KalmanFilterTools.jl
WORK IN PROGRESS
KalmanFilterTools provides efficient code to perform various computations pertaining to state space models and the Kalman Filter, such as the Kalman filter proper, the Kalman smoother or computing the log likelihood for the model.
Because such operations are very often computed in an iterative manner, all operations are computed /in place/. One function allocate the necessary workspace and another function performs the computations.
Installation
KalmanFilterTools.jl is available on GitLab:
(v1.4) pkg> add https://git.dynare.org/julia-packages/kalmanfiltertools.jl.gitJulia version
KalmanFilterTools requires Julia version >= 1.4
State Space model
KalmanFilterTools handles state space models of the following form:
y_t = Z a_t + \epsilon_t
a_{t+1} = Ta_t + R\eta_t
\epsilon_t \sim N(0,H)
\eta_t \sim N(0,Q)y_t: observation vector ny x 1
a_t: state vector ns x 1
\epsilon_t: measurement error vector ny x 1
\eta_t: shocks vector np x 1
Z: ny x ns matrix
T: ns x ns matrix
R: ns x np matrix
H: ny x ny covariance matrix
Q: ns x ns covariance matrix
Example
Computing the log likelihood
using KalmanFilterTools
data = ....
Z = ...
T = ...
R = ...
Q = ...
a = ...
P = ...
ny, ns = size(Z)
np = size(R, 2)
nobs = size(data,2)
first_obs = 1
last_obs = nobs
presample = 0
kalman_ws = KalmanLikelihoodWs{Float64, Integer}(ny, ns, np, nobs)
llk = kalman_likelihood(data, Z, H, T, R, Q, a, P, first_obs, last_obs, presample, kalman_ws)