$$ \DeclareMathOperator{\E}{E} \DeclareMathOperator{\mean}{mean} \DeclareMathOperator{\Var}{Var} \DeclareMathOperator{\Cov}{Cov} \DeclareMathOperator{\Cor}{Cor} \DeclareMathOperator{\Bias}{Bias} \DeclareMathOperator{\MSE}{MSE} \DeclareMathOperator{\sd}{sd} \DeclareMathOperator{\se}{se} \DeclareMathOperator{\rank}{rank} \DeclareMathOperator*{\argmin}{arg\,min} \DeclareMathOperator*{\argmax}{arg\,max} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\VEC}{vec} \newcommand{\mat}[1]{\boldsymbol{#1}} \newcommand{\vec}[1]{\boldsymbol{#1}} \newcommand{\T}{'} \newcommand{\distr}[1]{\mathcal{#1}} \newcommand{\dnorm}{\distr{N}} \newcommand{\dmvnorm}[1]{\distr{N}_{#1}} \newcommand{\dt}[1]{\distr{T}_{#1}} \newcommand{\cia}{\perp\!\!\!\perp} \DeclareMathOperator*{\plim}{plim} $$
State Space Models in Stan
1
Introduction
2
The Linear State Space Model
3
Filtering and Smoothing
3.1
Filtering
3.2
Smoothing
3.2.1
State Smoothing
3.2.2
Disturbance smoothing
3.2.3
Fast state smoothing
3.3
Simulation smoothers
3.3.1
Mean correction simulation smoother
3.3.2
de Jong-Shephard method
3.3.3
Forward-filter backwards-smoother (FFBS)
3.4
Missing observations
3.5
Forecasting matrices
4
Stan Functions
4.1
Utility Functions
4.1.1
to_symmetric_matrix
4.1.2
to_matrix_colwise
4.1.3
to_matrix_rowwise
4.1.4
to_vector_colwise
4.1.5
to_vector_rowwise
4.1.6
symmat_size
4.1.7
find_symmat_dim
4.1.8
vector_to_symmat
4.1.9
symmat_to_vector
4.2
Filtering
4.2.1
ssm_filter_update_a
4.2.2
ssm_filter_update_P
4.2.3
ssm_filter_update_v
4.2.4
ssm_filter_update_F
4.2.5
ssm_filter_update_Finv
4.2.6
ssm_filter_update_K
4.2.7
ssm_filter_update_L
4.2.8
ssm_filter_update_ll
4.3
Filtering
4.3.1
ssm_filter_idx
4.3.2
ssm_filter_size
4.3.3
ssm_filter_get_loglik
4.3.4
ssm_filter_get_v
4.3.5
ssm_filter_get_Finv
4.3.6
ssm_filter_get_K
4.3.7
ssm_filter_get_a
4.3.8
ssm_filter_get_P
4.3.9
ssm_filter
4.3.10
ssm_filter_states
4.3.11
ssm_filter_states_get_a
4.3.12
ssm_filter_states_get_P
4.3.13
ssm_filter_states
4.4
Log-likelihood
4.4.1
ssm_lpdf
4.5
Time-Invariant Kalman Filter
4.5.1
ssm_check_matrix_equal
4.5.2
ssm_constant_lpdf
4.6
Common Smoother Functions
4.6.1
ssm_smooth_update_r
4.6.2
ssm_smooth_update_N
4.6.3
ssm_smooth_state_size
4.6.4
ssm_smooth_state_get_mean
4.6.5
ssm_smooth_state_get_var
4.6.6
ssm_smooth_state
4.6.7
ssm_smooth_eps_size
4.6.8
ssm_smooth_eps_get_mean
4.6.9
ssm_smooth_eps_get_var
4.6.10
ssm_smooth_eps
4.6.11
ssm_smooth_eta
4.6.12
ssm_smooth_eta_get_mean
4.6.13
ssm_smooth_eta_get_var
4.6.14
ssm_smooth_eta
4.6.15
ssm_smooth_faststate
4.7
Simulators and Smoothing Simulators
4.7.1
ssm_sim_idx
4.7.2
ssm_sim_size
4.7.3
ssm_sim_get_y
4.7.4
ssm_sim_get_a
4.7.5
ssm_sim_get_eps
4.7.6
ssm_sim_get_eta
4.7.7
ssm_sim_rng
4.8
Simulation Smoothers
4.8.1
ssm_simsmo_state_rng
4.8.2
ssm_simsmo_eta_rng
4.8.3
ssm_simsmo_eps_rng
4.9
Stationary
4.9.1
pacf_to_acf
4.9.2
constrain_stationary
4.9.3
acf_to_pacf
4.9.4
unconstrain_stationary
4.9.5
kronecker_prod
4.9.6
arima_stationary_cov
5
Other Software
5.1
R packages
5.2
Other
5.2.1
Stata
5.2.2
Python
Published with bookdown
State Space Models in Stan
State Space Models in Stan
Jeffrey B. Arnold
2016-07-01
Chapter 1
Introduction
This contains documentation for “State Space Models in Stan”