We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.

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Monte Carlo Statistical Methods

The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT.

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Unscented filtering and nonlinear estimation

Methods for the systematic application of Monte Carlo integration with importance sampling to Bayesian inference in econometric models are developed. Conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of Monte Carlo replications increases, and the numerical accuracy of this approximation may be assessed reliably, are set forth. Methods for the analytical verification of these conditions are discussed

Bayesian Inference in Econometric Models Using Monte Carlo Integration

This paper surveys the most important developments in multivariate ARCH-type modelling. It reviews the model specifications, the inference methods, and the main areas of application of these models in financial econometrics.

Multivariate GARCH Models: A Survey

We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy decouples, in part, the cooperative management of the network formation from the network maneuvers. The underlying coordination framework uses virtual bodies and artificial potentials. We focus on gradient climbing missions in which the mobile sensor network seeks out local maxima or minima in the environmental field. The network can adapt its configuration in response to the sensed environment in order to optimize its gradient climb.

Cooperative control of mobile sensor networks:Adaptive gradient climbing in a distributed environment

textAdaptive Polar Sampling (APS) algorithms are proposed for Bayesian analysis of models with 
nonelliptical, possibly, multimodal posterior distributions. A location-scale transformation 
and a transformation to polar coordinates are used. After the transformation to polar 
coordinates, a Metropolis-Hastings method or, alternatively, an importance sampling 
method is applied to sample directions and, conditionally on these, distances are 
generated by inverting the cumulative distribution function. A sequential procedure is 
applied to update the initial location and scaling matrix in order to sample directions 
in an efficient way. Tested on a set of canonical mixture models that feature multimodality, 
strong correlation, and skewness, the APS algorithms compare favourably with the standard 
Metropolis-Hastings and importance samplers in terms of flexibility and robustness. APS is 
applied to several econometric and statistical examples. The empirical results for a 
regression model with scale contamination, an ARMA-GARCH-Student t model with near 
cancellation of roots and heavy tails, a mixture model for economic growth, and a 
nonlinear threshold model for industrial production growth confirm the practical 
flexibility and robustness of APS.

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Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods

This paper proposes a class of asymmetric Autoregressive Conditional Duration models, which extends the ACD model of Engle and Russell (1997). The asymmetry consists of letting the duration process depend on the state of the price process in the beginning and at the end of each duration. If the price has increased, the parameters of the ACD can differ from what they are if the price has decreased. Thus, the model is also a transition model for the price process, with durations following an ACD process. The logarithmic version of the model is applied to the bid/ask price revision process by the specialist for the IBM stock on the New York Stock Exchange. The empirical evidence in favour of asymmetry is compelling.

Asymmetric ACD models: introducing price information in ACD models with a two state transition model

The general-to-specific (GETS) approach to modelling is widely employed in the modelling of economic series, but less so in financial volatility modelling due to computational complexity when many explanatory variables are involved. This study proposes a simple way of avoiding this problem and undertakes an out-of-sample forecast evaluation of the methodology applied to the modelling of weekly exchange rate volatility. Our findings suggest that GETS specifications are especially valuable in conditional forecasting, since the specification that employs actual values on the uncertain information performs particularly well.

General to specific modelling of exchange rate volatility: a forecast evaluation

Several models have been developed to capture the dynamics of the conditional correlations between time series of financial returns, but few studies have investigated the determinants of the correlation dynamics. A common opinion is that the market volatility is a major determinant of the correlations. We extend some models to capture explicitly the dependence of the correlations on the volatility of the market of interest. The models differ in the way by which the volatility influences the correlations, which can be transmitted through linear or nonlinear, and direct or indirect effects. They are applied to different data sets to verify the presence and possible regularity of the volatility impact on correlations.

Modeling the dependence of conditional correlations on volatility

This paper introduces a new framework for the dynamic modelling of univariate and multivariate point processes. The so-called latent factor intensity (LFI) model is based on the assumption that the intensity function consists of univariate or multivariate observation driven dynamic components and a univariate dynamic latent factor. In this sense, the model corresponds to a dynamic extension of a doubly stochastic Poisson process. We illustrate alternative parameterizations of the observation driven component based on autoregressive conditional intensity (ACI) specifications, as well as Hawkes types models. Based on simulation studies, it is shown that the proposed model provides a flexible tool to capture the joint dynamics of multivariate point processes. Since the latent component has to be integrated out, the model is estimated by simulated maximum likelihood based upon efficient importance sampling techniques. Applications of univariate and bivariate LFI models to transaction data extracted from the German XETRA trading system provide evidence for an improvement of the econometric specification when observable as well as unobservable dynamic components are taken into account.

Luc Bauwens

Papers

Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods

Asymmetric ACD models: introducing price information in ACD models with a two state transition model

General to specific modelling of exchange rate volatility: a forecast evaluation

Modeling the dependence of conditional correlations on volatility

Dynamic latent factor models for intensity processes