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Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error

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  • Hansen, Peter R.
  • Lunde, Asger

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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  • Hansen, Peter R. & Lunde, Asger, 2014. "Estimating The Persistence And The Autocorrelation Function Of A Time Series That Is Measured With Error," Econometric Theory, Cambridge University Press, vol. 30(01), pages 60-93, February.
  • Handle: RePEc:cup:etheor:v:30:y:2014:i:01:p:60-93_00
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    Cited by:

    1. Diebold, Francis X. & Yılmaz, Kamil, 2014. "On the network topology of variance decompositions: Measuring the connectedness of financial firms," Journal of Econometrics, Elsevier, vol. 182(1), pages 119-134.
    2. Bollerslev, Tim & Hood, Benjamin & Huss, John & Pedersen, Lasse Heje, 2018. "Risk Everywhere: Modeling and Managing Volatility," CEPR Discussion Papers 12687, C.E.P.R. Discussion Papers.
    3. Matteo Barigozzi & Brownlees Christian & Gallo Giampiero & David Veredas, "undated". "Disentangling systematic and idiosyncratic risks for large panels of assets," ULB Institutional Repository 2013/136237, ULB -- Universite Libre de Bruxelles.
    4. Gabriele La Spada & Fabrizio Lillo, 2011. "The effect of round-off error on long memory processes," Papers 1107.4476, arXiv.org, revised Mar 2013.
    5. Hautsch, Nikolaus & Kyj, Lada M. & Malec, Peter, 2011. "The merit of high-frequency data in portfolio allocation," CFS Working Paper Series 2011/24, Center for Financial Studies (CFS).
    6. Barigozzi, Matteo & Brownlees, Christian & Gallo, Giampiero M. & Veredas, David, 2014. "Disentangling systematic and idiosyncratic dynamics in panels of volatility measures," Journal of Econometrics, Elsevier, vol. 182(2), pages 364-384.
    7. Rasmus T. Varneskov & Pierre Perron, 2018. "Combining long memory and level shifts in modelling and forecasting the volatility of asset returns," Quantitative Finance, Taylor & Francis Journals, vol. 18(3), pages 371-393, March.
    8. Eduardo Rossi & Paolo Santucci de Magistris, 2014. "Estimation of Long Memory in Integrated Variance," Econometric Reviews, Taylor & Francis Journals, vol. 33(7), pages 785-814, October.
    9. 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.
    10. Liu, Lily Y. & Patton, Andrew J. & Sheppard, Kevin, 2015. "Does anything beat 5-minute RV? A comparison of realized measures across multiple asset classes," Journal of Econometrics, Elsevier, vol. 187(1), pages 293-311.
    11. Christian M. Hafner & Arie Preminger, 2016. "The effect of additive outliers on a fractional unit root test," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 401-420, October.
    12. Christensen, K. & Podolskij, M. & Thamrongrat, N. & Veliyev, B., 2017. "Inference from high-frequency data: A subsampling approach," Journal of Econometrics, Elsevier, vol. 197(2), pages 245-272.
    13. Ahoniemi, Katja & Lanne, Markku, 2013. "Overnight stock returns and realized volatility," International Journal of Forecasting, Elsevier, vol. 29(4), pages 592-604.
    14. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, vol. 192(1), pages 1-18.
    15. Diebold, Francis X. & Yilmaz, Kamil, 2015. "Financial and Macroeconomic Connectedness: A Network Approach to Measurement and Monitoring," OUP Catalogue, Oxford University Press, number 9780199338306.
    16. Patton, Andrew J., 2011. "Data-based ranking of realised volatility estimators," Journal of Econometrics, Elsevier, vol. 161(2), pages 284-303, April.
    17. La Spada Gabriele & Lillo Fabrizio, 2014. "The effect of round-off error on long memory processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(4), pages 1-38, September.
    18. Preve, Daniel, 2015. "Linear programming-based estimators in nonnegative autoregression," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 225-234.
    19. repec:eee:ecofin:v:42:y:2017:i:c:p:393-420 is not listed on IDEAS

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    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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