When the covariance between the risk factors of asset prices is due to both Brownian and jump components, the realized covariation (RC) approaches the sum of the integrated covariation (IC) with the sum of the co-jumps, as the observation frequency increases to infinity, in a finite and fixed time horizon. In this paper the two components are consistently separately estimated within a semimartingale framework with possibly infinite activity jumps. The threshold (or truncated) estimator is used, which substantially excludes from RC all terms containing jumps. Unlike in Jacod (2007, Universite de Paris-6) and Jacod (2008, Stochastic Processes and Their Applications 118, 517–559), no assumptions on the volatilities’ dynamics are required. In the presence of only finite activity jumps: 1) central limit theorems (CLTs) for and for further measures of dependence between the two Brownian parts are obtained; the estimation error asymptotic variance is shown to be smaller than for the alternative estimators of IC in the literature; 2) by also selecting the observations as in Hayashi and Yoshida (2005, Bernoulli 11, 359–379), robustness to nonsynchronous data is obtained. The proposed estimators are shown to have good finite sample performances in Monte Carlo simulations even with an observation frequency low enough to make microstructure noises’ impact on data negligible.

This paper considers the factor model Xt = ΛFt + et. Assuming a normal distribution for the idiosyncratic error et conditional on the factors {Ft}, conditional maximum likelihood estimators of the factor and factor-loading spaces are derived. These estimators are called generalized principal component estimators (GPCEs) without the normality assumption. This paper derives asymptotic distributions of the GPCEs of the factor and factor-loading spaces. It is shown that variance of the GPCE of the common component is smaller than that of the principal component estimator studied in Bai (2003, Econometrica 71, 135–172). The approximate variance of the forecasting error using the GPCE-based factor estimates is derived and shown to be smaller than that based on the principal component estimator. The feasible GPCE (FGPCE) of the factor space is shown to be asymptotically equivalent to the GPCE. The GPCE and FGPCE are shown to be more efficient than the principal component estimator in finite samples.

This paper studies the problem of estimating the set of finite-dimensional parameter values defined by a finite number of moment inequality or equality conditions and gives conditions under which the estimator defined by the set of parameter values that satisfy the estimated versions of these conditions is consistent in Hausdorff metric. This paper also suggests extremum estimators that with probability approaching 1 agree with the set consisting of parameter values that satisfy the sample versions of the moment conditions. In particular, it is shown that the set of minimizers of the sample generalized method of moments (GMM) objective function is consistent for the set of minimizers of the population GMM objective function in Hausdorff metric.

In this paper we propose consistent integrated conditional moment tests for the validity of parametric conditional distribution models, based on the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment test is proposed. As an empirical application we test the validity of a few common health economic count data models.

In this paper we construct a statistic to test a specific form of the conditional density function. The main point of this work is to consider a functional explanatory variable, and the statistic is constructed following recent advances in nonparametric functional data analysis. The asymptotic behavior of the test statistic is studied under both the null hypothesis and some local alternative hypothesis. Then, the finite sample behavior of the method is studied through simulated examples. This paper is one of the first in the setting of nonparametric specification tests when functional data are involved.

In the linear instrumental variables model with possibly weak instruments we derive the asymptotic size of testing procedures when instruments locally violate the exogeneity assumption. We study the tests by Anderson and Rubin (1949, The Annals of Mathematical Statistics 20, 46–63), Moreira (2003, Econometrica 71, 1027–1048), and Kleibergen (2005, Econometrica 73, 1103–1123) and their generalized empirical likelihood versions. These tests have asymptotic size equal to nominal size when the instruments are exogenous but are size distorted otherwise. While in just-identified models all the tests that we consider are equally size-distorted asymptotically, the Anderson-Rubin type tests are less size-distorted than the tests of Moreira (2003) and Kleibergen in over-identified situations. On the other hand, we also show that there are parameter sequences under which the former test asymptotically overrejects more frequently. Given that strict exogeneity of instruments is often a questionable assumption, our findings should be important to applied researchers who are concerned about the degree of size distortion of their inference procedure. We suggest robustness of asymptotic size under local model violations as a new alternative measure to choose among competing testing procedures. We also investigate the subsampling and hybrid tests introduced in Andrews and Guggenberger (2010a, Journal of Econometrics 158, 285–305) and show that they do not offer any improvement in terms of size-distortion reduction over the Anderson-Rubin type tests.

Three important issues surround testing for a unit root in practice: uncertainty as to whether or not a linear deterministic trend is present in the data; uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not, and the possible presence of nonstationary volatility in the data. Assuming homoskedasticity, Harvey, Leybourne, and Taylor (2011, Journal of Econometrics, forthcoming) propose decision rules based on a four-way union of rejections of quasi-differenced (QD) and ordinary least squares (OLS) detrended tests, both with and without a linear trend, to deal with the first two problems. In this paper we first discuss, again under homoskedasticity, how these union tests may be validly bootstrapped using the sieve bootstrap principle combined with either the independent and identically distributed (i.i.d.) or wild bootstrap resampling schemes. This serves to highlight the complications that arise when attempting to bootstrap the union tests. We then demonstrate that in the presence of nonstationary volatility the union test statistics have limit distributions that depend on the form of the volatility process, making tests based on the standard asymptotic critical values or, indeed, the i.i.d. bootstrap principle invalid. We show that wild bootstrap union tests are, however, asymptotically valid in the presence of nonstationary volatility. The wild bootstrap union tests therefore allow for a joint treatment of all three of the aforementioned issues in practice.

Consistency, asymptotic normality, and efficiency of the maximum likelihood estimator for stationary Gaussian time series were shown to hold in the short memory case by Hannan (1973, Journal of Applied Probability 10, 130–145) and in the long memory case by Dahlhaus (1989, Annals of Statistics 34, 1045–1047). In this paper we extend these results to the entire stationarity region, including the case of antipersistence and noninvertibility.

This paper considers the problem of variance estimation for the sample mean in the context of long memory and negative memory time series dynamics, adopting the fixed-bandwidth approach now popular in the econometrics literature. The distribution theory generalizes the short memory results of Kiefer and Vogelsang (2005, Econometric Theory 21, 1130–1164). In particular, our results highlight the dependence on the kernel (we include flat-top kernels), whether or not the kernel is nonzero at the boundary, and, most important, whether or not the process is short memory. Simulation studies support the importance of accounting for memory in the construction of confidence intervals for the mean.