Indirect Inference with Time Series Observed with Error

54 Pages Posted: 29 Jan 2018

See all articles by Eduardo Rossi

Eduardo Rossi

Department of Economics and Management

Paolo Santucci de Magistris

Aarhus University - CREATES

Date Written: January 21, 2018


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. Instead, if the condition for identification is satisfied, the measurement error parameters can be estimated jointly with the structural ones leading to a consistent and asymptotically Gaussian estimator. The issues of identification and misspecification of ME are discussed in detail. Based on the encompassing principle, we show that II can still be consistent for the parameters of interest when the conditional distribution of ME is misspecified, as long as the structural model for the observed series encompasses the auxiliary. We illustrate the reliability of this procedure in the estimation of stochastic volatility models based on realized volatility measures contaminated by microstructure noise. The empirical application stresses the importance of a realistic specification of the microstructure noise distribution to match the features of the observed log-returns at high frequencies.

Keywords: Indirect inference, measurement error, misspecification, identification, stochastic volatility models

JEL Classification: C13, C15, C22, C58

Suggested Citation

Rossi, Eduardo and Santucci de Magistris, Paolo, Indirect Inference with Time Series Observed with Error (January 21, 2018). Available at SSRN: or

Eduardo Rossi (Contact Author)

Department of Economics and Management ( email )

Via San Felice 5
27100 Pavia
++ (Phone)

Paolo Santucci de Magistris

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allè 4
Aarhus V, 8210

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