ARmh {bayess} R Documentation

## Metropolis–Hastings evaluation of the posterior associated with an AR(p) model

### Description

This function is associated with Chapter 6 on dynamic models. It implements a Metropolis–Hastings algorithm on the coefficients of the AR(p) model resorting to a simulation of the real and complex roots of the model. It includes jumps between adjacent numbers of real and complex roots, as well as random modifications for a given number of real and complex roots.

### Usage

ARmh(x, p = 1, W = 10^3)


### Arguments

 x time series to be modelled as an AR(p) model p order of the AR(p) model W number of iterations

### Details

Even though Bayesian Essentials with R does not cover the reversible jump MCMC techniques due to Green (1995), which allows to explore spaces of different dimensions at once, this function relies on a simple form of reversible jump MCMC when moving from one number of complex roots to the next.

### Value

 psis  matrix of simulated \psi_i's mus  vector of simulated \mu's sigs  vector of simulated \sigma^2's llik  vector of corresponding likelihood values (useful to check for convergence) pcomp  vector of simulated numbers of complex roots

### References

Green, P.J. (1995) Reversible jump MCMC computaton and Bayesian model choice. Biometrika 82, 711–732.

ARllog
data(Eurostoxx50)