This paper derives sufficient conditions for global identification innonlinear models characterized by a finite number of unconditional momentrestrictions. The main contribution of this paper is to provide a set ofassumptions that are alternative to those of Gale-Nikaidô-Fisher-Rothenberg,and which when satisfied guarantee that the moment conditions globallyidentify the parameters of interest.

Models with single-index structures are among the many existing popularsemiparametric approaches for either the conditional mean or the conditionalvariance. This paper focuses on a single-index model for the conditionalquantile. We propose an adaptive estimation procedure and an iterativealgorithm which, under mild regularity conditions, is proved to convergewith probability 1. The resulted estimator of the single-index parametricvector is root-n consistent, asymptotically normal, andbased on simulation study, is more efficient than the average derivativemethod in Chaudhuri, Doksum, and Samarov (1997, Annals of Statistics 19, 760–777). Theestimator of the link function converges at the usual rate for nonparametricestimation of a univariate function. As an empirical study, we apply thesingle-index quantile regression model to Boston housing data. Byconsidering different levels of quantile, we explore how the covariates, ofeither social or environmental nature, could have different effects onindividuals targeting the low, the median, and the high end of the housingmarket.

This paper considers the problem of estimating expected values of functionsthat are inversely weighted by an unknown density using the k-nearest neighbor (k-NN) method. Itestablishes the -consistency and the asymptotic normality of anestimator that allows for strictly stationary time-series data. Theconsistency of the Bartlett estimator of the derived asymptotic variance isalso established. The proposed estimator is also shown to be asymptoticallysemiparametric efficient in the independent random sampling scheme. MonteCarlo experiments show that the proposed estimator performs well in finitesample applications.

Despite substantial criticism, variants of the capital asset pricing model(CAPM) remain to this day the primary statistical tools for portfoliomanagers to assess the performance of financial assets. In the CAPM, therisk of an asset is expressed through its correlation with the market,widely known as the beta. There is now a general consensus among economiststhat these portfolio betas are time-varying and that, consequently, anyappropriate analysis has to take this variability into account. Recentadvances in data acquisition and processing techniques have led to anincreased research output concerning high-frequency models. Within thisframework, we introduce here a modified functional CAPM and sequentialmonitoring procedures to test for the constancy of the portfolio betas. Asour main results we derive the large-sample properties of these monitoringprocedures. In a simulation study and an application to S&P 100 data weshow that our method performs well in finite samples.

The least absolute shrinkage and selection operator (LASSO) is a widely usedstatistical methodology for simultaneous estimation and variable selection.It is a shrinkage estimation method that allows one to select parsimoniousmodels. In other words, this method estimates the redundant parameters aszero in the large samples and reduces variance of estimates. In recentyears, many authors analyzed this technique from a theoretical and appliedpoint of view. We introduce and study the adaptive LASSO problem fordiscretely observed multivariate diffusion processes. We prove oracleproperties and also derive the asymptotic distribution of the LASSOestimator. This is a nontrivial extension of previous results by Wang andLeng (2007, Journal of the American Statistical Association, 102(479), 1039–1048) on LASSOestimation because of different rates of convergence of the estimators inthe drift and diffusion coefficients. We perform simulations and real dataanalysis to provide some evidence on the applicability of this method.

This paper proposes a nonparametric test of Granger causality in quantile.Zheng (1998, Econometric Theory 14, 123–138) studied the idea to reduce the problem oftesting a quantile restriction to a problem of testing a particular type ofmean restriction in independent data. We extend Zheng’s approach to the caseof dependent data, particularly to the test of Granger causality inquantile. Combining the results of Zheng (1998) and Fan and Li (1999, Journal of Nonparametric Statistics 10,245–271), we establish the asymptotic normal distribution of the teststatistic under a β-mixing process. The test is consistentagainst all fixed alternatives and detects local alternatives approachingthe null at proper rates. Simulations are carried out to illustrate thebehavior of the test under the null and also the power of the test underplausible alternatives. An economic application considers the causalrelations between the crude oil price, the USD/GBP exchange rate, and thegold price in the gold market.

For many time series in empirical macro and finance, it is assumed that thelogarithm of the series is a unit root process. Since we may want to assumea stable growth rate for the macroeconomics time series, it seems natural topotentially model such a series as a unit root process with drift. Thisassumption implies that the level of such a time series is the exponentialof a unit root process with drift and therefore, it is of substantialinterest to investigate analytically the behavior of the exponential of aunit root process with drift. This paper shows that the sum of theexponential of a random walk with drift converges in distribution, afterrescaling by the exponential of the maximum value of the random walkprocess. A similar result was established in earlier work for unit rootprocesses without drift. The results derived here suggest the conjecturethat also in the case when the Dickey-Fuller test or the KPSS statistic isapplied to the exponential of a unit root process with drift, these testswill asymptotically indicate stationarity.

This note demonstrates that the conditions of Kotlarski’s (1967, Pacific Journal of Mathematics 20(1), 69–76) lemma can be substantially relaxed. Inparticular, the condition that the characteristic functions of M, U1, and U2 are nonvanishing can be replaced with muchweaker conditions: The characteristic function of U1 can be allowed to have real zeros, as longas the derivative of its characteristic function at those points is not alsozero; that of U2 can have an isolated number ofzeros; and that of M need satisfy no restrictions on itszeros. We also show that Kotlarski’s lemma holds when the tails of U1 are no thicker than exponential,regardless of the zeros of the characteristic functions of U1, U2, or M.