as.ucarima.um: Coerce a Univariate Model to UCARIMA form

In tfarima: Transfer Function and ARIMA Models

Coerce a Univariate Model to UCARIMA form

Description

Converts an object of class "um" (univariate model) to its equivalent "ucarima" representation, i.e., the ARIMA-model-based decomposition of unobserved components (trend, seasonal, cycle, irregular, etc.) implied by the univariate ARIMA structure, following the approach of Hillmer and Tiao (1982).

Usage

## S3 method for class 'um'
as.ucarima(
  object,
  ar = NULL,
  i = NULL,
  single = FALSE,
  canonical = FALSE,
  cwfact = c("roots", "iter", "best"),
  pfrac = c("gcd", "solve"),
  tol = 1e-05,
  envir = parent.frame(),
  ...
)

Arguments

object	An object of class "um".
ar	Autoregressive lag polynomial for the signal component.
i	Integration lag polynomial for the signal component.
single	Logical. If TRUE, extracts a single component; if FALSE, extracts multiple components.
canonical	Logical. If TRUE, applies the canonical decomposition constraint.
cwfact	Method for Cramer-Wold factorization: "roots" polynomial (Godolphin 1976), "wilson" iterative algorithm (Wilson 1969), or the "best" of both methods.
pfrac	Method for partial fraction decomposition: "gcd" (extended Euclidean algorithm) or "solve" (linear system solver).
tol	Numerical tolerance for zero and unit values. Default is 1e-5.
envir	Environment for evaluation.
...	Additional arguments.

Details

The UCARIMA decomposition expresses a univariate ARIMA model as the sum of independent component ARIMA models (trend, seasonal, cycle, irregular, etc.) obtained through the factorization of its spectral density. This provides a model-based interpretation of signal extraction and seasonal adjustment.

References

Hillmer, S. C., & Tiao, G. C. (1982). An ARIMA-model-based approach to seasonal adjustment. Journal of the American Statistical Association, 77(377), 63–70.

Burman, J. P. (1980). Seasonal adjustment by signal extraction. Journal of the Royal Statistical Society: Series A, 143(3), 321–337.

Godolphin, E. J. (1976). On the Cramer–Wold factorization. Biometrika, 63(2), 367–372. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/63.2.367")}

Tunnicliffe Wilson, G. (1969). Factorization of the covariance generating function of a pure moving average process. SIAM Journal on Numerical Analysis, 6(1), 1–7. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/0706001")}

See Also

ucarima

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