Neil Shephard

Overview

Neil Shephard is an econometrician and statistician (Oxford, later Harvard). His research centers on simulation-based inference for latent-variable time series models, particularly stochastic volatility. He is best known for the Kim-Shephard-Chib (1998) multi-move MCMC sampler for SV models, the Pitt-Shephard (1999) auxiliary particle filter, and (with Barndorff-Nielsen) the development of realized volatility theory linking high-frequency data to integrated variance.

Key Contributions

• Kim-Shephard-Chib (1998): Multi-move Gibbs sampler for SV models; log-squared-return transformation + 7-component Gaussian mixture for $\log\chi^2(1)$ errors + Carter-Kohn (1994) simulation smoother draws full $\{h_t\}$ path in one block; importance reweighting corrects approximation to exact inference; inefficiency factors 1–3 vs. 20–200 for single-move; Bayes factors decisively favor SV over GARCH/t-GARCH. See Kim-Shephard-Chib (1998) and Stochastic Volatility.
• Pitt-Shephard (1999) auxiliary particle filter: Improves on the bootstrap particle filter by using a one-step-ahead look-ahead to construct proposal densities; reduces variance of likelihood estimates; M=20,000 particles routine for SV models.
• Chib-Nardari-Shephard (2002): Co-developed SVt and SVJt models with efficient MCMC and marginal likelihood comparison; showed fat-tailed SV decisively beats Gaussian-plus-jumps for S&P 500.
• Chib-Nardari-Shephard (2006): Co-developed high-dimensional factor-SV model scaling to $p=50$ series and 688 parameters; key contribution is the reduced blocking scheme (marginalizing $b$ over latent factors $f$) that reduces MCMC inefficiency factors from >1,000 to 1–30; particle filter for marginal likelihood; 10-index application demonstrates MSV superiority over MGARCH alternatives.
• Barndorff-Nielsen-Shephard (2001/2002): Established that realized volatility (sum of squared intraday returns) converges to integrated variance; derived the asymptotic theory for RV-based inference on SV models.
• Barndorff-Nielsen-Shephard (2006): Time-changed Lévy processes — RV is an inconsistent estimator of the time-change whenever the driving Lévy process $Z$ has jumps ($k_4 > 0$); the irreducible variance component $k_4\Delta\xi$ does not vanish as sampling frequency increases; RV ACF underestimates true variance ACF; 4th cumulant test for jumps; QL estimation via Kalman filter or Durbin algorithm for OU/superposition/LNOU/long-memory models. See Barndorff-Nielsen and Shephard (2006) and Time-Changed Lévy Process.
• Omori-Chib-Shephard-Nakajima (2007): With Yasuhiro Omori, Siddhartha Chib, and Jouchi Nakajima; extends KSC (1998) multi-move sampler to ASV with leverage; 10-component bivariate normal mixture with $\rho$-independent approximation quality; TOPIX application confirms $\hat\rho = -0.362$ and decisive Bayes factor for leverage. See Stochastic Volatility and Omori-Chib-Shephard-Nakajima (2007).

Related

• Stochastic Volatility
• Realized Volatility
• Time-Changed Lévy Process
• Ole E. Barndorff-Nielsen
• Siddhartha Chib
• Federico Nardari
• Eric Jacquier
• Nicholas Polson