Parameter least-squares estimation for time-inhomogeneous Ornstein–Uhlenbeck process

Getut Pramesti

Monte Carlo Methods and Applications, 2023, vol. 29, issue 1, 1-32

Abstract: We address the least-squares estimation of the drift coefficient parameter θ = ( λ , A , B , ω p ) \theta=(\lambda,A,B,\omega_{p}) of a time-inhomogeneous Ornstein–Uhlenbeck process that is observed at high frequency, in which the discretized step size ℎ satisfies h → 0 h\to 0 . In this paper, under the conditions n ⁢ h → ∞ nh\to\infty and n ⁢ h 2 → 0 nh^{2}\to 0 , we prove the consistency and the asymptotic normality of the estimators. We obtain the convergence of the parameters at rate n ⁢ h \sqrt{nh} , except for ω p \omega_{p} at n 3 ⁢ h 3 \sqrt{n^{3}h^{3}} . To verify our theoretical findings, we do a simulation study. We then illustrate the use of the proposed model in fitting the energy use of light fixtures in one Belgium household and the stock exchange.

Keywords: Least-squares estimator; estimation; Ornstein–Uhlenbeck process (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1515/mcma-2022-2127

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