1 ~ N(a_1,P_1)$ independently of each other. In case of non-Gaussian observations, the observation equation is of form $p(y_t|\theta_t) = p(y_t|Z_t\alpha_t)$, with $p(y_t|\theta_t)$ being one of the following:
If observations are Poisson distributed, parameter of Poisson distribution is $u_t\lambda_t$ and $\theta_t = log(\lambda_t)$.
If observations are from binomial distribution, $u$ is a vector specifying number the of trials at times $1,\ldots,n$, and $\theta_t = log[\pi_t/(1-\pi_t)]$, where $\pi_t$ is the probability of success at time $t$.
For non-Gaussian models $u_t=1$ as a default. For Gaussian models, parameter is omitted.
Only univariate observations are supported when observation equation is non-Gaussian.
arimaSSM for state space representation of
ARIMA model, regSSM for state space
representation of a regression model, and
structSSM for structural time series model.