Offering a unifying theoretical perspective not readily available in any other text, this innovative guide to econometrics uses simple geometrical arguments to develop students' intuitive understanding of basic and advanced topics, emphasizing throughout the practical applications of modern theory and nonlinear techniques of estimation. One theme of the text is the use of artificial regressions for estimation, reference, and specification testing of nonlinear models, including diagnostic tests for parameter constancy, serial correlation, heteroscedasticity, and other types of mis-specification. Explaining how estimates can be obtained and tests can be carried out, the authors go beyond a mere algebraic description to one that can be easily translated into the commands of a standard econometric software package. Covering an unprecedented range of problems with a consistent emphasis on those that arise in applied work, this accessible and coherent guide to the most vital topics in econometrics today is indispensable for advanced students of econometrics and students of statistics interested in regression and related topics. It will also suit practising econometricians who want to update their skills. Flexibly designed to accommodate a variety of course levels, it offers both complete coverage of the basic material and separate chapters on areas of specialized interest.

Estimation and Inference in Econometrics

In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

Non-Gaussian processes of Ornstein–Uhlenbeck (OU) type offer the possibility of capturing important distributional deviations from Gaussianity and for flexible modelling of dependence structures. This paper develops this potential, drawing on and extending powerful results from probability theory for applications in statistical analysis. Their power is illustrated by a sustained application of OU processes within the context of finance and econometrics. We construct continuous time stochastic volatility models for financial assets where the volatility processes are superpositions of positive OU processes, and we study these models in relation to financial data and theory.

Non-Gaussian Ornstein–Uhlenbeck-based models and some of their uses in financial economics

Matrix Differential Calculus with Applications in Statistics and Econometrics

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

Identification, estimation and testing of conditionally heteroskedastic factor models

We provide numerically reliable analytical expressions for the score, Hessian, and information matrix of conditionally heteroscedastic dynamic regression models when the conditional distribution is multivariatet. We also derive one-sided and two-sided Lagrange multiplier tests for multivariate normality versus multivariate t based on the first two moments of the squared norm of the standardized innovations evaluated at the Gaussian pseudo-maximum likelihood estimators of the conditional mean and variance parameters. Finally, we illustrate our techniques through both Monte Carlo simulations and an empirical application to 26 U.K. sectorial stock returns that confirms that their conditional distribution has fat tails.

Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models With Student t Innovations

In the context of univariate GARCH models we show how analytic first and second derivatives of the log-likelihood can be successfully employed for estimation purposes. Maximum likelihood GARCH estimation usually relies on the numerical approximation to the log-likelihood derivatives, on the grounds that an exact analytic differentiation is much too burdensome. We argue that this is not the case and that the computational benefit of using the analytic derivatives (first and second) may be substantial. Furthermore, we make a comparison of various gradient algorithms that are used for the maximization of the GARCH Gaussian likelihood. We suggest the implementation of a globally efficient computation algorithm that is obtained by suitably combining the use of the estimated information matrix with that of the exact Hessian during the maximization process. As this would appear a straightforward extension, we then study the finite sample performance of the exact Hessian and its approximations (that is, the estimated information, outer products and misspecification robust matrices) in inference.

Analytic derivatives and the computation of GARCH estimates

We investigate several important inference issues for factor models with dynamic heteroskedasticity in the common factors. First, we show that such models are identified if we take into account the time-variation in the variances of the factors. Our results also apply to dynamic versions of the APT, dynamic factor models, and vector autoregressions. Secondly, we propose a consistent two-step estimation procedure which does not rely on knowledge of any factor estimates, and explain how to compute correct standard errors. Thirdly, we develop a simple preliminary LM test for the presence of ARCH effects in the common factors. Finally, we conduct a Monte Carlo analysis of the finite sample properties of the proposed estimators and hypothesis tests.

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Identification, Estimation And Testing Of Conditionally Heteroskedastic Factor Models

GARCH models are commonly used as latent processes in econometrics, financial economics and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.

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Gabriele Fiorentini

Papers

Identification, estimation and testing of conditionally heteroskedastic factor models

Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models With Student t Innovations

Analytic derivatives and the computation of GARCH estimates

Identification, Estimation And Testing Of Conditionally Heteroskedastic Factor Models

Likelihood-Based Estimation of Latent Generalized ARCH Structures