Maximum likelihood estimation for the non-ergodic fractional Ornstein–Uhlenbeck process

Katsuto Tanaka ()

Statistical Inference for Stochastic Processes, 2015, vol. 18, issue 3, 315-332

Abstract: For the non-ergodic fractional Ornstein–Uhlenbeck (fO–U) process driven by the fractional Brownian motion, we deal with the maximum likelihood estimator (MLE) 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 distribution of the MLE, and explore its distributional properties by paying attention to the influence of $$H$$ H and the sampling span $$T$$ T . We also derive the asymptotic distribution of the MLE as $$T$$ T becomes large. It is shown that, unlike the ergodic case, the asymptotic distribution depends on $$H$$ H . We further consider the unit root testing problem in the fO–U process and compute the powers of the test based on the MLE. Copyright Springer Science+Business Media Dordrecht 2015

Keywords: Fractional Ornstein–Uhlenbeck process; Non-ergodic case; Maximum likelihood estimator; Characteristic function; Numerical integration; Unit root test; Primary 60H05; 60H35; Secondary 62M10 (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:18:y:2015:i:3:p:315-332

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DOI: 10.1007/s11203-014-9110-9

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