Kastner-Frühwirth-Schnatter (2014) ASIS for Boosting MCMC Estimation of Stochastic Volatility Models

Summary

Kastner and Frühwirth-Schnatter show how the ancillarity-sufficiency interweaving strategy (ASIS) can be applied to stochastic volatility (SV) models to greatly improve MCMC sampling efficiency across the whole parameter range. Bayesian SV inference is highly sensitive to parameterization: the centered version breaks down when the volatility-of-volatility is small, while the non-centered version is deficient when the latent log-variance is highly persistent. Interweaving the two — "combining the best of different worlds" — yields efficient sampling for all parameters and makes previously infeasible parameter constellations estimable without pre-selecting a parameterization.

Key Claims

• Parameterization-dependent mixing. MCMC efficiency for SV depends strongly on the true parameters: the centered parameterization (CP) mixes poorly when $\sigma_\eta$ (vol-of-vol) is small; the non-centered parameterization (NCP) mixes poorly when persistence $\phi$ is high — complementary failure modes.
• Interweaving (ASIS). Applying Yu-Meng's (2011) ancillarity-sufficiency interweaving to SV, they update $(\mu,\phi,\sigma_\eta)$ in both the CP and NCP within each sweep (mapping the latent log-volatilities between the two), inheriting the strengths of each.
• Efficiency everywhere. The interwoven sampler achieves high efficiency for all parameters throughout the parameter space, and enables inference for constellations infeasible under a single parameterization — with no need to choose one in advance.
• Auxiliary-mixture sampling. Log-volatilities are drawn via the Kim-Shephard-Chib / Omori-et-al. mixture-of-normals approximation to the $\log\chi^2$ error, making the state update a Gaussian FFBS step.
• Software. The approach is implemented in the stochvol R package.

Concepts Introduced or Extended

• Ancillarity-Sufficiency Interweaving Strategy
• Stochastic Volatility

Entities Mentioned

• Gregor Kastner
• Sylvia Frühwirth-Schnatter

Quotes

"While draws from the posterior utilizing the standard centered parameterization break down when the volatility of volatility parameter in the latent state equation is small, non-centered versions of the model show deficiencies for highly persistent latent variable series … an interweaving strategy … greatly improve[s] sampling efficiency for all parameters and throughout the entire parameter range."

My Take

A textbook demonstration that how you write a latent-variable model, not just how you sample it, decides whether MCMC works. The insight the paper exploits — that centered and non-centered augmentations fail in opposite regimes — turns an awkward "which parameterization?" dilemma into a non-choice: interweave both and be robust everywhere. For stochastic volatility, whose interesting cases (near-deterministic or near-unit-root volatility) are exactly the ones that stall single-parameterization samplers, that robustness is decisive, and the stochvol implementation made it the default recipe. It is the data-augmentation counterpart to the auxiliary-mixture trick (Kim-Shephard-Chib) already used to Gaussianize the SV measurement equation — two orthogonal efficiency gains that compose.