tf: Transfer function for input

In tfarima: Transfer Function and ARIMA Models

Transfer function for input

Description

tf creates a rational transfer function for an input, V(B) = w0(1 - w_1B - ... - w_qB^q)/(1-d_1B - ... - d_pB^p)B^dX_t. Note that in this specification the constant term of the MA polynomial is factored out so that both polynomials in the numerator and denominator are normalized and can be specified with the lagpol function in the same way as the operators of univariate models.

Usage

tf(
  x = NULL,
  delay = 0,
  w0 = 0.01,
  ar = NULL,
  ma = NULL,
  um = NULL,
  n.back = NULL,
  par.prefix = "",
  envir = parent.frame()
)

Arguments

x	Input time series. A ts object or numeric vector. If NULL, input should be provided inside the um object.
delay	Integer. Number of periods to delay the input (d in the transfer function).
w0	Numeric. Constant term of the transfer function polynomial V(B).
ar	Character string or list. Specification of autoregressive polynomials in the denominator.
ma	Character string or list. Specification of moving average polynomials in the numerator.
um	Univariate model object. Model for the stochastic component of the input series.
n.back	Integer. Number of backcasts to compute for extending the input series backward.
par.prefix	Character. Prefix for parameter names in transfer function.
envir	Environment. Environment for evaluating function arguments. If NULL, uses the calling environment.

Value

An object of class "tf" containing the transfer function specification. Key components include:

x

Input time series data (possibly extended with backcasts).

delay

Number of periods delay in the transfer function.

w0

Constant gain parameter.

phi

AR polynomial coefficients (denominator).

theta

MA polynomial coefficients (numerator).

p, q

Orders of AR and MA polynomials respectively.

param

Named list of all model parameters.

um

Univariate model for the input series.

References

Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.

Wei, W.W.S. (2006) Time Series Analysis Univariate and Multivariate Methods. 2nd Edition, Addison Wesley, New York, 33-59.

See Also

um.

Examples

x <- rep(0, 100)
x[50] <- 1
tfx <- tf(x, w0 = 0.8, ar = "(1 - 0.5B)(1 - 0.7B^12)")

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