Distributions of the Maximum Likelihood and Minimum Contrast Estimators Associated with the Fractional Ornstein-Uhlenbeck Process
AbstractWe discuss some inference problems associated with the fractional Ornstein-Uhlenbeck (fO-U) process driven by the fractional Brownian motion (fBm). In particular, we are concerned with the estimation of the drift parameter, assuming that the Hurst parameter H is known and is in [1/2, 1). Under this setting we compute the distributions of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) for the drift parameter, and explore their distributional properties by paying attention to the influence of H and the sampling span M. We shall also derive the asymptotic distributions of the two estimators as M becomes large. We further deal with the ordinary least squares estimator (OLSE) and examine the asymptotic relative efficiency. It is shown that the MCE is asymptotically efficient, while the OLSE is inefficient. We also consider the unit root testing problem in the fO-U process and compute the power of the tests based on the MLE and MCE.
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Bibliographic InfoPaper provided by Graduate School of Economics, Hitotsubashi University in its series Discussion Papers with number 2011-07.
Length: 27 p.
Date of creation: Aug 2011
Date of revision:
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-08-22 (All new papers)
- NEP-ECM-2011-08-22 (Econometrics)
- NEP-ETS-2011-08-22 (Econometric Time Series)
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- Hu, Yaozhong & Nualart, David, 2010. "Parameter estimation for fractional Ornstein-Uhlenbeck processes," Statistics & Probability Letters, Elsevier, vol. 80(11-12), pages 1030-1038, June.
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