In this paper, we give a general time-varying parameter model, where the multidimensional parameter , which possibly includes jumps , follows a local martingale . The quantity of interest is defined as the integrated value over time of the parameter process \Theta = T^{-1} \int_0^T \theta_t^* dt. We provide a local parametric estimator (LPE) of \Theta and conditions under which we can show the central limit theorem.  The framework is restricted to the specific convergence rate n^{1/2}. Several examples of LPE , in which the conditions are shown to be satisfied assuming that the microstructure noise is O_p(1/\sqrt{n : estimation of volatility, powers of volatility, high-frequency covariance and volatility when incorporating trading information . The LPE considered in those cases are variations of the maximum likelihood estimator. We also treat the case of time-varying model with uncertainty zones and the time-varying MA(1).
In this paper, we give a general time-varying parameter model, where the multidimensional parameter possibly includes jumps . The quantity of interest is defined as the integrated value over time of the parameter process \Theta = T^{-1} \int_0^T \theta_t^* dt. We provide a local parametric estimator (LPE) of \Theta and conditions under which we can show the central limit theorem. Roughly speaking those conditions correspond to some uniform limit theory in the parametric version of the problem. The framework is restricted to the specific convergence rate n^{1/2}. Several examples of LPE are studied : estimation of volatility, powers of volatility, volatility when incorporating trading information and time-varying MA(1).
D
, which
D
, follows a local martingale
A
Roughly speaking those conditions correspond to some uniform limit theory in the parametric version of the problem.
R
, in which the conditions are shown to be satisfied assuming that the microstructure noise is O_p(1/\sqrt{n
are studied
D
high-frequency covariance and
R
. The LPE considered in those cases are variations of the maximum likelihood estimator. We also treat the case of time-varying model with uncertainty zones and the
and