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).
# S3 method for 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(),
...
)An object of class "um".
Autoregressive lag polynomial for the signal component.
Integration lag polynomial for the signal component.
Logical. If TRUE, extracts a single component; if
FALSE, extracts multiple components.
Logical. If TRUE, applies the canonical decomposition
constraint.
Method for Cramer-Wold factorization: "roots" polynomial
(Godolphin 1976), "wilson" iterative algorithm (Wilson 1969), or the
"best" of both methods.
Method for partial fraction decomposition: "gcd"
(extended Euclidean algorithm) or "solve" (linear system solver).
Numerical tolerance for zero and unit values. Default is
1e-5.
Environment for evaluation.
Additional arguments.
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.
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. 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. tools:::Rd_expr_doi("10.1137/0706001")
ucarima