EM0 {astsa} R Documentation

## 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

### 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

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]