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Indirect inference with time series observed with error

Author

Listed:
  • Eduardo Rossi

    () (University of Pavia)

  • Paolo Santucci de Magistris

    () (Aarhus University and CREATES)

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.

Suggested Citation

  • Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Indirect inference with time series observed with error," CREATES Research Papers 2014-57, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2014-57
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    File URL: ftp://ftp.econ.au.dk/creates/rp/14/rp14_57.pdf
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    References listed on IDEAS

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    More about this item

    Keywords

    Indirect inference; measurement error; stochastic volatility; realized volatility;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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