Identification and Inference for Multivariate Cointegrated and Ergodic Gaussian Diffusions

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Abstract

Inference is considered in the multivariate continuous time Gaussian Ornstein–Uhlenbeck (OU) model on the basis of observations in discrete time. Under the hypothesis of ergodicity as well as cointegration, the classical identification or ‘aliasing’ problem is re-addressed and new results given. Exact conditions are given for (i) identification of individual parameters, as well as results for, (ii) identification of rank and cointegration parameters, and, furthermore (iii) for the existence of a continuous time OU process which embeds a discrete time vector autoregression. Estimation and cointegration rank inference are discussed. An empirical illustration is given in which the ‘cost-of-carry’ hypothesis is investigated.

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