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

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  • 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.

Suggested Citation

  • Peter R. Hansen & Asger Lunde, 2010. "Estimating the Persistence and the Autocorrelation Function of a Time Series that is Measured with Error," CREATES Research Papers 2010-08, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2010-08
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    References listed on IDEAS

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    More about this item

    Keywords

    Persistence; Autocorrelation Function; Measurement Error; Instrumental Variables; Realized Variance; Realized Kernel; Volatility;
    All these keywords.

    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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