Before revision:  Finally, as an example of how to apply the limit theory provided in this paper, we build a time-varying friction parameter extension of the (semiparametric) model with uncertainty zones (Robert and Rosenbaum (2012)) , which is noisy and endogenous, and we show that we can verify the conditions for the estimation of integrated volatility  .
After revision:  Finally, as an example of how to apply the limit theory provided in this paper, we build a time-varying friction parameter extension of the (semiparametric) model with uncertainty zones (Robert and Rosenbaum (2012)) , which is noisy and endogenous, and we show that we can verify the conditions for the estimation of integrated volatility . Moreover, practical applications in time series, such as the optimal block length and local bias-correction, are discussed and numerical simulations are carried on the local MLE of a time-varying parameter MA(1) model to illustrate them .