tf function

Transfer function for input

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.

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

Arguments

• x: input, a ts object or a numeric vector.
• delay: integer.
• w0: constant term of the polynomial V(B), double.
• ar: list of stationary AR polynomials.
• ma: list of MA polynomials.
• um: univariate model for stochastic input.
• n.back: number of backcasts to extend the input.
• par.prefix: prefix name for parameters.
• envir: environment in which the function arguments are evaluated. If NULL the calling environment of this function will be used.

Returns

An object of the class "tf".

Examples

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

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.