ssm: State Space Model

In astsa: Applied Statistical Time Series Analysis

State Space Model

Description

Fits a simple univariate state space model to data. The parameters are estimated (the state regression parameter may be fixed). State predictions, filters, and smoothers and corresponding error variances are evaluated at the estimates. The sample size must be at least 20.

Usage

ssm(y, A, phi, alpha, sigw, sigv, fixphi = FALSE)

Arguments

y	data
A	measurement value (fixed constant)
phi	initial value of phi, may be fixed
alpha	initial value for alpha
sigw	initial value for sigma[w]
sigv	initial value for sigma[v]
fixphi	if TRUE, the phi parameter is fixed

Details

The script works for a specific univariate state space model,

x_t = \alpha + \phi x_{t-1} + w_t \quad {\rm and} \quad y_t = A x_t + v_t.

The initial state conditions use a default calculation and cannot be specified. The parameter estimates are printed and the script returns the state predictors and smoothers. The regression parameter \phi may be fixed.

Value

At the MLEs, these are returned invisibly:

Xp	time series - state prediction, x_t^{t-1}
Pp	corresponding MSPEs, P_t^{t-1}
Xf	time series - state filter, x_t^t
Pf	corresponding MSEs, P_t^t
Xs	time series - state smoother, x_t^n
Ps	corresponding MSEs, P_t^n

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

Examples

## Not run: 

u = ssm(gtemp_land, A=1, alpha=.01, phi=1, sigw=.05, sigv=.15)
tsplot(gtemp_land, type='o', col=4)
lines(u$Xs, col=6, lwd=2)

## End(Not run)

astsa documentation built on May 29, 2024, 10:29 a.m.