Canonical Decomposition
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.
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, ...)
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 .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.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.
Burman, J. P. (1980) Seasonal Adjustment by Signal Extraction . Journal of the Royal Statistical Society. Series A (General), 143 (3), pp. 321-337. tools:::Rd_expr_doi("10.2307/2982132") .
Hillmer, S. C. and Tiao, G. C. (1982) An ARIMA-Model-Based Approach to Seasonal Adjustment . Journal of the American Statistical Association, 77 (377), pp. 63-70. tools:::Rd_expr_doi("10.1080/01621459.1982.10477767") .
acgf2poly, pseudo.spectrum, optimize.