Distributions of the maximum likelihood and minimum contrast estimators associated with the fractional Ornstein–Uhlenbeck process

Katsuto Tanaka ()

Statistical Inference for Stochastic Processes, 2013, vol. 16, issue 3, 173-192

Abstract: We 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 $$H$$ H is known and is in $$[1/2, 1)$$ [ 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 $$H$$ H and the sampling span $$M$$ M . We also 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. Copyright Springer Science+Business Media Dordrecht 2013

Keywords: Fractional Ornstein–Uhlenbeck process; Maximum likelihood estimator; Minimum contrast estimator; Characteristic function; Unit root test; Primary 60H05; 60H35; Secondary 62M10 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:16:y:2013:i:3:p:173-192

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DOI: 10.1007/s11203-013-9085-y

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