Construct an object of class ssm_ung by defining the corresponding terms
of the observation and state equation:
ssm_ung(
y,
Z,
T,
R,
a1,
P1,
distribution,
phi = 1,
u = 1,
init_theta = numeric(0),
D,
C,
state_names,
update_fn = default_update_fn,
prior_fn = default_prior_fn
)Observations as time series (or vector) of length \(n\).
System matrix Z of the observation equation. Either a vector of length m, a m x n matrix, or object which can be coerced to such.
System matrix T of the state equation. Either a m x m matrix or a m x m x n array, or object which can be coerced to such.
Lower triangular matrix R the state equation. Either a m x k matrix or a m x k x n array, or object which can be coerced to such.
Prior mean for the initial state as a vector of length m.
Prior covariance matrix for the initial state as m x m matrix.
Distribution of the observed time series. Possible choices are
"poisson", "binomial", "gamma", and "negative binomial".
Additional parameter relating to the non-Gaussian distribution. For negative binomial distribution this is the dispersion term, for gamma distribution this is the shape parameter, and for other distributions this is ignored.
Constant parameter for non-Gaussian models. For Poisson, gamma, and negative binomial distribution, this corresponds to the offset term. For binomial, this is the number of trials.
Initial values for the unknown hyperparameters theta.
Intercept terms \(D_t\) for the observations equation, given as a 1 x 1 or 1 x n matrix.
Intercept terms \(C_t\) for the state equation, given as a m times 1 or m times n matrix.
Names for the states.
Function which returns list of updated model
components given input vector theta. This function should take only one
vector argument which is used to create list with elements named as
Z, T, R, a1, P1, D, C, and
phi,
where each element matches the dimensions of the original model.
If any of these components is missing, it is assumed to be constant wrt. theta.
Function which returns log of prior density given input vector theta.
Object of class ssm_ung.
$$p(y_t | D_t + Z_t \alpha_t), (\textrm{observation equation})$$ $$\alpha_{t+1} = C_t + T_t \alpha_t + R_t \eta_t, (\textrm{transition equation})$$
where \(\eta_t \sim N(0, I_k)\) and \(\alpha_1 \sim N(a_1, P_1)\) independently of each other, and \(p(y_t | .)\) is either Poisson, binomial, gamma, or negative binomial distribution.