Theoretical cross-covariances of auxilary AR process in ARMA(p,q)

Description

The auxilary AR processes in the ARMA(p,q) model phi(B)z(t)=theta(B)a(t) are defined by phi(B)u(t)=-a(t) and theta(B)v(t)=a(t). The upper off-diagonal p-by-q block of the ARMA information matrix is obtained from the cross-covariances of u(t) and v(t). This function obtains these covariances.

Usage

tccfAR(phi, theta)

Arguments

Details

A set of linear equations which determine the covariances is solved. The algorithm is similar in spirit to that for the autocovariances (McLeod, 1975).

Value

vector of cross-covariances

Author(s)

A.I. McLeod

References

McLeod, A.I. (1975), Derivation of the theoretical autocorrelation function of autoregressive moving-average time series, Applied Statistics 24, 255-256.

See Also

InformationMatrixARMA

Examples

tccfAR(0.9,0.5)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(FitARMA)
Loading required package: FitAR
Loading required package: lattice
Loading required package: leaps
Loading required package: ltsa
Loading required package: bestglm
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FitARMA/tccfAR.Rd_%03d_medium.png", width=480, height=480)
> ### Name: tccfAR
> ### Title: Theoretical cross-covariances of auxilary AR process in
> ###   ARMA(p,q)
> ### Aliases: tccfAR
> ### Keywords: ts
> 
> ### ** Examples
> 
> tccfAR(0.9,0.5)
[1] 1.8181818 0.9090909
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>