Talks

Research

The Quantilogram and its Furry Friends

The Stochastic Dominance Project

The Froot-Stein Model Revisited

Some Papers

(The following papers can be viewed or downloaded in Postscript or Acrobat format.)

Hot off The Press

• "A Smoothed Least Squares Estimator For The Threshold Regression Models" (with M. Seo) We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen (2000) to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold effect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the threshold parameters themselves. We compare our confidence intervals with those of Hansen (2000) in a simulation study and show that our methods outperform his for large values of the threshold.
  Revised March, 2006.
  
  
• "Higher-order Asymptotic Theory When a Parameter is on a Boundary with an Application to GARCH Models" (with Emma M. Iglesias) Andrews (1999) derived the first order asymptotic theory for a very general class of estimators when a parameter is on a boundary. We derive the second order asymptotic theory in this setting in some special cases. We focus on the behaviour of the QMLE in stationary and nonstationary GARCH models when constraints are imposed in the maximisation procedure. We show how in this case both a first and second-order bias appears in the estimator, and how it can be quite large. We provide two types of bias-correction mechanisms for the researcher to choose in practice: either to bias correct only for a first order, or for a first and second order bias. We show that when some constraints are imposed, it is advisable to bias correct not only for the first order, but also for the second order bias.
  February, 2006.
  
  
• "Discussion of Quantile Autoregression by Koenker and Xiao" (with C. Hafner)
  January, 2006.
  
  
• "Nonparametric Transformation to White Noise" (with Enno Mammen) 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 2 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 asymptotic normality and achieve efficiency improvements over the usual estimators in the special case of a nonparametric regression subject to time series errors, e.g., Xiao et al. (2003). 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 non-standard in the unit root case. We also investigate its finite sample performance and demonstrate its effectiveness.
  November, 2005.
  
  
• "Testing for the Stochastic Dominance Efficiency of a given Portfolio" (with Thierry Post and Yoon-Jae Whang) We propose a new test of the stochastic dominance efficiency of a given asset over a class of portfolios. We establish its null and alternative asymptotic properties, and define a method for consistently estimating critical values. We present some numerical evidence that our tests work well in moderate sized samples.
  November, 2005.
  
  
• "Discussion of Aït-Sahalia and Barndorff-Nielsen and Shephard" "Technical Appendix" (with I. Kalnina)
  October, 2005.
  
  
• "Semiparametric Estimation of a Characteristic-based Factor Model of Common Stock Returns" (with G. Connor) We introduce an alternative version of the Fama-French three-factor model of stock returns together with a new estimation methodology. We assume that the factor betas in the model are smooth nonlinear functions of observed security characteristics. We develop an estimation procedure that combines nonparametric kernel methods for constructing mimicking portfolios with parametric nonlinear regression to estimate factor returns and factor betas simultaneously. The methodology is applied to US common stocks and the empirical findings compared to those of Fama and French.
  Revised, September, 2005
  
  "Local Linear Fitting under Near Epoch Dependence" (with Z. Lu) Local linear fitting in modelling of nonlinear processes under strong (i.e., $\alpha$--) mixing conditions has been investigated extensively. However, it is often a difficult step to establish the strong mixing of a nonlinear process composed of several parts such as the popular combination of ARMA and GARCH models. In this paper we develop an asymptotic theory of local linear fitting for near-epoch dependent (NED) processes. We establish the pointwise asymptotic normality of the local linear kernel estimators under some restrictions on the amount of dependence. Simulations and application examples illustrate that the proposed approach can work quite well for the medium size of economic time series.
  Revised, September 2005.
  
  
• "Are There Monday Effects In Stock Markets? A Stochastic Dominance Approach" (with Young-Hyun Cho and Yoon-Jae Whang) We provide a test of the Monday effect in daily stock index returns based on the stochastic dominance criterion. We apply our test to a number of stock indexes including large caps and small caps as well as UK and Japanese indexes. We find strong evidence of Monday effect in some cases under this stronger criterion. However, we also confirm previous studies that the effect is concentrated in the second half of the month and on days when the previous Friday return was negative. The effect is also reversed or weakened in the big US indices post 1987. Overall the evidence in support of a single Monday effect is weak.
  August, 2005
  
  
• "Nonparametric Matching and Efficient Estimation of Homothetically Separable Functions" (with Arthur Lewbel) For vectors x and w, let r(x,w) be a function that can be nonparametrically estimated consistently and asymptotically normally. We provide consistent, asymptotically normal estimators for the functions g and h, where r(x,w)=h[g(x),w], g is linearly homogeneous and h is monotonic in g. This framework encompasses homothetic and homothetically separable functions. Such models reduce the curse of dimensionality, provide a natural generalization of linear index models, and are widely used in utility, production, and cost function applications. We also propose an improvement to our estimator of g that achieves the same performance as an estimator based on local least squares knowing h. We provide simulation evidence on the small sample performance of our estimators.
  Revised, July 2005
  
  
• "A Smoothed Least Squares Estimator For The Threshold Regression Models" (with M. Seo) We propose a smoothed least squares estimator of the parameters of a threshold regression model. Our model generalizes that considered in Hansen (2000) to allow the thresholding to depend on a linear index of observed regressors, thus allowing discrete variables to enter. We also do not assume that the threshold effect is vanishingly small. Our estimator is shown to be consistent and asymptotically normal thus facilitating standard inference techniques based on estimated standard errors or standard bootstrap for the threshold parameters themselves. We compare our confidence intervals with those of Hansen (2000) in a simulation study and show that our methods outperform his for large values of the threshold. We also include an application.
  July, 2005.
  
  
• "ESTIMATION OF A SEMIPARAMETRIC IGARCH(1,1) MODEL" (with Woocheol Kim) We propose a semiparametric IGARCH model that allows for persistence in variance but also allows for more flexible functional form. We assume that the difference of the squared process is weakly stationary. We propose an estimation strategy based on the nonparametric instrumental variable method. We establish the rate of convergence of our estimator.
  February, 2005.
  
  
• "A Closed-form Estimator for the GARCH(1,1)-Model" (with Dennis Kristensen) We propose a closed-form estimator for the linear GARCH(1,1) model. The estimator has the advantage over the often used quasi-maximum-likelihood estimator (QMLE) that it can be easily implemented, and does not require the use of any numerical optimisation procedures or the choice of initial values of the conditional variance process. We derive the asymptotic properties of the estimator, showing T^{(?-1)/?}-consistency for some ??(1,2) when the 4th moment exists and root-T-asymptotic normality when the 8th moment exists. We demonstrate that a finite number of Newton-Raphson iterations using our estimator as starting point will yield asymptotically the same distribution as the QMLE when the 4th moment exists. A simulation study confirms our theoretical results.
  Revised January, 2005. Forthcoming in Econometric Theory
  
  
• "A Nonparametric Regression Estimator that Adapts to Error Distribution of Unknown Form" (with Zhijie Xiao) Motivated by efficiency considerations we propose a new estimator for nonparametric regression based on estimated local likelihood estimation. We show that our estimator is asymptotically equivalent to the infeasible local likelihood estimator [Staniswalis (1989), Fan, Farmen, and Gijbels (1998), and Fan and Chen (1999)], which requires specification of the error distribution, and hence our estimator improves on standard nonparametric estimators when the error distribution is not normal. We investigate the finite sample performance of our procedure on simulated data. An empirical application to the IBM transaction data is conducted to study seasonality of high frequency intra-day stock returns.
  Revised, November 2004
  
  "The Froot-Stein Model Revisited" (with N. Hogh and J. Nielsen) We investigate the model of Froot and Stein (1998), a model that has very strong implications for risk management. We argue that their conclusions are too strong and need to be qualified. We also argue that their analysis is incorrect and incomplete. Specifically, there are some unusual consequences of their model, which may be linked to the chosen pricing formula.
  Revised, September 2004. Forthcoming in British Actuarial Journal.
  
  
• "A Quantilogram Approach to Evaluating Directional Predictability" (with Yoon-Jae Whang) In this note we propose a simple method of measuring directional predictability and testing for the hypothesis that a given time series has no directional predictability. The test is based on the correlogram of quantile hits. We provide the distribution theory needed to conduct inference, propose some model free upper bound critical values, and apply our methods to stock index return data. The empirical results suggests some directional predictability in returns especially in mid range quantiles like 5%-10%.
  Revised, September 2004
  
  
• pdf "ESTIMATING SEMIPARAMETRIC ARCH(?) MODELS BY KERNEL SMOOTHING METHODS"(with Enno Mammen) We investigate a class of semiparametric ARCH\textbf{(}$\infty $\textbf{) }% models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the `news impact' function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric and nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S\&P500 index returns. We find some evidence of asymmetric news impact functions in the daily and weekly data, consistent with the parametric analysis.
  Revised, September 2004. Forthcoming in Econometrica
  
  
• "An Optimal Estimator of True Mark under Double Blind Marking" We propose an optimal way of combining the marks of two double blind markers with a view to avoiding lengthy introspective arguments about student quality.
  June, 2004
  
  
• "Nonparametric Inference for Unbalanced Time Series" This paper is concerned with the practical problem of conducting inference in a vector time series setting when the data is unbalanced or incomplete. In this case, one can work only with the common sample, to which a standard HAC/bootstrap theory applies, but at the expense of throwing away data and perhaps losing efficiency. An alternative is to use some sort of imputation method, but this requires additional modelling assumptions, which we would rather avoid. We show how the sampling theory changes and how to modify the resampling algorithms to accommodate the problem of missing data. We also discuss efficiency and power. Unbalanced data of the type we consider are quite common in financial panel data, see for example Connor and Korajczyk (1993). These data also occur in cross-country studies.
  April, 2004. Forthcoming in Econometric Theory.
  
  
• "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton model: An Integrated Approach" (with Andrew Jeffrey, Dennis Kristensen, Thong Nguyen, and Peter C.B. Phillips) We propose a new nonparametric estimator for the volatility structure of the zero coupon yield curve inside the Heath-Jarrow-Morton framework. The estimator incorporates cross-sectional restrictions along the maturity dimension, and also allows for measurement errors, which can arise from estimation of the yield curve from noisy data. The estimates are implemented with daily CRSP bond data.
  Forthcoming in Journal of Financial Econometrics
  
  
• "Consistent Testing For Stochastic Dominance: A Subsampling Approach"(with Esfandiar Maasoumi and Yoon-Jae Whang) We propose a procedure for estimating the critical values of the extended Kolmogorov-Smirnov tests of Stochastic Dominance of arbitrary order in the general $K$-prospect case. We allow for the observations to be serially dependent and, for the first time, we can accommodate \textit{general} dependence amongst the \textit{prospects} which are to be ranked. Also, the prospects may be the residuals from certain conditional models, opening the way for \textit{conditional} ranking. We also propose a test of Prospect Stochastic Dominance. Our method is based on subsampling and we show that the resulting tests are consistent and powerful against some $N^{-1/2}$ local alternatives. We also propose some heuristic methods for selecting subsample size and demonstrate in simulations that they perform reasonably. We describe an alternative method for obtaining critical values based on recentering the test statistic and using full sample bootstrap methods. We compare the two methods in theory and in practice.
  Forthcoming in Review of Economic Studies, August 2004
  
  
• "The Common and Specific Components of Dynamic Volatility" (with G.C.Connor and R.A. Korajczyk) This paper develops a dynamic approximate factor model in which returns are time-series heteroskedastic. The heteroskedasticity has three components: a factor-related component, a common asset-specific component, and a purely asset-specific component. We develop a new multivariate GARCH model for the factor-related component. We develop a univariate stochastic volatility model linked to a cross-sectional series of individual GARCH models for the common asset-specific component and the purely asset-specific component. We apply the analysis to monthly US equity returns for the period January 1926 to December 2000. We find that all three components contribute to the heteroskedasticity of individual equity returns. Factor volatility and the common component in asset-specific volatility have long-term secular trends as well as short-term autocorrelation. Factor volatility has correlation with interest rates and the business cycle.
  Revised, July 2003. Forthcoming Journal of Econometrics
  
  
• pdf "A LIVE METHOD FOR GENERALIZED ADDITIVE VOLATILITY MODELS (with W. Kim) We investigate a new separable nonparametric model for time series, which includes many ARCH models and AR models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal integration or projection method. We also consider a more efficient two-step likelihood-based procedure, and show that this yields both asymptotic and finite sample performance gains.
  Revised, December 2003. Forthcoming Econometric Theory
  
  
• pdf "Estimation of Semiparametric Models when the Criterion Function is not Smooth"(with Xiaohong Chen and Ingrid Van Keilegom) We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some preliminary nonparametric estimators. Our results extend existing theories like those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We apply our results to two examples: a `hit rate' and a partially linear median regression with some endogenous regressors.
  Forthcoming in Econometrica, March 2003
  
  
• pdf "Semiparametric Regression Analysis with Missing Response at Random " (with Qihua Wang, Wolfgang H\"ardle) We develop inference tools in a semiparametric partially linear regression model with missing response data. A class of estimators is defined that includes as special cases: a semiparametric regression imputation estimator, a marginal average estimator and a (marginal) propensity score weighted estimator. We show that any of our class of estimators is asymptotically normal. The three special estimators have the same asymptotic variance. They achieve the semiparametric efficiency bound in the homoskedastic Gaussian case. We show that the Jackknife method can be used to consistently estimate the asymptotic variance. Our model and estimators are defined with a view to avoid the curse of dimensionality, that severely limits the applicability of existing methods. The empirical likelihood method is developed. It is shown that when missing responses are imputed using the semiparametric regression method the empirical log-likelihood is asymptotically a scaled chi-square variable. An adjusted empirical log-likelihood ratio, which is asymptotically standard chi-square, is obtained. Also, a bootstrap empirical log-likelihood ratio is derived and its distribution is used to approximate that of the imputed empirical log-likelihood ratio. A simulation study is conducted to compare the adjusted and bootstrap empirical likelihood with the normal approximation based method in terms of coverage accuracies and average lengths of confidence intervals. Based on biases and standard errors, a comparison is also made by simulation between the proposed estimators and the related estimators.
  Forthcoming in Journal of the American Statistical Association
  
  
• postscript pdf "MORE EFFICIENT KERNEL ESTIMATION IN NONPARAMETRIC REGRESSION WITH AUTOCORRELATED ERRORS" (with Zhijie Xiao, Raymond J. Carroll, and E. Mammen) We propose a modification of kernel time series regression estimators that improves efficiency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that has to be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. It is shown that the proposed estimation procedure is more efficient than the conventional kernel method. We also provide simulation evidence to suggest that gains can be achieved in moderate sized samples.
  Forthcoming in Journal of the American Statistical Association
  
  
• "Limit Theorems for Estimating the Parameters of Differentiated Product Demand Systems" (with S. Berry and A. Pakes) We give an asymptotic distribution theory for a class of Generalized Method of Moments estimators that frequently arise in the study of differentiated product markets when the number of observations is associated with the number of products within a given market. We allow for three sources of error: the sampling error in estimating market share, the simulation error in approximating the equilibrium share, and the underlying model error. The limiting distribution of the parameter estimator is normal provided there are certain restrictions on the three sources of error.
  Forthcoming in the Review of Economic Studies
  
  
• "ESTIMATING FEATURES OF A DISTRIBUTION FROM BINOMIAL DATA" Revised September, 2002 (with Arthur Lewbel and Daniel McFadden) A statistical problem that arises in several fields is that of estimating the features of an unknown distribution, which may be conditioned on covariates, using a sample of binomial observations on whether draws from this distribution exceed threshold levels set by experimental design. One application is destructive duration analysis, where the process is censored at an observation test time. Another is referendum contingent valuation in resource economics, where one is interested in features of the distribution of values placed by consumers on a public good such as endangered species. Sample consumers are asked whether they would vote for a referendum that would provide the good at a cost specified by experimental design. This paper provides estimators for moments and quantiles of the unknown distribution in this problem under a variety of nonparametric and semiparametric specifications.
  
  
  
• "Asymptotic Expansions for some Semiparametric Program Evaluation Estimators" (with H. Ichimura) We investigate the performance of a class of semiparametric estimators of the treatment effect via asymptotic expansions. We derive approximations to the first two moments of the estimator that are valid to `second order'. We use these approximations to define a method of bandwidth selection. We also propose a degrees of freedom like bias correction that improves the second order properties of the estimator but without requiring estimation of higher order derivatives of the unknown propensity score. We provide some numerical calibrations of the results.
  Paper written for the Festschrift of Tom Rothenberg
  Revised, September 2002
  
  
  
• "An Alternative way of Computing Efficient Instrumental Variable Estimators" (with X. Chen) We propose a new way of constructing efficient semiparametric instrumental variable estimators. Our method is to combine a large number of possibly inefficient estimators rather than combining the instruments into an optimal instrument function. We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of root-n consistent estimators whose cardinality increases with sample size. We show that the semiparametrically efficient estimator lies in our class. We investigate the finite sample performance of our estimator and show that it does quite well.
  
  
• "Is there chaos in the world economy? A nonparametric test using consistent standard errors "(with M. Shintani) A positive Lyapunov exponent is one practical definition of chaos. We develop a formal test for chaos in a noisy system based on estimates of the sign of the Lyapunov exponent. The test utilizes nonparametric regression techniques including local quadratic regression and neural networks. When our procedures are applied to international real output series, the Lyapunov exponent estimates are negative and the positivity hypothesis of the exponent is significantly rejected in most cases. This suggests that the traditional exogenous models are better able to explain business cycle fluctuations than is the chaotic endogenous approach. Some caveats include the small sample sizes, nonstationarity and nonlinearity of the systems we investigate.
  Forthcoming in International Economic Review, June 2001
  
  
• "Accounting for Correlation in Marginal Longitudinal Nonparametric Regression" (with Enno Mammen, Xihong Lin, and Raymond Carroll) We consider nonparametric regression in a marginal longitudinal data framework. Previous work by Lin and Carroll (2000) has shown that the kernel nonparametric regression methods extant in the literature for such correlated data have the discouraging property that they generally do not improve upon methods that ignore the correlation structure entirely. The latter methods are called working independence methods. We construct a two-stage kernel-based estimator that asymptotically uniformly improves upon the working independence estimator. A small simulation study is given in support of the asymptotics, and includes comparisons with regression splines.
  
  
  
• "Estimation of Linear Regression Models from Bid-Ask Data by a Spread-Tolerant Estimator" We investigate a class of estimators for linear regression models where the dependent variable is subject to bid-ask censoring. Our estimation method is based on a definition of error that is zero when the predictor lies between the actual bid price and ask price, and linear outside this range. Our estimator minimizes a sum of such squared errors; it is nonlinear, and indeed the criterion function itself is non-smooth. We establish its asymptotic properties using the approach of Pakes and Pollard (1989). We compare the estimator with mid-point OLS.
  Forthcoming in The Annals of Economics and Finance
  
  
• "Flexible Term Structure Estimation: Which Method is Preferred?" "Table 1" "Table 2" "Table 3 "Table 4" "Table 5" "Figure 1" "Figure 2" (with Thong Nguyen and Andrew Jeffrey) We show that the recently developed nonparametric procedure for fitting the term structure of interest rates developed by Linton, Mammen, Nielsen, and Tanggaard (2000) overall performs notably better than the highly flexible McCulloch (1975) cubic spline and Fama and Bliss (1987) bootstrap methods. However, if interest is limited to the Treasury bill region alone then the Fama-Bliss method demonstrates superior performance. We further show, via simulation, that using the estimated short rate from the Linton-Mammen-Nielsen-Tanggaard procedure as a proxy for the short rate has higher precision then the commonly used proxies of the one and three month Treasury bill rates. It is demonstrated that this precision is important when using proxies to estimate the stochastic process governing the evolution of the short rate.
  
  
  

  Higher Order Approximations

  
  

  Additive Nonparametric Models and their Estimation

  
  

  Papers with Finance Applications

  
  

  Miscellaneous Nonparametric Stuff