ssm: Time Invariant State Space Model

In tfarima: Transfer Function and ARIMA Models

Time Invariant State Space Model

Description

ssm creates an S3 object representing a time-invariant state space model:

Usage

ssm(z, b, C, S, xreg = NULL, bc = FALSE, cform = TRUE, tol = 1e-05)

Arguments

z	an object of class ts.
b	vector of coefficients (m-dimensional).
C	matrix of coefficients (m x m).
S	covariance matrix of the error vector [u(t), v(t)], (m+1 x m+1).
xreg	design matrix of regressors.
bc	logical. If TRUE logs are taken.
cform	logical. If TRUE state equation is given in contemporaneous form, otherwise it is written in lagged form.
tol	tolerance to check if a value is zero or one.

Details

z(t) = b'x(t-j) + u(t) (observation equation), x(t) = Cx(t-1) + v(t) (state equation), j = 0 for contemporaneous form or j = 1 for lagged form. Note: the lagged form (j=1) is equivalent to the future form x(t+1) = Cx(t) + v(t+1).

Value

An object of class ssm containing:

z	the input time series
b	observation coefficients
C	state transition matrix
S	error covariance matrix
xreg	regressor matrix (if provided)
a	regression coefficients for xreg (if computed)
z.name	name of the input series
bc	Box-Cox transformation indicator
m	number of state variables
cform	form indicator (contemporaneous vs lagged)
is.adm	admissibility flag

References

Durbin, J. and Koopman, S.J. (2012) Time Series Analysis by State Space Methods, 2nd ed., Oxford University Press, Oxford.

Harvey, A.C. (1989) Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge.

Examples

# Local level model
b <- 1
C <- as.matrix(1)
ssm1 <- ssm(Nile, b, C, S = diag(c(irr = 1, lvl = 0.5)) )
ssm1

tfarima documentation built on Nov. 5, 2025, 7:43 p.m.