The limit distribution of conventional test statistics for predictability may depend on the degree of persistence of the predictors. Therefore, diverging results and conclusions may arise because of the different asymptotic theories adopted. Using differencing transformations, we introduce a new class of estimators and test statistics for predictive regression models with Gaussian limit distribution that is instead insensitive to the degree of persistence of the predictors. This desirable feature allows to construct Gaussian confidence intervals for the parameter of interest in stationary, nonstationary, and even locally explosive settings. Besides the limit distribution, we also study the efficiency and the rate of convergence of our new class of estimators. We show that the rate of convergence is $\sqrt n $ in stationary cases, while it can be arbitrarily close to n in nonstationary settings, still preserving the Gaussian limit distribution. Monte Carlo simulations confirm the high reliability and accuracy of our test statistics.

In a Gaussian, heterogeneous, cross-sectionally independent panel with incidental intercepts, Moon, Perron, and Phillips (2007, Journal of Econometrics 141, 416–459) present an asymptotic power envelope yielding an upper bound to the local asymptotic power of unit root tests. In case of homogeneous alternatives this envelope is known to be sharp, but this paper shows that it is not attainable for heterogeneous alternatives. Using limit experiment theory we derive a sharp power envelope. We also demonstrate that, among others, one of the likelihood ratio based tests in Moon et al. (2007, Journal of Econometrics 141, 416–459), a pooled generalized least squares (GLS) based test using the Breitung and Meyer (1994, Applied Economics 25, 353–361) device, and a new test based on the asymptotic structure of the model are all asymptotically UMP (Uniformly Most Powerful). Thus, perhaps somewhat surprisingly, pooled regression-based tests may yield optimal tests in case of heterogeneous alternatives. Although finite-sample powers are comparable, the new test is easy to implement and has superior size properties.

Many quantities of interest in economics and finance can be represented as partially observed functional data. Examples include structural business cycle estimation, implied volatility smile, the yield curve. Having embedded these quantities into continuous random curves, estimation of the covariance function is needed to extract factors, perform dimensionality reduction, and conduct inference on the factor scores. A series expansion for the covariance function is considered. Under summability restrictions on the absolute values of the coefficients in the series expansion, an estimation procedure that is resilient to overfitting is proposed. Under certain conditions, the rate of consistency for the resulting estimator achieves the minimax rate, allowing the observations to be weakly dependent. When the domain of the functional data is K(>1) dimensional, the absolute summability restriction of the coefficients avoids the so called curse of dimensionality. As an application, a Box–Pierce statistic to test independence of partially observed functional data is derived. Simulation results and an empirical investigation of the efficiency of the Eurodollar futures contracts on the Chicago Mercantile Exchange are included.

It is well known that the least squares estimator (LSE) of an AR(p) model with i.i.d. (independent and identically distributed) noises is n1/αL(n)-consistent when the tail index α of the noise is within (0,2) and is n1/2-consistent when α ≥ 2, where L(n) is a slowly varying function. When the noises are not i.i.d., however, the case is far from clear. This paper studies the LSE of AR(p) models with heavy-tailed G-GARCH(1,1) noises. When the tail index α of G-GARCH is within (0,2), it is shown that the LSE is not a consistent estimator of the parameters, but converges to a ratio of stable vectors. When α ε [2,4], it is shown that the LSE is n1–2/α-consistent if α ε (2,4), logn-consistent if α = 2, and n1/2 / logn-consistent if α = 4, and its limiting distribution is a functional of stable processes. Our results are significantly different from those with i.i.d. noises and should warn practitioners in economics and finance of the implications, including inconsistency, of heavy-tailed errors in the presence of conditional heterogeneity.

Volatility component models have received considerable attention recently, not only because of their ability to capture complex dynamics via a parsimonious parameter structure, but also because it is believed that they can handle well structural breaks or nonstationarities in asset price volatility. This paper revisits component volatility models from a statistical perspective and attempts to explore the stationarity of the underlying processes. There is a clear need for such an analysis, since any discussion about nonstationarity presumes we know when component models are stationary. As it turns out, this is not the case and the purpose of the paper is to rectify this. We also look into the sampling behavior of the maximum likelihood estimates of recently proposed volatility component models and establish their consistency and asymptotic normality.

This paper investigates a general semiparametric stochastic discount factor formulation that avoids functional form misspecification. A new semiparametric estimation procedure is proposed which combines orthogonality conditions and local linear fitting to give a semiparametric generalized estimating equation approach. Asymptotic properties of the estimators are established and we explore the empirical usefulness of the proposed approach to value-weighted stock returns.

In this paper, we develop tests for structural breaks of factor loadings in dynamic factor models. We focus on the joint null hypothesis that all factor loadings are constant over time. Because the number of factor loading parameters goes to infinity as the sample size grows, conventional tests cannot be used. Based on the fact that the presence of a structural change in factor loadings yields a structural change in second moments of factors obtained from the full sample principal component estimation, we reduce the infinite-dimensional problem into a finite-dimensional one and our statistic compares the pre- and postbreak subsample second moments of estimated factors. Our test is consistent under the alternative hypothesis in which a fraction of or all factor loadings have structural changes. The Monte Carlo results show that our test has good finite-sample size and power.

Data envelopment analysis (DEA) and free disposal hull (FDH) estimators are widely used to estimate efficiencies of production units. In applications, both efficiency scores for individual units as well as average efficiency scores are typically reported. While several bootstrap methods have been developed for making inference about the efficiencies of individual units, until now no methods have existed for making inference about mean efficiency levels. This paper shows that standard central limit theorems do not apply in the case of means of DEA or FDH efficiency scores due to the bias of the individual scores, which is of larger order than either the variance or covariances among individual scores. The main difficulty comes from the fact that such statistics depend on efficiency estimators evaluated at random points. Here, new central limit theorems are developed for means of DEA and FDH scores, and their efficacy for inference about mean efficiency levels is examined via Monte Carlo experiments.

Despite their theoretical advantages, Integrated Conditional Moment (ICM) specification tests are not commonly employed in the econometrics practice. An important reason is that the employed test statistics are nonpivotal, and so critical values are not readily available. This article proposes an omnibus test in the spirit of the ICM tests of Bierens and Ploberger (1997, Econometrica 65, 1129–1151) where the test statistic is based on the minimized value of a quadratic function of the residuals of time series econometric models. The proposed test falls under the category of overidentification restriction tests started by Sargan (1958, Econometrica 26, 393–415). The corresponding projection interpretation leads us to propose a straightforward wild bootstrap procedure that requires only linear regressions to estimate the critical values irrespective of the model functional form. Hence, contrary to other existing ICM tests, the critical values are easily calculated while the test preserves the admissibility property of ICM tests.

Long memory in stochastic volatility (LMSV) models are flexible tools for the modeling of persistent dynamic volatility, which is a typical characteristic of financial time series. However, their empirical applicability is limited because of the complications inherent in the estimation of the model and in the extraction of the volatility component. This paper proposes a new technique for volatility extraction, based on a semiparametric version of the optimal Wiener–Kolmogorov filter in the frequency domain. Its main characteristics are its simplicity and generality, because no parametric specification is needed for the volatility component and it remains valid for both stationary and nonstationary signals. The applicability of the proposal is shown in a Monte Carlo and in a daily series of returns from the Dow Jones Industrial index.

Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a stepwise manner that involves the determination of cointegrating rank and autoregressive lag order in a reduced rank vector autoregression followed by estimation and inference. This paper proposes an automated approach to cointegrated system modeling that uses adaptive shrinkage techniques to estimate vector error correction models with unknown cointegrating rank structure and unknown transient lag dynamic order. These methods enable simultaneous order estimation of the cointegrating rank and autoregressive order in conjunction with oracle-like efficient estimation of the cointegrating matrix and transient dynamics. As such they offer considerable advantages to the practitioner as an automated approach to the estimation of cointegrated systems. The paper develops the new methods, derives their limit theory, discusses implementation, reports simulations, and presents an empirical illustration with macroeconomic aggregates.

In this paper, we derive the asymptotic properties of the system generalized method of moments (GMM) estimator in dynamic panel data models with individual and time effects when both N and T, the dimensions of cross-section and time series, are large. Specifically, we show that the two-step system GMM estimator is consistent when a suboptimal weighting matrix where off-diagonal blocks are set to zero is used. Such consistency results theoretically support the use of the system GMM estimator in large N and T contexts even though it was originally developed for large N and small T panels. Simulation results indicate that the large N and large T asymptotic results approximate the finite sample behavior reasonably well unless persistency of data is strong and/or the variance ratio of individual effects to the disturbances is large.