Estimating the persistence and the autocorrelation function of a time series that is measured with error

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 that are imperfect estimates of actual volatility. In an empirical analysis using realized measures for the Dow Jones industrial average 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 that are based on the IV estimator have better finite sample properties in this context.