LibBi

StochasticVolatility package

Version 1.0.0 by Lawrence Murray

Simple stochastic volatility model.

Synopsis

./run.sh

This samples from the posterior distribution using both PMCMC (Andrieu, Doucet & Holenstein 2010) and SMC$^2$ (Chopin, Papaspiliopoulos & Jacob 2013).

The oct/ directory contains a few functions for plotting these results (GNU Octave and OctBi required), in particular the plot_and_print() function, which produces PDF files in the figs/ directory.

Description

This package implements a simple stochastic volatility model. The model is fit to 3 years of daily Standard & Poors 500 log returns, from 12 January 2002 to 30 December 2005, obtained from Yahoo Finance. The same range of data was used in Andrieu, Doucet & Holenstein (2010).

The transition model is given by:

with $\sigma_v$ the standard deviation. The observation model is given by:

References

Andrieu, C.; Doucet, A. & Holenstein, R. Particle Markov Chain Monte Carlo Methods. Journal of the Royal Statistical Society B, 2010, 72, 269-302.

Chopin, N.; Jacob, P. & Papaspiliopoulos, O. SMC$^2$: An Efficient Algorithm for Sequential Analysis of State Space Models. Journal of the Royal Statistical Society B, 2013, 75, 397-426.