pcAR2acf: Compute periodic autocorrelations from PAR coefficients

In GeoBosh/pcts: Periodically Correlated and Periodically Integrated Time Series

Compute periodic autocorrelations from PAR coefficients

Description

Compute periodic autocorrelations from PAR coefficients. This effectively solves the inverse problem to that solved by the periodic Levinson-Durbin algorithm but does not use a recursion.

Usage

pcAR2acf(coef, sigma2, p, maxlag = 10)

Arguments

coef	PAR coefficients, a matrix, see Details.
sigma2	innovations variances.
p	PAR order.
maxlag	How many lags to compute.

Details

coef is a matrix with the coefficients for season i in the i-th row. The coefficients start from lag 1.

The first few autocorrelations are computed by solving a linear system, see the references. The rest, are generated using the periodic Yule-Walker equations.

Value

a matrix, in which row s contains the acf's for season s for lags 0, 1, ..., maxlag (in this order).

Author(s)

Georgi N. Boshnakov

References

\insertRef

boshnakov1996pcarmapcts

\insertRef

b:Varna92pcts

See Also

pcarma_acvf_lazy, which does the main computation, but note that the coefficients for it start from lag zero

Examples

m <- rbind( c(0.81, 0), c(0.4972376, 0.4972376) )
si2 <- PeriodicVector(c(0.3439000, 0.1049724))

pcAR2acf(m)
pcAR2acf(m, si2)
pcAR2acf(m, si2, 2)
pcAR2acf(m, si2, 2, maxlag = 10)


# same using pcarma_acvf_lazy directly
m1 <- rbind( c(1, 0.81, 0), c(1, 0.4972376, 0.4972376) )

testphi <- slMatrix(init = m1)
myf <- pcarma_acvf_lazy(testphi, testtheta, si2, 2, 0, 2, maxlag = 10)
myf(1:2, 0:9)    # get a matrix of values

all(myf(1:2, 0:9) == pcAR2acf(m, si2, 2, maxlag = 9)) # TRUE

GeoBosh/pcts documentation built on Dec. 8, 2023, 9:57 p.m.