bayess (version 1.4)

ARmh: 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

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

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.

References

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

See Also

ARllog

Examples

data(Eurostoxx50)
x=Eurostoxx50[, 4]
resAR5=ARmh(x=x,p=5,W=50)
plot(resAR5$mus,type="l",col="steelblue4",xlab="Iterations",ylab=expression(mu))