R: Canonical Decomposition

canonical.decomposition {tsdecomp}

R Documentation

Canonical Decomposition

Description

Given the partial fraction decomposition of the pseudo-spectrum, the canonical decomposition allocates the variance of each component so that the variance of the irregular is maximised. Then, the coefficients of the numerators in the pseudo-spectrum (relationship given in pseudo.spectrum) are converted into the MA coefficients of the model for each component by means of acgf2poly.

Usage

canonical.decomposition(num.trend, den.trend, 
  num.trans, den.trans, num.seas, den.seas, quotient, optim.tol = 1e-04, ...)
## S3 method for class 'tsdecCanDec'
print(x, units = c("radians", "degrees", "pi"), digits = 4, ...)

Arguments

`num.trend`	numeric vector, the coefficients of the MA polynomial related to the trend component in the relationship given in `pseudo.spectrum`.
`den.trend`	numeric vector, the coefficients of the AR polynomial related to the trend component in the relationship given in `pseudo.spectrum`.
`num.trans`	numeric vector, the coefficients of the MA polynomial related to the transitory component in the relationship given in `pseudo.spectrum`.
`den.trans`	numeric vector, the coefficients of the AR polynomial related to the transitory component in the relationship given in `pseudo.spectrum`.
`num.seas`	numeric vector, the coefficients of the MA polynomial related to the seasonal component in the relationship given in `pseudo.spectrum`.
`den.seas`	numeric vector, the coefficients of the AR polynomial related to the seasonal component in the relationship given in `pseudo.spectrum`.
`quotient`	numeric vector, the quotient of the polynomial division of the polynomials in the LHS of the relationship given in `pseudo.spectrum`. (Different from zero only when the degree of the MA polynomial is equal or higher than the degree of the AR polynomial in the fitted model).
`optim.tol`	numeric, the convergence tolerance to be used by `optimize`.
`units`	character, the units in which the argument of the roots are printed. `units="pi"` prints the argument in radians as multiples of `\pi`.
`x`	an object of class `tsdecCanDec` returned by `canonical.decomposition`.
`digits`	numeric, the number of significant digits to be used by `print`.
`...`	further arguments to be passed to `poly2acgf` or `print`.

Value

An object of class tsdecCanDec containing the MA coefficients of the ARIMA models obtained for the unobserved components (e.g., trend, seasonal) and the variance of the corresponding disturbance terms.

References

Burman, J. P. (1980) ‘Seasonal Adjustment by Signal Extraction’. Journal of the Royal Statistical Society. Series A (General), 143(3), pp. 321-337. doi: 10.2307/2982132.