EM Algorithm for Time Invariant State Space Models
Estimation of the parameters in a simple state space via the EM algorithm.
EM0(num, y, A, mu0, Sigma0, Phi, cQ, cR, max.iter = 50, tol = 0.01)
num |
number of observations |
y |
observation vector or time series |
A |
time-invariant observation matrix |
mu0 |
initial state mean vector |
Sigma0 |
initial state covariance matrix |
Phi |
state transition matrix |
cQ |
Cholesky-like decomposition of state error covariance matrix Q – see details below |
cR |
Cholesky-like decomposition of state error covariance matrix R – see details below |
max.iter |
maximum number of iterations |
tol |
relative tolerance for determining convergence |
Practically, the script only requires that Q or R may be reconstructed as
Phi |
Estimate of Phi |
Q |
Estimate of Q |
R |
Estimate of R |
mu0 |
Estimate of initial state mean |
Sigma0 |
Estimate of initial state covariance matrix |
like |
-log likelihood at each iteration |
niter |
number of iterations to convergence |
cvg |
relative tolerance at convergence |
D.S. Stoffer
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