Statistical estimation of multivariate Ornstein–Uhlenbeck processes and applications to co-integration

Vicky Fasen

Journal of Econometrics, 2013, vol. 172, issue 2, 325-337

Abstract: Ornstein–Uhlenbeck models are continuous-time processes which have broad applications in finance as, e.g., volatility processes in stochastic volatility models or spread models in spread options and pairs trading. The paper presents a least squares estimator for the model parameter in a multivariate Ornstein–Uhlenbeck model driven by a multivariate regularly varying Lévy process with infinite variance. We show that the estimator is consistent. Moreover, we derive its asymptotic behavior and test statistics. The results are compared to the finite variance case. For the proof we require some new results on multivariate regular variation of products of random vectors and central limit theorems. Furthermore, we embed this model in the setup of a co-integrated model in continuous time.

Keywords: Asymptotic; Co-integration; Continuous-time process; Multivariate regular variation; Ornstein–Uhlenbeck process; Point estimation; Stable Lévy process; t-ratio statistic; Wald-statistic (search for similar items in EconPapers)
JEL-codes: C13 C23 (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:172:y:2013:i:2:p:325-337

DOI: 10.1016/j.jeconom.2012.08.019

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