acov2ma {tsdecomp}

Convert Autocovariances to Coefficients of a Moving Average

Description

Convert autocovariances to coefficients of a moving average.

Usage

acov2ma.init(x, tol = 0.00001, maxiter = 100)
acov2ma(x, tol = 1e-16, maxiter = 100, init = NULL)

Arguments

x

a numeric vector containing the autocovariances.

tol

numeric, convergence tolerance.

maxiter

numeric, maximum number of iterations.

init

numeric, vector of initial coefficients.

Details

acov2ma.init is based on procedure (17.35) described in Pollock (1999). acov2ma is the Newton-Raphson procedure (17.39) described in the same reference.

Value

A list containing the vector of coefficients and the variance of the innovations in the moving average model; convergence code and number of iterations.

References

Pollock, D. S. G. (1999) A Handbook of Time-Series Analysis Signal Processing and Dynamics. Academic Press. Chapter 17. doi: 10.1016/B978-012560990-6/50002-6

Examples

set.seed(123)
x <- arima.sim(n=200, model=list(ma=c(0.7,-0.3)))
#sample autocovariances
a <- c(var(x), cov(x[-1], x[-200]), cov(x[-c(1,2)], x[-c(199,200)]))
#inferred coefficients and variance
acov2ma(a, init=acov2ma.init(a, maxit=10)$macoefs)
#compare with maximum-likelihood
arima(x, order=c(2,0,0), include.mean=FALSE)