tf: 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()
)

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.

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.

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.

Examples

Run this code


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