# ar1_lg: Univariate Gaussian model with AR(1) latent process In bssm: Bayesian Inference of Non-Linear and Non-Gaussian State Space Models

 ar1_lg R Documentation

## 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 <- rnorm(1, mu, sigma / sqrt(1 - rho^2))
y <- rnorm(1, beta * x + z, 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 May 4, 2022, 1:06 a.m.