astsa (version 1.1)

EM0: EM Algorithm for Time Invariant State Space Models

Description

Estimation of the parameters in the model (6.1)--(6.2) via the EM algorithm. See Example 6.8 on page 342

Usage

EM0(num, y, A, mu0, Sigma0, Phi, cQ, cR, max.iter = 50, tol = 0.01)

Arguments

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

Value

• 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

Details

Practically, the script only requires that Q or R may be reconstructed as t(cQ)%*%(cQ) or t(cR)%*%(cR), respectively.

References

http://www.stat.pitt.edu/stoffer/tsa3/