pmhtutorial (version 1.5)

example3_sv: Parameter estimation in a simple stochastic volatility model

Description

Minimal working example of parameter estimation in a stochastic volatility model using the particle Metropolis-Hastings algorithm with a bootstrap particle filter providing an unbiased estimator of the likelihood. The code estimates the parameter posterior for three parameters using real-world data.

Usage

example3_sv(noBurnInIterations = 2500, noIterations = 7500,
  noParticles = 500, initialTheta = c(0, 0.9, 0.2),
  stepSize = diag(c(0.1, 0.01, 0.05)^2), syntheticData = FALSE)

Arguments

noBurnInIterations

The number of burn-in iterations in the PMH algorithm. Must be smaller than noIterations.

noIterations

The number of iterations in the PMH algorithm. 100 iterations takes about a minute on a laptop to execute.

noParticles

The number of particles to use when estimating the likelihood.

initialTheta

The initial guess of the parameters theta.

stepSize

The step sizes of the random walk proposal. Given as a covariance matrix.

syntheticData

If TRUE, data is not downloaded from the Internet. This is only used when running tests of the package.

Value

The function returns the estimated marginal parameter posteriors for each parameter, the trace of the Markov chain and the resulting autocorrelation function. The data is also presented with an estimate of the log-volatility.

The function returns a list with the elements:

• thhat: The estimate of the mean of the parameter posterior.

• xhat: The estimate of the mean of the log-volatility posterior.

• thhatSD: The estimate of the standard deviation of the parameter posterior.

• xhatSD: The estimate of the standard deviation of the log-volatility posterior.

• iact: The estimate of the integrated autocorrelation time for each parameter.

• estCov: The estimate of the covariance of the parameter posterior.

• theta: The trace of the chain exploring the parameter posterior.

Details

The Particle Metropolis-Hastings (PMH) algorithm makes use of a Gaussian random walk as the proposal for the parameters. The data are scaled log-returns from the OMXS30 index during the period from January 2, 2012 to January 2, 2014.

This version of the code makes use of a somewhat well-tuned proposal as a pilot run to estimate the posterior covariance and therefore increase the mixing of the Markov chain.

References

Dahlin, J. & Schon, T. B. "Getting Started with Particle Metropolis-Hastings for Inference in Nonlinear Dynamical Models." Journal of Statistical Software, Code Snippets, 88(2): 1--41, 2019.

Examples

# NOT RUN {
    example3_sv(noBurnInIterations=200, noIterations=1000)
# }