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.

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]