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This paper deals with higher order asymptotic properties for three indirect inference estimators. We provide conditions that ensure the validity of locally uniform, with respect to the parameter, Edgeworth approximations. When these are of sufficiently high order they also form integrability conditions that validate locally uniform moment approximations. We derive the relevant second order bias and MSE approximations for the three estimators as functions of the respective approximations for the auxiliary estimator. We confirm that in the special case of deterministic weighting and affinity of the binding function, one of them is second order unbiased. The other two estimators do not have this property under the same conditions. Moreover, in this case, the second order approximate MSEs imply the superiority of the first estimator. We generalize to multistep procedures that provide recursive indirect inference estimators which are locally uniformly unbiased at any given order. Furthermore, in a particular case, we manage to validate locally uniform Edgeworth expansions for one of the estimators without any differentiability requirements for the estimating equations. We examine the bias-MSE results in a small Monte Carlo exercise.

This article examines the existence of locally uniform Edgeworth expansions for the distributions of parameterized random vectors. This could be useful for the establishment of high-order asymptotic properties for estimators and test statistics that are potentially based on moments of those vectors. We derive sufficient conditions either in the case of stationary stochastic processes exhibiting weak dependence or in the case of smooth transformations of such expansions.

This paper introduces and discusses some of the statistical properties of a timevarying parameter stochastic volatility (SV) in mean model. We derive the autocovariance function of an observed series, under the assumption that the conditional variance follows a flexible parameterization, which nests the autoregressive SV and the exponential GARCH specifications. Furthermore, the mean parameter can be time varying. We also present the autocovariance functions of higher orders and discuss identification issues. Our result can be applied so that the properties of the observed data may be compared with the theoretical properties of the models, thus facilitating model identification. Furthermore, they can be employed in the estimation and derivation of misspecification tests.