Efficient estimation in dynamic conditional quantile models

In this paper we consider the problem of semiparametric efficient estimation in conditional quantile models with time series data. We construct an M-estimator which achieves the semiparametric efficiency bound recently derived by Komunjer and Vuong (forthcoming). Our efficient M-estimator is obtained by minimizing an objective function which depends on a nonparametric estimator of the conditional distribution of the variable of interest rather than its density. The estimator is new and not yet seen in the literature. We illustrate its performance through a Monte Carlo experiment.     

Adaptive estimation of autoregressive models with time-varying variances

Stable autoregressive models are considered with martingale differences errors scaled by an unknown nonparametric time-varying function generating heterogeneity. An important special case involves structural change in the error variance, but in most practical cases the pattern of variance change over time is unknown and may involve shifts at unknown discrete points in time, continuous evolution or combinations of the two. This paper develops kernel-based estimators of the residual variances and associated adaptive least squares (ALS) estimators of the autoregressive coefficients. Simulations show that efficiency gains are achieved by the adaptive procedure.     

Semiparametric efficient adaptive estimation of asymmetric GARCH models

In this paper we derive a semiparametric efficient adaptive estimator of an asymmetric GARCH model. Applying some general results from Drost et al. [1997. The Annals of Statistics 25, 786–818], we first estimate the unknown density function of the disturbances by kernel methods, then apply a one-step Newton–Raphson method to obtain a more efficient estimator than the quasi-maximum likelihood estimator. The proposed semiparametric estimator is adaptive for parameters appearing in the conditional standard deviation model with respect to the unknown distribution of the disturbances.     

Distribution-free tests for time series models specification

We consider a class of time series specification tests based on quadratic forms of weighted sums of residuals autocorrelations. Asymptotically distribution-free tests in the presence of estimated parameters are obtained by suitably transforming the weights, which can be optimally chosen to maximize the power function when testing in the direction of local alternatives. We discuss in detail an asymptotically optimal distribution-free alternative to the popular Box–Pierce when testing in the direction of AR or MA alternatives. The performance of the test with small samples is studied by means of a Monte Carlo experiment.     

Nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters

We consider nonparametric/semiparametric estimation and testing of econometric models with data dependent smoothing parameters. Most of the existing works on asymptotic distributions of a nonparametric/semiparametric estimator or a test statistic are based on some deterministic smoothing parameters, while in practice it is important to use data-driven methods to select the smoothing parameters. In this paper we give a simple sufficient condition that can be used to establish the first order asymptotic equivalence of a nonparametric estimator or a test statistic with stochastic smoothing parameters to those using deterministic smoothing parameters. We also allow for general weakly dependent data.     

Estimation of semiparametric locally stationary diffusion models

This paper proposes a class of locally stationary diffusion processes. The model has a time varying but locally linear drift and a volatility coefficient that is allowed to vary over time and space. The model is semiparametric because we allow these functions to be unknown and the innovation process is parametrically specified, indeed completely known. We propose estimators of all the unknown quantities based on long span data. Our estimation method makes use of the property of local stationarity. We establish asymptotic theory for the proposed estimators as the time span increases, so we do not rely on infill asymptotics. We apply this method to interest rate data to illustrate the validity of our model. Finally, we present a simulation study to provide the finite-sample performance of the proposed estimators.     

Local polynomial estimation of nonparametric simultaneous equations models

We define a new procedure for consistent estimation of nonparametric simultaneous equations models under the conditional mean independence restriction of Newey et al. [1999. Nonparametric estimation of triangular simultaneous equation models. Econometrica 67, 565–603]. It is based upon local polynomial regression and marginal integration techniques. We establish the asymptotic distribution of our estimator under weak data dependence conditions. Simulation evidence suggests that our estimator may significantly outperform the estimators of Pinkse [2000. Nonparametric two-step regression estimation when regressors and errors are dependent. Canadian Journal of Statistics 28, 289–300] and Newey and Powell [2003. Instrumental variable estimation of nonparametric models. Econometrica 71, 1565–1578].     

Semi-nonparametric estimation and misspecification testing of diffusion models

Novel transition-based misspecification tests of semiparametric and fully parametric univariate diffusion models based on the estimators developed in [Kristensen, D., 2010. Pseudo-maximum likelihood estimation in two classes of semiparametric diffusion models. Journal of Econometrics 156, 239-259] are proposed. It is demonstrated that transition-based tests in general lack power in detecting certain departures from the null since they integrate out local features of the drift and volatility. As a solution to this, tests that directly compare drift and volatility estimators under the relevant null and alternative are also developed which exhibit better power against local alternatives.     

Nonparametric transformation to white noise

We consider a semiparametric distributed lag model in which the “news impact curve” m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with serially correlated errors. We propose an estimator of the news impact curve based on a dynamic transformation that produces white noise errors. This yields an estimating equation for m that is a type two linear integral equation. We investigate both the stationary case and the case where the error has a unit root. In the stationary case we establish the pointwise asymptotic normality. In the special case of a nonparametric regression subject to time series errors our estimator achieves efficiency improvements over the usual estimators, see Xiao et al. [2003. More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98, 980–992]. In the unit root case our procedure is consistent and asymptotically normal unlike the standard regression smoother. We also present the distribution theory for the parameter estimates, which is nonstandard in the unit root case. We also investigate its finite sample performance through simulation experiments.     

Nonparametric estimation of conditional VaR and expected shortfall

This paper considers a new nonparametric estimation of conditional value-at-risk and expected shortfall functions. Conditional value-at-risk is estimated by inverting the weighted double kernel local linear estimate of the conditional distribution function. The nonparametric estimator of conditional expected shortfall is constructed by a plugging-in method. Both the asymptotic normality and consistency of the proposed nonparametric estimators are established at both boundary and interior points for time series data. We show that the weighted double kernel local linear conditional distribution estimator has the advantages of always being a distribution, continuous, and differentiable, besides the good properties from both the double kernel local linear and weighted Nadaraya–Watson estimators. Moreover, an ad hoc data-driven fashion bandwidth selection method is proposed, based on the nonparametric version of the Akaike information criterion. Finally, an empirical study is carried out to illustrate the finite sample performance of the proposed estimators.     

Nonparametric estimation of distributional policy effects

This paper proposes a fully nonparametric procedure to evaluate the effect of a counterfactual change in the distribution of some covariates on the unconditional distribution of an outcome variable of interest. In contrast to other methods, we do not restrict attention to the effect on the mean. In particular, our method can be used to conduct inference on the change of the distribution function as a whole, its moments and quantiles, inequality measures such as the Lorenz curve or Gini coefficient, and to test for stochastic dominance. The practical applicability of our procedure is illustrated via a simulation study and an empirical example.     

Nonparametric testing for smooth structural changes in panel data models

Detecting and modeling structural changes in time series models have attracted great attention. However, relatively little effort has been paid to the testing of structural changes in panel data models despite their increasing importance in economics and finance. In this paper, we propose a new approach to testing structural changes in panel data models. Unlike the bulk of the literature on structural changes, which focuses on detection of abrupt structural changes, we consider smooth structural changes for which model parameters are unknown deterministic smooth functions of time except for a finite number of time points. We use nonparametric local smoothing method to consistently estimate the smooth changing parameters and develop two consistent tests for smooth structural changes in panel data models. The first test is to check whether all model parameters are stable over time. The second test is to check potential time-varying interaction while allowing for a common trend. Both tests have an asymptotic $N(0,1)$ distribution under the null hypothesis of parameter constancy and are consistent against a vast class of smooth structural changes as well as abrupt structural breaks with possibly unknown break points alternatives. Simulation studies show that the tests provide reliable inference in finite samples and two empirical examples with respect to a cross-country growth model and a capital structure model are discussed.     

Nonparametric simultaneous testing for structural breaks

In this paper we consider a regression model with errors that are martingale differences. This modeling includes the regression of both independent and time series data. The aim is to study the appearance of structural breaks in both the mean and the variance functions, assuming that such breaks may occur simultaneously in both the functions. We develop nonparametric testing procedures that simultaneously test for structural breaks in the conditional mean and the conditional variance. The asymptotic distribution of an adaptive test statistic is established, as well as its asymptotic consistency and efficiency. Simulations illustrate the performance of the adaptive testing procedure. An application to the analysis of financial time series also demonstrates the usefulness of the proposed adaptive test in practice.     

Nonparametric spatial regression under near-epoch dependence

This paper establishes asymptotic normality and uniform consistency with convergence rates of the local linear estimator for spatial near-epoch dependent (NED) processes. The class of the NED spatial processes covers important spatial processes, including nonlinear autoregressive and infinite moving average random fields, which generally do not satisfy mixing conditions. Apart from accommodating a larger class of dependent processes, the proposed asymptotic theory allows for triangular arrays of heterogeneous random fields located on unevenly spaced lattices and sampled over regions of arbitrary configuration. All these features make the results applicable in a wide range of empirical settings.     

Nonparametric trending regression with cross-sectional dependence

Panel data, whose series length T$T$ is large but whose cross-section size N$N$ need not be, are assumed to have common time trend, of unknown form. The model includes additive, unknown, individual-specific components and allows for spatial or other cross-sectional dependence and/or heteroscedasticity. A simple smoothed nonparametric trend estimate is shown to be dominated by an estimate which exploits availability of cross-sectional data. Asymptotically optimal bandwidth choices are justified for both estimates. Feasible optimal bandwidths, and feasible optimal trend estimates, are asymptotically justified, finite sample performance of the latter being examined in a Monte Carlo study. Potential extensions are discussed.     

Nonparametric estimation and inference on conditional quantile processes

This paper presents estimation methods and asymptotic theory for the analysis of a nonparametrically specified conditional quantile process. Two estimators based on local linear regressions are proposed. The first estimator applies simple inequality constraints while the second uses rearrangement to maintain quantile monotonicity. The bandwidth parameter is allowed to vary across quantiles to adapt to data sparsity. For inference, the paper first establishes a uniform Bahadur representation and then shows that the two estimators converge weakly to the same limiting Gaussian process. As an empirical illustration, the paper considers a dataset from Project STAR and delivers two new findings.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

Nonparametric stochastic frontiers: A local maximum likelihood approach

This paper proposes a new approach to handle nonparametric stochastic frontier (SF) models. It is based on local maximum likelihood techniques. The model is presented as encompassing some anchorage parametric model in a nonparametric way. First, we derive asymptotic properties of the estimator for the general case (local linear approximations). Then the results are tailored to a SF model where the convoluted error term (efficiency plus noise) is the sum of a half normal and a normal random variable. The parametric anchorage model is a linear production function with a homoscedastic error term. The local approximation is linear for both the production function and the parameters of the error terms. The performance of our estimator is then established in finite samples using simulated data sets as well as with a cross-sectional data on US commercial banks. The methods appear to be robust, numerically stable and particularly useful for investigating a production process and the derived efficiency scores.     

Nonparametric IV estimation of local average treatment effects with covariates

In this paper nonparametric instrumental variable estimation of local average treatment effects (LATE) is extended to incorporate covariates. Estimation of LATE is appealing since identification relies on much weaker assumptions than the identification of average treatment effects in other nonparametric instrumental variable models. Including covariates in the estimation of LATE is necessary when the instrumental variable itself is confounded, such that the IV assumptions are valid only conditional on covariates. Previous approaches to handle covariates in the estimation of LATE relied on parametric or semiparametric methods. In this paper, a nonparametric estimator for the estimation of LATE with covariates is suggested that is root-n asymptotically normal and efficient.