Enrique Sentana

Quadratic Arch Models

We introduce a new model for time-varying conditional variances as the most general quadratic version possible within the ARCH class. Hence, it encompasses all the existing restricted quadratic variance functions. Its properties are very similar to those of GARCH models, but avoids some of their criticisms. In univariate applications to daily U.S. and monthly U.K. stock market returns, QARCH adequately represents volatility and risk premia. QARCH is easy to incorporate in multivariate models to capture dynamic asymmetries that GARCH rules out. Such asymmetries are found in an empirical application of a conditional factor model to 26 U.K. sectorial stock returns.

Identification, estimation and testing of conditionally heteroskedastic factor models

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.

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

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.

Marginalization and contemporaneous aggregation in multivariate GARCH processes

Abstract We first of all show that contemporaneous aggregation of independent univariate GARCH processes yields a weak GARCH process as introduced by Drost and Nijman (1993). Subsequently we analyze the dependence of the parameters in the aggregate on the parameters in the underlying models and show that the variance parameters after aggregation depend on the underlying variance and kurtosis parameters. Then we generalize the results by showing that a linear combination of variables generated by a multivariate GARCH process will also be weak GARCH. Finally we derive the marginal (weak GARCH) processes implied by several multivariate GARCH processes.

The econometrics of mean‐variance efficiency tests: a survey

This paper provides a comprehensive survey of the econometrics of mean-variance efficiency tests. Starting with the classic F-test of Gibbons et al. (1989) and its generalized method of moments version, I analyse the effects of the number of assets and portfolio composition on test power. I then discuss asymptotically equivalent tests based on portfolio weights, and study the trade-offs between efficiency and robustness of using parametric and semi-parametric likelihood procedures that assume either elliptical innovations or elliptical returns. After reviewing finite sample tests, I conclude with a discussion of mean-variance-skewness efficiency and spanning tests, and other interesting extensions. Copyright The Author(s). Journal compilation Royal Economic Society 2009

Parametric Properties of Semi-Nonparametric Distributions, with Applications to Option Valuation

We derive the statistical properties of the SNP densities of Gallant and Nychka (1987). We show that these densities, which are always positive, are more general than the truncated Gram-Charlier expansions of Jondeau and Rochinger (2001), who impose parameter restrictions to ensure positivity. We also use the SNP densities for option valuation. We relate real and risk-neutral measures, obtain closed-form prices for European options, and study the ?Greeks?. We show that SNP densities generate wider option price ranges than the truncated expansions. In an empirical application to S&P 500 index options, we find that the SNP model beats the standard and Practitioner?s Black-Scholes formulas, and truncated expansions.

Distributional Tests in Multivariate Dynamic Models with Normal and Student T Innovations

We derive Lagrange Multiplier and Likelihood Ratio specifi cation tests for the null hypotheses of multivariate normal and Student t innovations using the Generalised Hyperbolic distribution as our alternative hypothesis. We decompose the corresponding Lagrange Multiplier-type tests into skewness and kurtosis components, from which we obtain more powerful one-sided Kuhn-Tucker versions that are equivalent to the Likelihood Ratio test, whose asymptotic distribution we provide. We conduct detailed Monte Carlo exercises to study our proposed tests in finite samples. Finally, we present an empirical application to ten US sectoral stock returns, which indicates that their conditional distribution is mildly asymmetric and strongly leptokurtic.

A Unifying Approach to the Empirical Evaluation of Asset Pricing Models

Two main approaches are commonly used to empirically evaluate linear factor pricing models: regression and SDF methods, with centred and uncentred versions of the latter. We show that unlike standard two-step or iterated GMM procedures, single-step estimators such as continuously updated GMM yield numerically identical values for prices of risk, pricing errors, Jensens alphas and overidentifying restrictions tests irrespective of the model validity. Therefore, there is arguably a single approach regardless of the factors being traded or not, or the use of excess or gross returns. We illustrate our results by revisiting Lustig and Verdelhans (2007) empirical analysis of currency returns.

On the validity of the Jarque-Bera normality test in conditionally heteroskedastic dynamic regression models

We show that the Jarque-Bera test, originally devised for constant conditional variance models with no functional dependence between conditional mean and variance parameters, can be safely applied to a broad class of GARCH-M models, but not to all.

Spanning Tests in Return and Stochastic Discount Factor Mean Variance Frontiers: A Unifying Approach

We propose new approaches to test for spanning in the return and stochastic discount factor mean-variance frontiers, which assess if either the centred or uncentred mean and cost representing portfolios are shared by the initial and extended sets of assets. We show that our proposed tests are asymptotically equivalent to the existing spanning tests under the null and sequences of local alternatives, and analyse their asymptotic relative e.ciency. We also extend the theory of optimal GMM inference to deal with the singularities that arise in some spanning tests. Finally, we include an empirical application to money markets in Europe.