Marcel Scharth

Predicting Time-Varying Parameters with Parameter-Driven and Observation-Driven Models

This discussion paper led to a publication in the Review of Economics and Statistics . We study whether and when parameter-driven time-varying parameter models lead to forecasting gains over observation-driven models. We consider dynamic count, intensity, duration, volatility and copula models, including new specifications that have not been studied earlier in the literature. In an extensive Monte Carlo study, we find that observation-driven generalised autoregressive score (GAS) models have similar predictive accuracy to correctly specified parameter-driven models. In most cases, differences in mean squared errors are smaller than 1% and model confidence sets have low power when comparing these two alternatives. We also find that GAS models outperform many familiar observation-driven models in terms of forecasting accuracy. The results point to a class of observation-driven models with comparable forecasting ability to parameter-driven models, but lower computational complexity.

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State-Space Models

We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer to this method as numerically accelerated importance sampling. We show that the likelihood function for models with a high-dimensional state vector and a low-dimensional signal can be evaluated more efficiently using the new method. We report many efficiency gains in an extensive Monte Carlo study as well as in an empirical application using a stochastic volatility model for U.S. stock returns with multiple volatility factors. Supplementary materials for this article are available online.

Importance Sampling Squared for Bayesian Inference in Latent Variable Models

We consider Bayesian inference by importance sampling when the likelihood is analytically intractable but can be unbiasedly estimated. We refer to this procedure as importance sampling squared (IS2), as we can often estimate the likelihood itself by importance sampling. We provide a formal justification for importance sampling when working with an estimate of the likelihood and study its convergence properties. We analyze the effect of estimating the likelihood on the resulting inference and provide guidelines on how to set up the precision of the likelihood estimate in order to obtain an optimal tradeoff between computational cost and accuracy for posterior inference on the model parameters. We illustrate the procedure in empirical applications for a generalized multinomial logit model and a stochastic volatility model. The results show that the IS2 method can lead to fast and accurate posterior inference under the optimal implementation.

Realized volatility risk

In this paper we document that realized variation measures constructed from high-frequency returns reveal a large degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation measures are nearly gaussian, this unpredictability brings considerably more uncertainty to the empirically relevant ex ante distribution of returns. Carefully modeling this volatility risk is fundamental. We propose a dually asymmetric realized volatility (DARV) model, which incorporates the important fact that realized volatility series are systematically more volatile in high volatility periods. Returns in this framework display time varying volatility, skewness and kurtosis. We provide a detailed account of the empirical advantages of the model using data on the S&P 500 index and eight other indexes and stocks.

Particle efficient importance sampling

The efficient importance sampling (EIS) method is a general principle for the numerical evaluation of high-dimensional integrals that uses the sequential structure of target integrands to build variance minimising importance samplers. Despite a number of successful applications in high dimensions, it is well known that importance sampling strategies are subject to an exponential growth in variance as the dimension of the integration increases. We solve this problem by recognising that the EIS framework has an offline sequential Monte Carlo interpretation. The particle EIS method is based on non-standard resampling weights that take into account the construction of the importance sampler as a sequential approximation to the state smoothing density. We apply the method for a range of univariate and bivariate stochastic volatility specifications. We also develop a new application of the EIS approach to state space models with Student’s t state innovations. Our results show that the particle EIS method strongly outperforms both the standard EIS method and particle filters for likelihood evaluation in high dimensions. We illustrate the efficiency of the method for Bayesian inference using the particle marginal Metropolis–Hastings and importance sampling squared algorithms.

Markov Interacting Importance Samplers

We introduce a new Markov chain Monte Carlo (MCMC) sampler called the Markov Interacting Importance Sampler (MIIS). The MIIS sampler uses conditional importance sampling (IS) approximations to jointly sample the current state of the Markov Chain and estimate conditional expectations, possibly by incorporating a full range of variance reduction techniques. We compute Rao-Blackwellized estimates based on the conditional expectations to construct control variates for estimating expectations under the target distribution. The control variates are particularly efficient when there are substantial correlations between the variables in the target distribution, a challenging setting for MCMC. An important motivating application of MIIS occurs when the exact Gibbs sampler is not available because it is infeasible to directly simulate from the conditional distributions. In this case the MIIS method can be more efficient than a Metropolis-within-Gibbs approach. We also introduce the MIIS random walk algorithm, designed to accelerate convergence and improve upon the computational efficiency of standard random walk samplers. Simulated and empirical illustrations for Bayesian analysis show that the method significantly reduces the variance of Monte Carlo estimates compared to standard MCMC approaches, at equivalent implementation and computational effort.

Monte Carlo option pricing with asymmetric realized volatility dynamics

What are the advances introduced by realized volatility models in pricing options? In this short paper we analyze a simple option pricing framework based on the dually asymmetric realized volatility model, which emphasizes extended leverage effects and empirical regularity of high volatility risk during high volatility periods. We conduct a brief empirical analysis of the pricing performance of this approach against some benchmark models using data from the S&P 500 options in the 2001-2004 period. The results indicate that as expected the superior forecasting accuracy of realized volatility translates into significantly smaller pricing errors when compared to models of the GARCH family. Most importantly, our results indicate that the presence of leverage effects and a high volatility risk are essential for understanding common option pricing anomalies.