Parameter instability, stochastic volatility and estimation based on simulated likelihood: Evidence from the crude oil market

Stochastic volatility models with fixed parameters can be too restrictive for time-series analysis due to instability in the parameters that govern conditional volatility dynamics. We incorporate time-variation in the model parameters for the plain stochastic volatility model as well its extensions with: Leverage, volatility feedback effects and heavy-tailed distributed innovations. With regards to estimation, we rely on one recently discovered result, namely, that when an unbiasedly simulated estimated likelihood (available for example through a particle filter) is used inside a Metropolis-Hastings routine then the estimation error makes no difference to the equilibrium distribution of the algorithm, the posterior distribution. This in turn provides an off-the-shelf technique to estimate complex models. We examine the performance of this technique on simulated and crude oil returns from 1987 to 2016. We find that (i): There is clear evidence of time-variation in the model parameters, (ii): Time-varying parameter volatility models with leverage/Student's t-distributed innovations perform best, (iii): The timing of parameter changes align very well with events such as market turmoils and financial crises.