2018/08/23 by Thiago Rezende dos Santos, Santos, T. R.
Economics, Econometrics and Finance · Decision Sciences · #Financial Risk and Volatility Modeling #Forecasting Techniques and Applications
paper · pdf · doi:10.48550/arxiv.1809.01489
Several studies explore inferences based on stochastic volatility (SV)\nmodels, taking into account the stylized facts of return data. The common\nproblem is that the latent parameters of many volatility models are\nhigh-dimensional and analytically intractable, which means inferences require\napproximations using, for example, the Markov Chain Monte Carlo or Laplace\nmethods. Some SV models are expressed as a linear Gaussian state-space model\nthat leads to a marginal likelihood, reducing the dimensionality of the\nproblem. Others are not linearized, and the latent parameters are integrated\nout. However, these present a quite restrictive evolution equation. Thus, we\npropose a Bayesian GED-Gamma SV model with a direct marginal likelihood that is\na product of the generalized Student's t-distributions in which the latent\nstates are related across time through a stationary Gaussian evolution\nequation. Then, an approximation is made for the prior distribution of\nlog-precision/volatility, without the need for model linearization. This also\nallows for the computation of the marginal likelihood function, where the\nhigh-dimensional latent states are integrated out and easily sampled in blocks\nusing a smoothing procedure. In addition, extensions of our GED-Gamma model are\neasily made to incorporate skew heavy-tailed distributions. We use the Bayesian\nestimator for the inference of static parameters, and perform a simulation\nstudy on several properties of the estimator. Our results show that the\nproposed model can be reasonably estimated. Furthermore, we provide case\nstudies of a Brazilian asset and the pound/dollar exchange rate to show the\nperformance of our approach in terms of fit and prediction.\n Keywords: SV model, New sequential and smoothing procedures, Generalized\nStudent's t-distribution, Non-Gaussian errors, Heavy tails, Skewness\n