xEM1 function

EM Algorithm for General State Space Models - This script has been superseded by EM.

Estimation of the parameters in the general state space model via the EM algorithm. Inputs are not allowed; see the note. NOTE: This script has been superseded by EM and scripts starting with an x are scheduled to be phased out.

xEM1(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

Returns

• 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

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 and some help on using R for time series analysis can be found at https://nickpoison.github.io/.

Author(s)

D.S. Stoffer

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).

Note

NOTE: This script has been superseded by EM