Convert between periodic centering and intercepts

Convert a periodic mean to periodic intercept and vice versa.

Usage

permean2intercept(mean, coef, order, nseasons = nrow(coef))

intercept2permean(intercept, coef, order, nseasons = nrow(coef))

Arguments

mean: periodic mean, numeric.
coef: PAR coefficients, matrix.
order: PAR order, vector of positive integers.
nseasons: number of seasons, a.k.a. period.
intercept: periodic intercepts, numeric.

Details

A PAR model can be written in mean corrected or intercept form. permean2intercept calculates the intercepts from the means, while intercept2permean does the inverse (means from intercepts).

No check is made for periodic stationarity of the model. Converting from mean corrected to intercept form allways succeeds and in fact the means do not need to be means. In the opposite direction there may be problems due to unit roots and similar features.

Value

a numeric vector

Author

Georgi N. Boshnakov

Examples

mu <- c(1, 2)
pm1 <- PeriodicArModel(matrix(c(0.5, 0.5), nrow = 2), order = rep(1, 2), sigma2 = 1, mean = mu)

cc <- permean2intercept(mu, pm1@ar@coef, c(1,1))
cc
#> [1] 0.0 1.5
intercept2permean(cc, pm1@ar@coef, c(1,1))
#> [1] 1 2

d <- 4
mu <- 1:d
co <- rep(0.5, d)
pm1 <- PeriodicArModel(matrix(co, nrow = d), order = rep(1, d), sigma2 = 1, mean = mu)

cc <- permean2intercept(mu, pm1@ar@coef, order = rep(1, d))
cc
#> [1] -1.0  1.5  2.0  2.5
intercept2permean(cc, pm1@ar@coef, order = rep(1, d) )
#> [1] 1 2 3 4