Department of Economics and Business Economics

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

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  • Peter Reinhard Hansen
    Peter Reinhard HansenDenmark
  • Asger Lunde
  • School of Economics and Management
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.
Original languageEnglish
Place of publicationAarhus
PublisherInstitut for Økonomi, Aarhus Universitet
Number of pages38
StatePublished - 2010

    Research areas

  • Persistence, Autocorrelation Function, Measurement Error, Instrumental Variables, Realized Variance, Realized Kernel, Volatility

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