ar1_lg: Univariate Gaussian model with AR(1) latent process

In bssm: Bayesian Inference of Non-Linear and Non-Gaussian State Space Models

Univariate Gaussian model with AR(1) latent process

Description

Constructs a simple Gaussian model where the state dynamics follow an AR(1) process.

Usage

ar1_lg(y, rho, sigma, mu, sd_y, beta, xreg = NULL)

Arguments

y	A vector or a ts object of observations.
rho	A prior for autoregressive coefficient. Should be an object of class bssm_prior.
sigma	A prior for the standard deviation of noise of the AR-process. Should be an object of class bssm_prior
mu	A fixed value or a prior for the stationary mean of the latent AR(1) process. Should be an object of class bssm_prior or scalar value defining a fixed mean such as 0.
sd_y	A prior for the standard deviation of observation equation.
beta	A prior for the regression coefficients. Should be an object of class bssm_prior or bssm_prior_list (in case of multiple coefficients) or missing in case of no covariates.
xreg	A matrix containing covariates with number of rows matching the length of y. Can also be ts, mts or similar object convertible to matrix.

Value

An object of class ar1_lg.

Examples

set.seed(1)
mu <- 2
rho <- 0.7
sd_y <- 0.1
sigma <- 0.5
beta <- -1
x <- rnorm(30)
z <- y <- numeric(30)
z[1] <- rnorm(1, mu, sigma / sqrt(1 - rho^2))
y[1] <- rnorm(1, beta * x[1] + z[1], sd_y)
for(i in 2:30) {
  z[i] <- rnorm(1, mu * (1 - rho) + rho * z[i - 1], sigma)
  y[i] <- rnorm(1, beta * x[i] + z[i], sd_y)
}
model <- ar1_lg(y, rho = uniform(0.5, -1, 1), 
  sigma = halfnormal(1, 10), mu = normal(0, 0, 1), 
  sd_y = halfnormal(1, 10), 
  xreg = x,  beta = normal(0, 0, 1))
out <- run_mcmc(model, iter = 2e4)
summary(out, return_se = TRUE)

bssm documentation built on Nov. 2, 2023, 6:25 p.m.