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Estimating the Persistence and the Autocorrelation Function of a Time Series that is Measured with Error

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Author Info

  • Peter R. Hansen

    (Stanford University, Department of Economics, 579 Serra Mall, Stanford, CA 94305-6072, USA & CREATES)

  • Asger Lunde

    ()
    (Aarhus University, School of Economics and Management, Bartholins Allé 10, Aarhus, Denmark & CREATES)

Abstract

An economic time series can often be viewed as a noisy proxy for an underlying economic variable. Measurement errors will influence the dynamic properties of the observed process and may conceal the persistence of the underlying time series. In this paper we develop instrumental variable (IV) methods for extracting information about the latent process. Our framework can be used to estimate the autocorrelation function of the latent volatility process and a key persistence parameter. Our analysis is motivated by the recent literature on realized (volatility) measures, such as the realized variance, that are imperfect estimates of actual volatility. In an empirical analysis using realized measures for the DJIA stocks we find the underlying volatility to be near unit root in all cases. Although standard unit root tests are asymptotically justified, we find them to be misleading in our application despite the large sample. Unit root tests based on the IV estimator have better finite sample properties in this context.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-08.

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Length: 38
Date of creation: 04 Feb 2010
Date of revision:
Handle: RePEc:aah:create:2010-08

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: Persistence; Autocorrelation Function; Measurement Error; Instrumental Variables; Realized Variance; Realized Kernel; Volatility;

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Cited by:
  1. Gabriele La Spada & Fabrizio Lillo, 2011. "The effect of round-off error on long memory processes," Papers 1107.4476, arXiv.org, revised Mar 2013.
  2. Nikolaus Hautsch & Lada M. Kyj & Peter Malec, 2011. "The Merit of High-Frequency Data in Portfolio Allocation," SFB 649 Discussion Papers SFB649DP2011-059, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  3. Ahoniemi, Katja & Lanne, Markku, 2013. "Overnight stock returns and realized volatility," International Journal of Forecasting, Elsevier, vol. 29(4), pages 592-604.
  4. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2014. "Disentangling Systematic and Idiosyncratic Dynamics in Panels of Volatility Measures," Econometrics Working Papers Archive 2014_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Feb 2014.
  5. Kevin Sheppard & Lily Liu & Andrew J. Patton, 2013. "Does Anything Beat 5-Minute RV? A Comparison of Realized Measures Across Multiple Asset Classes," Economics Series Working Papers 645, University of Oxford, Department of Economics.
  6. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.

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