This paper develops an algorithm for the exact Gaussianestimation of a mixed-order continuous-time dynamicmodel, with unobservable stochastic trends, from asample of mixed stock and flow data. Its applicationyields exact maximum likelihood estimates when theinnovations are Brownian motion and either the modelis closed or the exogenous variables are polynomialsin time of degree not exceeding two, and it can beexpected to yield very good estimates under muchmore general circumstances. The paper includesdetailed formulae for the implementation of thealgorithm, when the model comprises a mixture offirst- and second-order differential equations andboth the endogenous and exogenous variables are amixture of stocks and flows.

This paper generalizes the univariate results of Chanand Tran (1989, Econometric Theory5, 354–362) and Phillips (1990, EconometricTheory 6, 44–62) to multivariate timeseries. We develop the limit theory for theleast-squares estimate of a VAR(l) for a random walkwith independent and identically distributed errorsand for I(1) processes with weakly dependent errorswhose distributions are in the domain of attractionof a stable law. The limit laws are represented byfunctional of a stable process. A semiparametriccorrection is used in order to asymptoticallyeliminate the “bias” term in the limit law. Theseresults are also an extension of the multivariatelimit theory for square-integrable disturbancesderived by Phillips and Durlauf (1986,Review of Economic Studies 53,473–495). Potential applications include tests formultivariate unit roots and cointegration.

This paper considers the analysis of cointegrated timeseries using principal components methods. Thesemethods have the advantage of requiring neither thenormalization imposed by the triangular errorcorrection model nor the specification of afinite-order vector autoregression. Anasymptotically efficient estimator of thecointegrating vectors is given, along with testsforcointegration and tests of certain linearrestrictions on the cointegrating vectors. Anillustrative application is provided.

We develop order T−1asymptotic expansions for the quasi-maximumlikelihood estimator (QMLE) and a two-stepapproximate QMLE in the GARCH(l,l) model. Wecalculate the approximate mean and skewness and,hence, the Edgeworth-B distribution function. Wesuggest several methods of bias reduction based onthese approximations.

This paper investigates the semiparametric efficiencyof the conditional maximum likelihood estimation insome panel models. The nonparametric component ofthe model is the unknown distribution of the fixedeffect. For the exponential panel model, thereexists a complete sufficient statistic for the fixedeffect. When the complete sufficient statistic doesnot depend on the parameter of interest, theconditional maximum likelihood estimator (CMLE)achieves the semiparametric efficiency bound. Inparticular, the CMLE is semiparametrically efficientfor the panel Poisson regression model and the panelnegative binomial model.