tfarima (version 0.4.1)

ssm: 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)

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

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).

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