General ARMA(p, q) latent operator under AZW: K W = Z eps, where K encodes the AR part and Z encodes the MA part.
Usage
arma(
mesh = NULL,
ar_order = 1,
ma_order = 1,
ar = NULL,
ma = NULL,
fix_ar = FALSE,
fix_ma = FALSE
)Arguments
- mesh
Integer vector or `inla.mesh.1d` object.
- ar_order
Integer p (0, 1, or 2).
- ma_order
Integer q (0, 1, or 2).
- ar
Numeric length-p vector of AR coefficients in (-1, 1). Defaults to zeros.
- ma
Numeric length-q vector of MA coefficients in (-1, 1). Defaults to zeros.
- fix_ar
Logical or length-p logical vector to fix AR coefficients.
- fix_ma
Logical or length-q logical vector to fix MA coefficients.
Details
- Supports p, q <= 2. The user provides standard AR/MA coefficients (ar, ma). For estimation, these are transformed in R into an unbounded parameter vector `theta_K` via PACF-style mappings so optimizers (e.g., Adam/SGD) operate on unconstrained variables while K and Z remain valid: - AR(1): phi1 = tanh(raw1/2). AR(2): pi1=tanh(raw1/2), pi2=tanh(raw2/2), phi2 = pi2, phi1 = pi1 * (1 - pi2). - MA(1): theta1 = tanh(raw1/2). MA(2): psi1=tanh(raw1/2), psi2=tanh(raw2/2), theta2 = psi2, theta1 = psi1 * (1 - psi2). - The returned operator includes both K (AR part) and Z (MA part). During estimation the backend updates Z synchronously every time `theta_K` changes.