uc0: Unobservable components (UC) for structural time series...

In tfarima: Transfer Function and ARIMA Models

Unobservable components (UC) for structural time series models

Description

uc0 constructs unobservable components by specifying their state-space representation matrices. This is the helper function used internally by uc to create predefined components like trends, seasonals, and cycles.

Usage

uc0(name, param, b, C = NULL, S = NULL)

Arguments

name	character, name of the UC.
param	a vector or list with the parameters of the UC.
b	vector of the UC in the observation equation.
C	matrix of the UC in the transition matrix.
S	covariance matrix of the error vector driving the UC.

Value

An S3 object of class uc.

Note

Matrices b, C and S can include symbolic expressions in terms of the parameters of the model. These parameters are defined in the param argument with their corresponding names. See the ssm function for more information about b, C and S.

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 linear trend component
param <- c(s2_lvl = 0.05, s2_slp = 0.025)
b <- c(1, 0)
C <- matrix(c(1, 1, 0, 1), 2, 2, byrow = TRUE)
S <- matrix(c("s2_lvl", "0", "0", "s2_slp"), 2, 2)
trend <- uc0("trend", param, b, C, S)

# Cycle component
param <- c(phi = 0.8, per = 5, s2c = 0.01)
b <- c(1, 0)
C <- matrix(c("phi*cos(2*pi/per)", "phi*sin(2*pi/per)", 
"-phi*sin(2*pi/per)", "phi*cos(2*pi/per)"), 2, 2, byrow = TRUE)
S <- matrix(c("s2c*(1 - phi^2)", "0", "0", "s2c*(1 - phi^2)"))
cycle <- uc0("cycle", param, b, C, S)

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