General multivariate nonlinear Gaussian state space models
Constructs an object of class ssm_nlg by defining the corresponding terms
of the observation and state equation.
ssm_nlg(
y,
Z,
H,
T,
R,
Z_gn,
T_gn,
a1,
P1,
theta,
known_params = NA,
known_tv_params = matrix(NA),
n_states,
n_etas,
log_prior_pdf,
time_varying = rep(TRUE, 4),
state_names = paste0("state", 1:n_states)
)y |
Observations as multivariate time series (or matrix) of length n. |
Z, H, T, R |
An external pointers for the C++ functions which define the corresponding model functions. |
Z_gn, T_gn |
An external pointers for the C++ functions which define the gradients of the corresponding model functions. |
a1 |
Prior mean for the initial state as a vector of length m. |
P1 |
Prior covariance matrix for the initial state as m x m matrix. |
theta |
Parameter vector passed to all model functions. |
known_params |
Vector of known parameters passed to all model functions. |
known_tv_params |
Matrix of known parameters passed to all model functions. |
n_states |
Number of states in the model. |
n_etas |
Dimension of the noise term of the transition equation. |
log_prior_pdf |
An external pointer for the C++ function which computes the log-prior density given theta. |
time_varying |
Optional logical vector of length 4, denoting whether the values of Z, H, T, and R vary with respect to time variable (given identical states). If used, this can speed up some computations. |
state_names |
Names for the states. |
The nonlinear Gaussian model is defined as
y_t = Z(t, α_t, θ) + H(t, θ) ε_t, (\textrm{observation equation})
α_{t+1} = T(t, α_t, θ) + R(t, θ)η_t, (\textrm{transition equation})
where ε_t \sim N(0, I_p), η_t \sim N(0, I_m) and α_1 \sim N(a_1, P_1) independently of each other, and functions Z, H, T, R can depend on α_t and parameter vector θ.
Compared to other models, these general models need a bit more effort from the user, as you must provide the several small C++ snippets which define the model structure. See examples in the vignette.
Object of class ssm_nlg.
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