Tests of Conditional Predictive Ability

We argue that the current framework for predictive ability testing (e.g., West, 1996) is not necessarily useful for real-time forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for out-of-sample comparison of predictive ability which delivers more practically relevant conclusions. Our approach is based on inference about conditional expectations of forecasts and forecast errors rather than the unconditional expectations that are the focus of the existing literature. Compared to previous approaches, our tests are valid under more general data assumptions (heterogeneity rather than stationarity) and estimation methods, and they can handle comparison of both nested and non-nested models, which is not currently possible.Forecast Evaluation, Asymptotic Inference, Parameter-reduction Methods

Maximum Likelihood and the Bootstrap for Nonlinear Dynamic Models

We provide a unified framework for analyzing bootstrapped extremum estimators of nonlinear dynamic models for heterogeneous dependent stochastic processes. We apply our results to the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) and prove the first order asymptotic validity of the bootstrap approximation to the true distribution of quasi-maximum likelihood estimators. We also consider bootstrap testing. In particular, we prove the first order asymptotic validity of the bootstrap distribution of suitable bootstrap analogs of Wald and Lagrange Multiplier statistics for testing hypotheses. Nous proposons une approche unifiée pour analyser la méthode de bootstrap appliquée aux estimateurs de pseudo-maximum de vraisemblance dans le contexte de modèles non linéaires dynamiques où les données sont caractérisées par une dépendance d'époque proche. Nous appliquons nos résultats à la méthode de bootstrap de blocs mouvants de Künsch (1989) et Liu et Singh (1992) et nous démontrons la validité asymptotique de premier ordre de l'approximation du bootstrap à la distribution asymptotique de l'estimateur de pseudo-maximum de vraisemblance. Nous considérons aussi l'application du bootstrap à la réalisation de tests d'hypothèses. En particulier, nous démontrons la validité asymptotique des versions de bootstrap des tests de Wald et du multiplicateur de Lagrange.Block bootstrap, quasi-maximum likelihood estimator, nonlinear dynamic model, near epoch dependence, Wald test, Bootstrap en bloc, pseudo-maximum de vraisemblance, modèle non linéaire dynamique, dépendance d'époque proche, test de Wald

The Bootstrap of the Mean for Dependent Heterogeneous Arrays

Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. A0501n purpose of this paper is thus to establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. The results apply to the moving blocks bootstrap of Künsch (1989) and Liu and Singh (1992) as well as to the stationary bootstrap of Politis and Romano (1994). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context. Actuellement, les conditions assurant la validité des méthodes de bootstrap pour la moyenne d'échantillon des (possiblement hétérogènes) fonctions de dépendance d'époque proche (DEP) des processus de mixage sont inconnues. Ainsi, un des objectifs principaux de cet article est d'établir la validité du bootstrap dans ce contexte, en élargissant l'applicabilité des méthodes de bootstrap à une classe de processus largement adéquats pour les applications en économie et en finance. Les résultats se rapportent au bootstrap de blocs mouvants de Künsch (1989) et Liu et Singh (1992), de même qu'au bootstrap stationnaire de Politis et Romano (1994). Plus particulièrement, nous démontrons que la consistance de l'estimateur de variance du bootstrap pour la moyenne d'échantillon résiste à l'hétéroscédasticité et à la dépendance de forme inconnue. La validité asymptotique de premier ordre de l'approximation du bootstrap à la distribution actuelle de la moyenne d'échantillon est également démontrée dans ce contexte DEP hétérogène.Block bootstrap, near epoch dependence, sample mean, Bootstrap en bloc, dépendance d'époque proche, moyenne d'échantillon

Granger Causality, Exogeneity, Cointegration, and Economic Policy Analysis

Policy analysis has long been a main interest of Clive Granger's. Here, we present a framework for economic policy analysis that provides a novel integration of several fundamental concepts at the heart of Granger's contributions to time-series analysis. We work with a dynamic structural system analyzed by White and Lu (2010) with well-defined causal meaning; under suitable conditional exogeneity restrictions, Granger causality coincides with this structural notion. The system contains target and control subsystems, with possibly integrated or cointegrated behavior. We ensure the invariance of the target subsystem to policy interventions using an explicitly causal partial equilibrium recursivity condition. Policy effectiveness is ensured by another explicit causality condition. These properties only involve the data generating process; models play a subsidiary role. Our framework thus complements that of Ericsson, Hendry, and Mizon (1998) (EHM) by providing conditions for policy analysis alternative to weak, strong, and super-exogeneity. This makes possible policy analysis for systems that may fail EHM's conditions. It also facilitates analysis of the cointegrating properties of systems subject to policymaker control. We discuss a variety of practical procedures useful for analyzing such systems and illustrate with an application to a simple model of the U.S. macroeconomy.

Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties

We examine several modified versions of the heteroskedasticity-consistent covariance matrix estimator of Hinkley and White. On the basis of sampling experiments which compare the performance of quasi t statistics, we find that one estimator, based on the jackknife, performs better in small samples than the rest. We also examine finite-sample properties using modified critical values based on Edgeworth approximations, as proposed by Rothenberg. In addition, we compare the power of several tests for heteroskedasticity and find that it may be wise to employ the jackknife heteroskedasticity-consistent covariance matrix even in the absence of detected heteroskedasticity.Jackknife, Heteroskedasticity, HCCME, Edgeworth approximations

Estimating average marginal effects in nonseparable structural systems

We provide nonparametric estimators of derivative ratio-based average marginal effects of an endogenous cause, X, on a response of interest, Y , for a system of recursive structural equations. The system need not exhibit linearity, separability, or monotonicity. Our estimators are local indirect least squares estimators analogous to those of Heckman and Vytlacil (1999, 2001) who treat a latent index model involving a binary X. We treat the traditional case of an observed exogenous instrument (OXI)and the case where one observes error-laden proxies for an unobserved exogenous instrument (PXI). For PXI, we develop and apply new results for estimating densities and expectations conditional on mismeasured variables. For both OXI and PXI, we use infnite order flat-top kernels to obtain uniformly convergent and asymptotically normal nonparametric estimators of instrument-conditioned effects, as well as root-n consistent and asymptotically normal estimators of average effects.

Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR

Engle and Manganelli (2004) propose CAViaR, a class of models suitable for estimating conditional quantiles in dynamic settings. Engle and Manganelli apply their approach to the estimation of Value at Risk, but this is only one of many possible applications. Here we extend CAViaR models to permit joint modeling of multiple quantiles, Multi-Quantile (MQ) CAViaR. We apply our new methods to estimate measures of conditional skewness and kurtosis defined in terms of conditional quantiles, analogous to the unconditional quantile-based measures of skewness and kurtosis studied by Kim and White (2004). We investigate the performance of our methods by simulation, and we apply MQ-CAViaR to study conditional skewness and kurtosis of S&P 500 daily returns. JEL Classification: C13, C32Asset returns, CAViaR, conditional quantiles, Dynamic quantiles, Kurtosis, Skewness

The Bootstrap of Mean for Dependent Heterogeneous Arrays

Presently, conditions ensuring the validity of bootstrap methods for the sample mean of (possibly heterogeneous) near epoch dependent (NED) functions of mixing processes are unknown. Here we establish the validity of the bootstrap in this context, extending the applicability of bootstrap methods to a class of processes broadly relevant for applications in economics and finance. Our results apply to two block bootstrap methods: the moving blocks bootstrap of Künsch ( 989) and Liu and Singh ( 992), and the stationary bootstrap of Politis and Romano ( 994). In particular, the consistency of the bootstrap variance estimator for the sample mean is shown to be robust against heteroskedasticity and dependence of unknown form. The first order asymptotic validity of the bootstrap approximation to the actual distribution of the sample mean is also established in this heterogeneous NED context.Actuellement, les conditions assurant la validité des méthodes de bootstrap pour la moyenne d'échantillon des fonctions (possiblement hétérogènes) de dépendance d'époque proche (DEP) des processus de mixage sont inconnues. Un des objectifs principaux de cet article est d'établir la validité du bootstrap dans ce contexte, élargissant ainsi l'applicabilité des méthodes de bootstrap à une classe de processus largement adéquats pour les applications en économie et en finance. Les résultats s'appliquent au bootstrap de blocs mouvants de Künsch ( 989) et Liu et Singh ( 992), de même qu'au bootstrap stationnaire de Politis et Romano ( 994). Plus particulièrement, nous démontrons que la convergence de l'estimateur de variance du bootstrap pour la moyenne d'échantillon est robuste à l'hétéroscédasticité et à la dépendance de forme inconnue. La validité asymptotique de premier ordre de l'approximation du bootstrap à la distribution asymptotique de la moyenne d'échantillon est également démontrée dans ce contexte DEP hétérogène

Mixtures of t-distributions for Finance and Forecasting

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. A feature that makes this family particularly desirable for econometric applications is that it possesses closed-form expressions for its anti-derivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we use a scaled and shifted t-distribution to produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-of-sample, than density forecasts obtained using normal or standard t-distributions. In the second application, we replicate the option-pricing exercise of Abadir and Rockinger (2003) using a mixture of scaled and shifted t-distributions and obtain comparably good results, while gaining analytical tractability.ARMA-GARCH models, neural networks, nonparametric density estimation, forecast accuracy, option pricing, risk neutral density