Parameter estimation in nonlinear multivariate stochastic differential equations based on splitting schemes
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Parameter estimation in nonlinear multivariate stochastic differential equations based on splitting schemes. / Pilipovic, Predrag; Samson, Adeline; Ditlevsen, Susanne.
I: Annals of Statistics, Bind 52, Nr. 2, 2024, s. 842-867.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Parameter estimation in nonlinear multivariate stochastic differential equations based on splitting schemes
AU - Pilipovic, Predrag
AU - Samson, Adeline
AU - Ditlevsen, Susanne
N1 - Publisher Copyright: © Institute of Mathematical Statistics, 2024.
PY - 2024
Y1 - 2024
N2 - The likelihood functions for discretely observed nonlinear continuous time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with advantages, disadvantages and limitations depending on the application. Most applications still use the Euler–Maruyama discretization, despite many proofs of its bias. More sophisticated methods, such as Kessler’s Gaussian approximation, Ozaki’s local linearization, Aït–Sahalia’s Hermite expansions or MCMC methods, might be complex to implement, do not scale well with increasing model dimension or can be numerically unstable. We propose two efficient and easy-to-implement likelihood-based estimators based on the Lie–Trotter (LT) and the Strang (S) splitting schemes. We prove that S has Lp convergence rate of order 1, a property already known for LT. We show that the estimators are consistent and asymptotically efficient under the less restrictive one-sided Lipschitz assumption. A numerical study on the 3-dimensional stochastic Lorenz system complements our theoretical findings. The simulation shows that the S estimator performs the best when measured on precision and computational speed compared to the state-of-the-art.
AB - The likelihood functions for discretely observed nonlinear continuous time models based on stochastic differential equations are not available except for a few cases. Various parameter estimation techniques have been proposed, each with advantages, disadvantages and limitations depending on the application. Most applications still use the Euler–Maruyama discretization, despite many proofs of its bias. More sophisticated methods, such as Kessler’s Gaussian approximation, Ozaki’s local linearization, Aït–Sahalia’s Hermite expansions or MCMC methods, might be complex to implement, do not scale well with increasing model dimension or can be numerically unstable. We propose two efficient and easy-to-implement likelihood-based estimators based on the Lie–Trotter (LT) and the Strang (S) splitting schemes. We prove that S has Lp convergence rate of order 1, a property already known for LT. We show that the estimators are consistent and asymptotically efficient under the less restrictive one-sided Lipschitz assumption. A numerical study on the 3-dimensional stochastic Lorenz system complements our theoretical findings. The simulation shows that the S estimator performs the best when measured on precision and computational speed compared to the state-of-the-art.
KW - Asymptotic normality
KW - consistency
KW - L convergence
KW - splitting schemes
KW - stochastic differential equations
KW - stochastic Lorenz system
U2 - 10.1214/24-AOS2371
DO - 10.1214/24-AOS2371
M3 - Journal article
AN - SCOPUS:85193785283
VL - 52
SP - 842
EP - 867
JO - Annals of Statistics
JF - Annals of Statistics
SN - 0090-5364
IS - 2
ER -
ID: 395025962