astsa (version 1.10)

EM0: EM Algorithm for Time Invariant State Space Models

Description

Estimation of the parameters in a simple state space via the EM algorithm.

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

%% ~Describe the value returned %% If it is a LIST, use %% \item{comp1 }{Description of 'comp1'} %% \item{comp2 }{Description of 'comp2'} %% ...

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/tsa4/