Indirect inference with time series observed with error

We propose the indirect inference estimator as a consistent method to estimate the parameters of a structural model when the observed series are contaminated by measurement error by considering the noise as a structural feature. We show that the indirect inference estimates are asymptotically biased if the error is neglected. When the condition for identification is satisfied, the structural and measurement error parameters can be consistently estimated. The issues of identification and misspecification of measurement error are discussed in detail. We illustrate the reliability of this procedure in the estimation of stochastic volatility models based on realized volatility measures contaminated by microstructure noise.