Integration for seasonal time series can take the form of seasonal periodic or nonperiodic integration. When seasonal time series are periodically integrated, we show that any cointegration is either full periodic cointegration or full nonperiodic cointegration, with no possibility of cointegration applying for only some seasons. In contrast, seasonally integrated series can be seasonally, periodically or nonperiodically cointegrated, with the possibility of cointegration applying for a subset of seasons. Cointegration tests are analyzed for periodically integrated series. A residual-based test is examined, and its asymptotic distribution is derived under the null hypothesis of no cointegration. A Monte Carlo analysis shows good performance in terms of size and power. The role of deterministic terms in the cointegrating test regression is also investigated. Further, we show that the asymptotic distribution of the error-correction test for periodic cointegration derived by Boswijk and Franses (1995, Review of Economics and Statistics 77, 436–454) does not apply for periodically integrated processes.The authors gratefully acknowledge the comments of participants at the conference on Unit Root and Cointegration Testing, University of the Algave, September–October 2005, and they particularly thank two anonymous referees and Helmut Lütkepohl (co-editor of this issue of Econometric Theory) for their constructive comments, which have substantially improved the generality of the results in the paper. Tomás del Barrio Castro acknowledges financial support from Ministerio de Educación y Ciencia SEJ2005-07781/ECON.

Aragon, Daouia, and Thomas-Agnan (2005, Econometric Theory 21, 358–389) introduced a new nonparametric frontier estimation. We prove the weak convergence of the empirical conditional quantile function. The distribution of the limit depends on the unknown conditional quantile density function. We provide a method to construct uniform confidence bands without estimating the conditional quantile density.

The stationarity conditions for an autoregressive (AR) process in general are reduced to a remarkably simple inequality if the lag coefficients are restricted to be identical. The condition is not only analytically elegant but also applicable in checking the validity of the stationarity conditions for such a restricted AR process of any order.We are deeply indebted to Professor Paolo Paruolo, NP co-editor of Econometric Theory, and anonymous referees for constructive comments and suggestions that led to significant improvements. Errors, if any, are solely ours.

02.6.1. Oblique projectorsTwo solutions are published, proposed independently by Götz Trinkler (the poser of the problem) and by Hans Joachim Werner. Excellent solutions have been independently proposed by G. Dhaene, L. Lauwers, S. Lawford, and H. Neudecker.—solution.

We study optimal bandwidth selection in nonparametric cointegrating regression where the regressor is a stochastic trend process driven by short or long memory innovations. Unlike stationary regression, the optimal bandwidth is found to be a random sequence which depends on the sojourn time of the process. All random sequences $h_{n}$ that lie within a wide band of rates as the sample size $n\rightarrow \infty $ have the property that local level and local linear kernel estimates are asymptotically normal, which enables inference and conveniently corresponds to limit theory in the stationary regression case. This finding reinforces the distinctive flexibility of data-based nonparametric regression procedures for nonstationary nonparametric regression. The present results are obtained under exogenous regressor conditions, which are restrictive but which enable flexible data-based methods of practical implementation in nonparametric predictive regressions within that environment.

We propose a robust inference method for predictive regression models under heterogeneously persistent volatility as well as endogeneity, persistence, or heavy-tailedness of regressors. This approach relies on two methodologies, nonlinear instrumental variable estimation and volatility correction, which are used to deal with the aforementioned characteristics of regressors and volatility, respectively. Our method is simple to implement and is applicable both in the case of continuous and discrete time models. According to our simulation study, the proposed method performs well compared with widely used alternative inference procedures in terms of its finite sample properties in various dependence and persistence settings observed in real-world financial and economic markets.

This interview with Michio Hatanaka is the first in this series given in the East, of which we are very proud. Hatanaka is a pioneer of econometrics in Japan. In the early 1950s he traveled to the United States to study as a graduate student at Vanderbilt University. That step was really unusual in the Japanese profession at that time. His stay in the States was extended to 1966, during which time he taught at Princeton and Rochester. His pathfinding behavior influenced and encouraged many Japanese scholars. Hatanaka started his academic career as a mathematical economist. This may partly explain why his research papers suggest deep economic thought as well as deep understanding of mathematics and statistics. His early contributions to econometrics are concerned with applying the spectral method to various economic problems. These contributions include the associate authorship of Spectral Analysis of Economic Time Series by C. W. J. Granger. His other contributions cover theoretical work on identification and estimation problems for dynamic econometric models, among which Hatanaka's efficient two-step estimator is well known. His research also includes empirical work on the Japanese economy and economic policy, which is relatively less known to people outside of Japan. His attitude toward research has set a standard for Japanese econometricians. His research papers are always a product of deep and full thought, and imbued with his own originality.

His achievements in administration are also impressive. During 1969–1971 and 1979–1980, he was director of the Institute of Social and Economic Research of Osaka University. And during 1983–1985 he was the dean of the faculty of economics at the same university. In addition, he served on the boards of several committees for the Japanese government and the Council of Science of Japan. Among his achievements in administration is the reform of the university entrance examination system, which was notoriously competitive and selective. This was really pathbreaking and led other universities to reform their systems.

This interview, which was given in Japanese, took place on November 20, 1989 in the Economics Department of Osaka University. What follows is a translated version of an edited transcript of that interview. We hope that the readers will share with us the privilege of hearing about the evolution of econometrics as encountered by him since just after the second world war.