Some Discrete Approximations to Continuous Time Stochastic Models

Summary The paper considers the asymptotic biases in various econometric estimators when data generated by a stochastic differential equation system of the form d y d t − A y (t) = B z (t) + a (t) are estimated by approximating these equations in the form y (t + δ) − y (t) / δ = 1 2 A y (t + δ) + y (t) + 1 2 B z (t + δ) + z (t) + v (t), where y (t) is a vector of endogenous variables, z (t) is a vector of exogenous variables and A and B are matrices of fixed coefficients, assumed estimated subject to certain a priori restrictions. It is shown that the asymptotic biases are O (δ2) as δ→0, on reasonable assumptions.