Estimation

maximum_likelihood!(model; init=NamedTuple(), method=:collapsed, pen=NoPen(), ϵ_abs=1e-7, ϵ_rel=1e-4, max_iter=1000)

Maximum Likelihood (ML) algorithm to estimate the hyper parameters of a linear Gaussian State Space model as defined by model, results are stored in model. Penalized ML estimation is allowed through pen. If pen` = NoPen()`` the optimization routine is L-BFGS, whenpen≂̸ NoPen()` optimization is doen through ADMM.

Arguments

• model::StateSpaceModel: state space model
• init::NamedTuple : initial model parameters
• method::Symbol : filtering method
• pen::Penalization : penalization type
• ϵ_abs::Real : absolute tolerance
• ϵ_rel::Real : relative tolerance
• max_iter::Integer : max number of iterations

Returns

• ll::Real : log-likelihood value

em!(model, pen; init=NamedTuple(), ϵ=1e-4, max_iter=1000)

Expectation-Maximization (EM) algorithm to estimate the hyper parameters of a linear Gaussian State Space model as defined by model, storing the results in model.

Arguments

• model::StateSpaceModel: state space model
• pen::NamedTuple : penalization parameters
• method::Symbol : filtering method
• init::NamedTuple : initial model parameters
• ϵ::Real : tolerance
• max_iter::Integer : max number of iterations

Returns

• ll::Real : log-likelihood value

ecm!(model, pen; init=NamedTuple(), ϵ=1e-4, max_iter=1000)

Expectation-Conditional Maximization (ECM) algorithm to estimate the hyper parameters of a linear Gaussian State Space model as defined by model, results are stored in model.

Arguments

• model::StateSpaceModel: state space model
• pen::NamedTuple : penalization parameters
• method::Symbol : filtering method
• init::NamedTuple : initial model parameters
• ϵ::Real : tolerance
• max_iter::Integer : max number of iterations

Returns

• ll::Real : log-likelihood value