We discuss an estimation procedure for continuous-time models based on discrete sampled data with a fixed unit of time between two consecutive observations. Because in general the conditional likelihood of the model cannot be derived, an indirect inference procedure following Gouriéroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8, 85–118) is developed. It is based on simulations of a discretized model. We study the asymptotic properties of this “quasi”-indirect estimator and examine some particular cases. Because this method critically depends on simulations, we pay particular attention to the appropriate choice of the simulation step. Finally, finite-sample properties are studied through Monte Carlo experiments.

This paper provides a polynomial factorization theorem that is then used to extend the characterization parts of the parametric representation theorems of Johansen (1992, Econometric Theory 8, 188–202) for vector autoregressive processes integrated of up to order 2. A characterization theorem is provided in the general case of an I(d) process. For the discussion of the complicated polynomial cointegration properties of such processes, the case of an I(3) process is considered as an example.

In this paper we consider a semiparametric version of the test for seasonal unit roots suggested by Hylleberg, Engle, Granger, and Yoo (1990, Journal of Econometrics 44, 215–238). The asymptotic theory is based on the analysis of a simple regression problem, and the results apply to tests at any given frequency in the range (0,π]. Monte Carlo simulations suggest that the test may have more power than the parametric test of Hylleberg et al. (1990). On the other hand, the semiparametric version suffers from severe size distortions in some situations.

This paper considers tests for structural change of the cointegrating vector and the adjustment vector in the error correction model with an unknown change point. This paper derives new tests for structural change, which are applicable to maximum likelihood estimation. Our tests for structural change of the cointegrating vector have the same nonstandard asymptotic distributions that have been found by Hansen (1992a, Journal of Business and Economic Statistics 10, 321–335). In contrast, the tests on the adjustment vector have the same asymptotic distributions that have been found by Andrews and Ploberger (1994, Econometrica 62, 1383–1414) for models with stationary variables. Asymptotic critical values are provided.

We obtain new central limit theorems (CLT's) and functional central limit theorems (FCLT's) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT's for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent observations: (1) A new CLT for any plug-in estimator of a cumulative distribution function (c.d.f.) (e.g., an empirical c.d.f., or a c.d.f. estimator based on a kernel density estimator), which can in turn deliver distribution results for many Von Mises functionals; (2) a new limiting distribution result for degenerate U-statistics, which delivers distribution results for Bierens's integrated conditional moment tests; (3) a new functional central limit result for Hilbert-valued stochastic approximation procedures, which delivers distribution results for nonparametric recursive generalized method of moment estimators, including nonparametric adaptive learning models.

Elizabeth Dolomont joined the Cowles Foundation as my secretary in 1984 and retired in December 1997. Over the intervening 14 years, Elizabeth has been my personal assistant at Yale in running the journal Econometric Theory.