Indirect inference with time series observed with error

Eduardo Rossi and Paolo Santucci de Magistris ()
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Paolo Santucci de Magistris: Aarhus University and CREATES, Postal: Department of Economics and Business, Aarhus University, Fuglesangs Allé 4, 8210 Aarhus V, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We analyze the properties of the indirect inference estimator when the observed series are contaminated by measurement error. We show that the indirect inference estimates are asymptotically biased when the nuisance parameters of the measurement error distribution are neglected in the indirect estimation. We propose to solve this inconsistency by jointly estimating the nuisance and the structural parameters. Under standard assumptions, this estimator is consistent and asymptotically normal. A condition for the identification of ARMA plus noise is obtained. The proposed methodology is used to estimate the parameters of continuous-time stochastic volatility models with auxiliary specifications based on realized volatility measures. Monte Carlo simulations shows the bias reduction of the indirect estimates obtained when the microstructure noise is explicitly modeled. Finally, an empirical application illustrates the relevance 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; stochastic volatility; realized volatility (search for similar items in EconPapers)
JEL-codes: C13 C15 C22 C58 (search for similar items in EconPapers)
Pages: 39
Date: 2014-12-31
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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