EM1 {astsa}R Documentation

EM Algorithm for General State Space Models

Description

Estimation of the parameters in the general state space model via the EM algorithm. Inputs are not allowed; see the note.

Usage

EM1(num, y, A, mu0, Sigma0, Phi, cQ, cR, max.iter = 100, tol = 0.001)

Arguments

num

number of observations

y

observation vector or time series; use 0 for missing values

A

observation matrices, an array with dim=c(q,p,n); use 0 for missing values

mu0

initial state mean

Sigma0

initial state covariance matrix

Phi

state transition matrix

cQ

Cholesky-like decomposition of state error covariance matrix Q – see details below

cR

R is diagonal here, so cR = sqrt(R) – also, see details below

max.iter

maximum number of iterations

tol

relative tolerance for determining convergence

Details

cQ and cR are the Cholesky-type decompositions of Q and R. In particular, Q = t(cQ)%*%cQ and R = t(cR)%*%cR is all that is required (assuming Q and R are valid covariance matrices).

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

Note

Inputs are not allowed (and hence not estimated). The script uses Ksmooth1 and everything related to inputs are set equal to zero when it is called.

It would be relatively easy to include estimates of 'Ups' and 'Gam' because conditional on the states, these are just regression coefficients. If you decide to alter EM1 to include estimates of the 'Ups' or 'Gam', feel free to notify me with a workable example and I'll include it in the next update.

Author(s)

D.S. Stoffer

References

You can find demonstrations of astsa capabilities at FUN WITH ASTSA.

The most recent version of the package can be found at https://github.com/nickpoison/astsa/.

In addition, the News and ChangeLog files are at https://github.com/nickpoison/astsa/blob/master/NEWS.md.

The webpages for the texts are https://www.stat.pitt.edu/stoffer/tsa4/ and https://www.stat.pitt.edu/stoffer/tsda/.


[Package astsa version 1.14 Index]