ar1: AR(1) process ('time_series_model')

In gmwmx2: Estimate Functional and Stochastic Parameters of Linear Models with Correlated Residuals and Missing Data

AR(1) process (time_series_model)

Description

Constructs a time_series_model for a stationary AR(1) process with parameter phi and innovation variance sigma2. The model is X_t = \phi X_{t-1} + \varepsilon_t, \; \varepsilon_t \stackrel{\text{i.i.d.}}{\sim} N(0, \sigma^2). The autocovariance is \gamma(h) = \mathrm{cov}(X_t, X_{t+h}) = \frac{\sigma^2}{1 - \phi^2}\,\phi^{\lvert h \rvert} .

Usage

ar1(phi = NULL, sigma2 = NULL)

Arguments

phi	AR(1) coefficient in (-1, 1).
sigma2	Innovation variance (> 0).

Value

A time_series_model object.

Examples

mod <- ar1(phi = 0.8, sigma2 = 1)
mod

gmwmx2 documentation built on June 10, 2026, 5:06 p.m.