• stochastic volatility
• indirect inference
• measurement error
• Kalman filter

Stochastic volatility models are able to reproduce many empirical regularities in financial time-series data, but their estimation is a challenging task. Indirect inference is often used for this purpose, even if it provides inconsistent estimations when data affected by measurement error are employed, for instance Realized Variance. To tackle this issue, Rossi and Santucci de Magistris (2018) suggest estimating, jointly with the model parameters, an additional parameter capturing noise component. In contrast, we propose a Kalman Filter approach, to obtain robust estimates from observed data. The estimation of two different stochastic volatility models on noisy data is carried out, following the indirect inference procedure according to both the methods mentioned, in order to compare their performances. Results show that the solution we propose may be a viable alternative to the noise specification approach, to cope with measurement error in observed data when indirect inference is applied.