This paper develops an algorithm for the exact Gaussian estimation of a mixed-order continuous-time dynamic model, with unobservable stochastic trends, from a sample of mixed stock and flow data. Its application yields exact maximum likelihood estimates when the innovations are Brownian motion and either the model is closed or the exogenous variables are polynomials in time of degree not exceeding two, and it can be expected to yield very good estimates under much more general circumstances. The paper includes detailed formulae for the implementation of the algorithm, when the model comprises a mixture of first- and second-order differential equations and both the endogenous and exogenous variables are a mixture of stocks and flows.

This paper generalizes the univariate results of Chan and Tran (1989, Econometric Theory 5, 354–362) and Phillips (1990, Econometric Theory 6, 44–62) to multivariate time series. We develop the limit theory for the least-squares estimate of a VAR(l) for a random walk with independent and identically distributed errors and for I(1) processes with weakly dependent errors whose distributions are in the domain of attraction of a stable law. The limit laws are represented by functional of a stable process. A semiparametric correction is used in order to asymptotically eliminate the “bias” term in the limit law. These results are also an extension of the multivariate limit theory for square-integrable disturbances derived by Phillips and Durlauf (1986, Review of Economic Studies 53, 473–495). Potential applications include tests for multivariate unit roots and cointegration.

This paper considers the analysis of cointegrated time series using principal components methods. These methods have the advantage of requiring neither the normalization imposed by the triangular error correction model nor the specification of a finite-order vector autoregression. An asymptotically efficient estimator of the cointegrating vectors is given, along with tests forcointegration and tests of certain linear restrictions on the cointegrating vectors. An illustrative application is provided.

We develop order T−1 asymptotic expansions for the quasi-maximum likelihood estimator (QMLE) and a two-step approximate QMLE in the GARCH(l,l) model. We calculate the approximate mean and skewness and, hence, the Edgeworth-B distribution function. We suggest several methods of bias reduction based on these approximations.

This paper investigates the semiparametric efficiency of the conditional maximum likelihood estimation in some panel models. The nonparametric component of the model is the unknown distribution of the fixed effect. For the exponential panel model, there exists a complete sufficient statistic for the fixed effect. When the complete sufficient statistic does not depend on the parameter of interest, the conditional maximum likelihood estimator (CMLE) achieves the semiparametric efficiency bound. In particular, the CMLE is semiparametrically efficient for the panel Poisson regression model and the panel negative binomial model.