Roman Liesenfeld

Univariate and multivariate stochastic volatility models: estimation and diagnostics

A Maximum Likelihood (ML) approach based upon an Efficient Importance Sampling (EIS) procedure is used to estimate several extensions of the standard Stochastic Volatility (SV) model for daily financial return series. EIS provides a highly generic procedure for a very accurate Monte Carlo evaluation of the marginal likelihood which depends upon high-dimensional interdependent integrals. Extensions of the standard SV model being analyzed only require minor modifications in the ML-EIS procedure. Furthermore, EIS can also be applied for filtering which provides the basis for several diagnostic tests. Our empirical analysis indicates that extensions such as a semi-nonparametric specification of the error term distribution in the return equation dominate the standard SV model. Finally, we also apply the ML-EIS approach to a multivariate factor model with stochastic volatility.

Time series of count data: modeling, estimation and diagnostics

Various models for time series of counts which can account for discreteness, overdispersion and serial correlation are compared. Besides observation- and parameter-driven models based upon corresponding conditional Poisson distributions, a dynamic ordered probit model as a flexible specification to capture the salient features of time series of counts is also considered. For all models, appropriate efficient estimation procedures are presented. For the parameter-driven specification this requires Monte-Carlo procedures like simulated maximum likelihood or Markov chain Monte Carlo. The methods, including corresponding diagnostic tests, are illustrated using data on daily admissions for asthma to a single hospital. Estimation results turn out to be remarkably similar across the different models.

Stochastic Volatility Models: Conditional Normality Versus Heavy-Tailed Distributions

Most of the empirical applications of the stochatic volatility (SV) model are based on the assumption that the conditional distribution of returns given the latent volatility process is normal. In this paper the SV model based on a conditional normal distribution is compa-red with SV specifications using conditional heavy-tailed distributions, especially Students i-distribution and the generalized error distribution. To estimate the SV specifications a si-mulated maximum likelihood approach is applied. The results based on German stock market data reveal that the SV model with a conditional normal distribution does not adequately account for the two following empirical facts simultaneously: the leptokurtic distribution of the returns and low but slowly decaying autocorrelation function of the squared returns. It is shown that these empirical facts are more adequately captured by a SV model with a conditional heavy-tailed distribution. Finally, it turns out that the choice of the conditional distribution has systematic effects on the parameter estimates of the volatility process.

A generalized bivariate mixture model for stock price volatility and trading volume

Abstract In the standard bivariate mixture model, the number of information arrivals which is typically modeled as a serially correlated random variable, determines the dynamics of stock price volatility and trading volume. An important limitation of this model is the assumption that the traders’ sensitivity to new information is constant over time, implying that every piece of information is treated alike. In this paper, I allow the latent number of information arrivals as well as the latent sensitivity to new information to be serially correlated random variables each endowed with their own dynamic behavior. In the resulting generalized mixture model, the behavior of volatility and volume results from the simultaneous interaction of the number of information arrivals and traders’ sensitivity to new information. The empirical results based on daily data for the IBM and Kodak stock reveals that the generalized mixture model improves the explanation of the behavior of volatility relative to the standard model. Furthermore, the short-run volatility dynamics are directed by the information arrival process, whereas the long-run dynamics are associated with the sensitivity to new information. Finally, the variation of the sensitivity to news is largely irrelevant for the behavior of trading volume which is mainly determined by the variation of the number of information arrivals.

Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models

In this paper, efficient importance sampling (EIS) is used to perform a classical and Bayesian analysis of univariate and multivariate stochastic volatility (SV) models for financial return series. EIS provides a highly generic and very accurate procedure for the Monte Carlo (MC) evaluation of high-dimensional interdependent integrals. It can be used to carry out ML-estimation of SV models as well as simulation smoothing where the latent volatilities are sampled at once. Based on this EIS simulation smoother, a Bayesian Markov chain Monte Carlo (MCMC) posterior analysis of the parameters of SV models can be performed.

Dynamic Bivariate Mixture Models: Modeling the Behavior of Prices and Trading Volume

Bivariate mixture models have been used to explain the stochastic behavior of daily price changes and trading volume on financial markets. In this class of models, price changes and volume follow a mixture of bivariate distributions with the unobservable number of price-relevant information serving as the mixing variable. The time series behavior of this mixing variable determines the dynamics of the price-volume system. In this article, bivariate mixture specifications with a serially correlated mixing variable are estimated by simulated maximum likelihood and analyzed concerning their ability to account for the observed dynamics on financial markets, especially the persistence in the variance of price changes. The results, based on German stock-market data, reveal that the dynamic bivariate mixture models cannot account for the persistence in the price-change variance.

Improving MCMC, using efficient importance sampling

A generic Markov Chain Monte Carlo (MCMC) framework, based upon Efficient Importance Sampling (EIS) is developed, which can be used for the analysis of a wide range of econometric models involving integrals without analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components, such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC-EIS approach is illustrated with simple univariate integration problems, and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes.

Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity

We propose a dynamic factor model for the analysis of multivariate time series count data. Our model allows for idiosyncratic as well as common serially correlated latent factors in order to account for potentially complex dynamic interdependence between series of counts. The model is estimated under alternative count distributions (Poisson and negative binomial). Maximum likelihood estimation requires high-dimensional numerical integration in order to marginalize the joint distribution with respect to the unobserved dynamic factors. We rely upon the Monte Carlo integration procedure known as efficient importance sampling, which produces fast and numerically accurate estimates of the likelihood function. The model is applied to time series data consisting of numbers of trades in 5-min intervals for five New York Stock Exchange (NYSE) stocks from two industrial sectors. The estimated model provides a good parsimonious representation of the contemporaneous correlation across the individual stocks and their serial correlation. It also provides strong evidence of a common factor, which we interpret as reflecting market-wide news.

A Nonlinear Forecasting Model of GDP Growth

We develop a model of GDP growth under which regime changes are triggered stochastically by an observable tension index, constructed as the geometric sum of deviations of actual GDP growth from a corresponding sustainable rate. Within expansionary regimes, the tension index tends to increase, which heightens the probability of a regime change. Given a regime change, the process becomes reversed, and the tension index begins to decline along a newly established path. Linking the behavior of the tension index to GDP growth enables us to capture floor and ceiling effects.

Determinants and dynamics of current account reversals: An empirical analysis

We use panel probit models with unobserved heterogeneity, state dependence and serially correlated errors in order to analyse the determinants and the dynamics of current account reversals for a panel of developing and emerging countries. The likelihood-based inference of these models requires high-dimensional integration for which we use efficient importance sampling. Our results suggest that current account balance, terms of trades, foreign reserves and concessional debt are important determinants of current account reversal. Furthermore, we find strong evidence for serial dependence in the occurrence of reversals. While the likelihood criterion suggest that state dependence and serially correlated errors are essentially observationally equivalent, measures of predictive performance provide support for the hypothesis that the serial dependence is mainly due to serially correlated country-specific shocks related to local political or macroeconomic events.