This paper develops semiparametric kernel-based estimators of risk-specific hazard functions for competing risks data. Both discrete and continuous failure times are considered. The maintained assumption is that the hazard function depends on explanatory variables only through an index. In contrast to existing semiparametric estimators, proportional hazards is not assumed. The new estimators are asymptotically normally distributed. The estimator of index coefficients is root-n consistent. The estimator of hazard functions achieves the one-dimensional rate of convergence. Thus the index assumption eliminates the “curse of dimensionality.” The estimators perform well in Monte Carlo experiments.I thank Denise Doiron for stimulating my interest in this research project and Catherine de Fontenay, Hans Christian Kongsted, Lars Muus, seminar participants, and two anonymous referees for comments on an earlier version of the paper. I gratefully acknowledge the hospitality of the University of Aarhus and the University of Copenhagen, where part of this research was undertaken.

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6/π2). This paper develops asymptotic expansions to the distribution of this statistic under the assumption of a known unit variance. The correction term for the density is shown to be independent of d, so that the MLE is second-order pivotal for d. This feature of the MLE is unusual, at least in time series contexts. Simulations show that the normal approximation is poor and that the expansions can make a significant improvement in accuracy provided the correction terms are computed without further asymptotic approximation.This paper was commenced and revised while Lieberman was visiting the Cowles Foundation during 2000–2002. Lieberman thanks the Cowles Foundation for support and hospitality during this visit. Phillips thanks the NSF for support under grants SBR 97-30295 and SES 0092509.

This paper proposes some tests for fitting a regression model with a long memory covariate process and with errors that form either a martingale difference sequence or a long memory moving average process, independent of the covariate. The tests are based on a partial sum process of the residuals from the fitted regression. The asymptotic null distribution of this process is discussed in some detail under each set of these assumptions. The proposed tests are shown to have known asymptotic null distributions in the case of martingale difference errors and also in the case of fitting a polynomial of a known degree through the origin when the errors have long memory. The theory is then illustrated with some examples based on the forward premium anomaly where a squared interest rate differential proxies a time dependent risk premium. The paper also shows that the proposed test statistic converges weakly to nonstandard distributions in some cases.The authors gratefully acknowledge the helpful comments of the co-editor Don Andrews and two anonymous referees. The research of the first two authors was partly supported by NSF grant DMS 00-71619.

The paper presents the asymptotic theory of the efficient method of moments when the model of interest is not correctly specified. The paper assumes a sequence of independent and identically distributed observations and a global misspecification. It is found that the limiting distribution of the estimator is still asymptotically normal, but it suffers a strong impact in the covariance matrix. A consistent estimator of this covariance matrix is provided. The large sample distribution on the estimated moment function is also obtained. These results are used to discuss the situation when the moment conditions hold but the model is misspecified. It also is shown that the overidentifying restrictions test has asymptotic power one whenever the limit moment function is different from zero. It is also proved that the bootstrap distributions converge almost surely to the previously mentioned distributions and hence they could be used as an alternative to draw inferences under misspecification. Interestingly, it is also shown that bootstrap can be reliably applied even if the number of bootstrap replications is very small.The authors express their gratitude to Professor A.R. Gallant for his support and for helpful discussions about this topic. They also thank Professor Donald Andrews for his revision and for the suggestion to read the work by Hall and Inoue (2003). They thank Hall and Inoue for sending them their technical report. Finally the authors thank two anonymous referees for their helpful comments, which led to a significant improvement of the paper. The views expressed in this paper are our sole responsibility. Víctor Aguirre-Torres acknowledges partial support from the Asociación Mexicana de la Cultura A.C. Manuel A. Domínguez acknowledges funding from CONACYT, research project J38076-D, and partial support from Asociación Mexicana de la Cultura A.C.

We define the Bernstein copula and study its statistical properties in terms of both distributions and densities. We also develop a theory of approximation for multivariate distributions in terms of Bernstein copulas. Rates of consistency when the Bernstein copula density is estimated empirically are given. In order of magnitude, this estimator has variance equal to the square root of the variance of common nonparametric estimators, e.g., kernel smoothers, but it is biased as a histogram estimator.We would thank Mark Salmon for interesting us in the copula function and Peter Phillips, an associate editor, and the referees for many valuable comments. All remaining errors are our sole responsibility.

This paper proposes a semiparametric approach by introducing a smooth scale function into the standard generalized autoregressive conditional heteroskedastic (GARCH) model so that conditional heteroskedasticity (CH) and scale change in financial returns can be modeled simultaneously. An estimation procedure combining kernel estimation of the scale function and maximum likelihood estimation of the GARCH parameters is proposed. Asymptotic properties of the estimators are investigated in detail. It is shown that asymptotically normal, -consistent parameter estimation is available. A data-driven algorithm is developed for practical implementation. Finite sample performance of the proposal is studied through simulation. The proposal is applied to model CH and scale change in the daily S&P 500 and DAX 100 returns. It is shown that both series have simultaneously significant scale change and CH.We are very grateful to the co-editor and two referees for their helpful comments and suggestions, which led to a substantial improvement of this paper. The paper was finished under the advice of Professor Jan Beran, Department of Mathematics and Statistics, University of Konstanz, Germany, and was financially supported by the Center of Finance and Econometrics (CoFE), University of Konstanz. We thank colleagues in CoFE, especially Professor Winfried Pohlmeier, for their interesting questions at a talk of the author. It was these questions that motivated the author to write this paper. Our special thanks go to Dr. Erik Lüders, Department of Finance and Insurance, Laval University, and Stern School of Business, New York University, for his helpful suggestions.

We examine properties of residual-based tests for the null of no cointegration for dynamic panels in which both the short-run dynamics and the long-run slope coefficients are permitted to be heterogeneous across individual members of the panel. The tests also allow for individual heterogeneous fixed effects and trend terms, and we consider both pooled within dimension tests and group mean between dimension tests. We derive limiting distributions for these and show that they are normal and free of nuisance parameters. We also provide Monte Carlo evidence to demonstrate their small sample size and power performance, and we illustrate their use in testing purchasing power parity for the post–Bretton Woods period.I thank Rich Clarida, Bob Cumby, Mahmoud El-Gamal, Heejoon Kang, Chiwha Kao, Andy Levin, Klaus Neusser, Masao Ogaki, David Papell, Pierre Perron, Abdel Senhadji, Jean-Pierre Urbain, Alan Taylor, and three anonymous referees for helpful comments on various earlier versions of this paper. The paper has also benefited from presentations at the 1994 North American Econometric Society Summer Meetings in Quebec City, the 1994 European Econometric Society Summer Meetings in Maastricht, and workshop seminars at the Board of Governors of the Federal Reserve, INSEE-CREST Paris, IUPUI, Ohio State, Purdue, Queens University Belfast, Rice University–University of Houston, and Southern Methodist University. Finally, I thank the following students who provided assistance in the earlier stages of the project: Younghan Kim, Rasmus Ruffer, and Lining Wan.

Typically in time series econometrics, for many statistics, a rescaled integrated process is replaced with Brownian motion to find the limit distribution. For averages of functions of a rescaled integrated process, Park and Phillips have shown that this remains true for functions with poles, as long as a sample-size-dependent region around the poles is excluded from consideration, the function is locally integrable, and some other regularity conditions hold. In this addendum, I show that under some regularity conditions on the function under consideration, there is no need for such a sample-size-dependent region around the pole in Park and Phillips' theorem, as long as the function under consideration is locally integrable.The author thanks four anonymous referees and Professor Phillips for their comments and suggestions and Benedikt Pötscher for suggestions and for pointing out an error in a previous version of this paper.

This note discusses the concept of aliasing and its use in the paper by H.J. Bierens (2001, Econometric Theory 17, 962–983), in the framework of a second-order autoregression with complex unit roots. The condition on the range of the angular frequency φ is extended to φ ∈ (0,2π) − {π}.Financial support from UPV-EHU research project 9/UPV-00038.321-13503/2001, Basque Government project PI9970 and Ministerio de ciencia y tecnología BEC2003-02028 is gratefully acknowledged.

This problem discusses an I(2) model in the VAR(1) case. The I(2) representation theorem of Johansen (1992) (JRT) holds also for VAR(1) processes. The I(2) model for VAR(k) processes has been discussed for k ≥ 2 in Johansen (1996, Ch. 9; 1997). We here discuss a parametrization for the I(2) case of VAR(1) that differs from the VAR(k) model.

I am delighted to announce the following Econometric Theory Awards for 2004.