bayess (version 1.4)

MAmh: Metropolis--Hastings evaluation of the posterior associated with an MA(p) model

Description

This function implements a Metropolis--Hastings algorithm on the coefficients of the MA(p) model, involving the simulation of the real and complex roots of the model. The algorithm includes jumps between adjacent numbers of real and complex roots, as well as random modifications for a given number of real and complex roots. It is thus a special case of a reversible jump MCMC algorithm (Green, 1995).

Usage

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

Arguments

x

time series to be modelled as an MA(p) model

p

order of the MA(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 log-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.

See Also

MAllog

Examples

data(Eurostoxx50)
x=Eurostoxx50[1:350, 5]
resMA5=MAmh(x=x,p=5,W=50)
plot(resMA5$mus,type="l",col="steelblue4",xlab="Iterations",ylab=expression(mu))