We describe a variety of seimparametric models and estimators for fractional cointegration. All of the estimators we consider are based on the discrete Fourier transform of the data. This includes the ordinary least squares estimator as a special case.We make a distinction between Type I and Type II models, which differ from each other in terms of assumptions about initialization, and which lead to different functional limit laws for the partial sum processes. We compare the estimators in terms of rate of convergence. We briefly discuss the problems of testing for cointegration and determining the cointegrating rank. We also discuss relevant modeling issues, such as the local parametrization of the phase function.
KeywordsOrdinary Little Square Fractional Brownian Motion Ordinary Little Square Estimator Memory Parameter Functional Central Limit Theorem
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