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

  • 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)

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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Paper provided by Department of Economics and Business Economics, Aarhus University 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
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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