Efficient Estimation in Semiparametric Time Series Models

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Semiparametric models play a major role in many fields and have been extensively studied over the last two decades. Great emphasis has been placed on models with independent (and identically) distributed observations and quite some progress has been made in this case. Models with dependent observations, however, been mainly neglected up to now from an efficiency point of view. The proposed research will tackle open issues in the construction of efficient estimates and tests in semiparametric models with an emphasis on models with dependent observations. Such models include stationary and ergodic Markov chains and other time series models which are plentiful in many fields such as econometrics and financial mathematics. Efficient estimation of the finite-dimensional component as well as aspects of the infinite-dimensional component will be addressed. The latter include innovation distributions in time series models, invariant distributions of ergodic Markov chains, and stationary distributions of several consecutive observations.The main emphasis of the proposed research will be to develop a methodology for the construction of efficient estimates in semiparametric models with dependent observations. In the process the proposed research will have to develop methods that deal with the difficulties associated with an efficient score function that cannot be calculated explicitly, a problem that is also of great interest for models with independent observations. Finally, the proposed research will continue the work of the principal investigator in semiparametric regression models with an emphasis on improving existing methods of constructing root-n consistent and efficient estimates.