autocov2MA: Convert autocovariances to MA parameters

In tfarima: Transfer Function and ARIMA Models

Convert autocovariances to MA parameters

Description

Computes MA polynomial coefficients and error variance from autocovariances.

Usage

autocov2MA(x, method = c("roots", "acov"), tol = 1e-05)

Arguments

x	Numeric vector of autocovariances (length q).
method	Estimation method: "roots" (Godolphin 1976) or "acov" (Wilson 1969). Default is "roots".
tol	Tolerance for zero autocovariance. Default 1e-5.

Value

Named vector: c(s2, ma0=1, ma1=-theta1, ..., maq=-thetaq).

References

Godolphin, E. J. (1976). On the Cramer-Wold factorization. Biometrika, 63(2), 367-372. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/63.2.367")}

Tunnicliffe Wilson, G. (1969). Factorization of the covariance generating function of a pure moving average process. SIAM Journal on Numerical Analysis, 6(1), 1-7. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/0706001")}

Examples

ma1 <- um(ma = "1 - 0.8B", sig2 = 0.5)
autocov2MA(autocov(ma1, 1))
autocov2MA(autocov(ma1, 1), method = "acov")

tfarima documentation built on Nov. 5, 2025, 7:43 p.m.