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For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties are well established. However, except for some speci…c cases, little is known about the estimation of the memory parameter for nonlinear processes. The purpose of this paper is to provide general conditions under which the local Whittle estimator of the memory parameter of a stationary process is consistent and to examine its rate of convergence. We show that these conditions are satis…ed for linear processes and a wide class of nonlinear models, among others, signal plus noise processes, nonlinear transforms of a Gaussian process t and EGARCH models. Special cases where the estimator satis…es the central limit theorem are discussed. The …nite sample performance of the estimator is investigated in a small Monte-Carlo study.JEL classi…cation. C14, C22. Short title: Consistent estimation of the memory parameter

Current trends in steels are focusing on refined martensitic microstructures to obtain high strength and toughness. An interesting manner to reduce the size of martensitic substructure is by reducing the size of the prior austenite grain (PAG). This work analyzes the effect of PAGS refinement by thermal cycling on different microstructural features of as-quenched lath martensite in a 0.3C-1.6Si-3.5Mn (wt pct) steel. The application of thermal cycling is found to lead to a refinement of the martensitic microstructures and to an increase of the density of high misorientation angle boundaries after quenching; these are commonly discussed to be key structural parameters affecting strength. Moreover, results show that as the PAGS is reduced, the volume fraction of retained austenite increases, carbides are refined and the concentration of carbon in solid solution as well as the dislocation density in martensite increase. All these microstructural modifications are related with the manner in which martensite forms from different prior austenite conditions, influenced by the PAGS.

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