Bayesian estimation of NIG models via Markov chain Monte Carlo methods

Abstract

SUMMARYThe normal inverse Gaussian (NIG) distribution is a promising alternative for modelling financial data since it is a continuous distribution that allows for skewness and fat tails. There is an increasing number of applications of the NIG distribution to financial problems. Due to the complicated nature of its density, estimation procedures are not simple. In this paper we propose Bayesian estimation for the parameters of the NIG distribution via an MCMC scheme based on the Gibbs sampler. Our approach makes use of the data augmentation provided by the mixture representation of the distribution. We also extend the model to allow for modelling heteroscedastic regression situations. Examples with financial and simulated data are provided.

Models for heavy-tailed asset returns

“…Obviously, the NIG distribution may not be adequate to deal with cases of extremely heavy tails such as those of Pareto or non-Gaussian stable laws. However, empirical experience suggests excellent fits of the NIG law to financial data (Karlis, 2002;Karlis and Lillestöl, 2004;Venter and de Jongh, 2002).…”

Estimating higher-order structure functions from geophysical turbulence time series: Confronting the curse of the limited sample size

“…However, in a typical laboratory or geophysical setting, these NIG parameters are not known a priori. One can then use the method of moments approach (see Appendix A) to estimate them, but this technique has been shown to be unstable [73]. A more robust approach would be to use the maximum likelihood estimator (MLE; [74,75]), for details see Appendix B.…”

Some New Bivariate IG and NIG-Distributions for Modelling Covariate Financial Returns

“…The estimation of NIG-parameters can be done by maximum likelihood methods directly, or via the EM-algorithm, see Karlis (2002), or by Bayesian estimation via Markov chain Monte Carlo, see Karlis and Lillestøl (2004). The latter two produce a Z-series as a bi-product of the estimation process.…”

“…The parameter estimates of the marginal NIG-distributions turned out to be as in Table 1. The estimation is Bayesian using a fairly uninformative prior and sampling from the posterior by a Markov chain Monte Carlo scheme as described in Karlis and Lillestøl (2004). The estimates are based on 1000 sample repeats.…”