Statistical inference for stochastic differential equations

Craigmile, Peter F.; Herbei, Radu; Liu, Ge; Schneider, Grant

doi:10.1002/wics.1585

Cited by 11 publications

(3 citation statements)

References 120 publications

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“…But for scalar SDEs and adequate time-series, exact limit distributions are known for drift and diffusion estimators under mild assumptions (Bandi and Phillips 2007). See Craigmile et al (2023) for additional review on statistical inference of SDEs.…”

Section: Introductionmentioning

confidence: 99%

Robust Bellman State Prediction with Learning and Model Preferences

Estey

2024

Preprint

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I contribute to stochastic modeling methodology in a theoretical framework spanning core decisions in the model's lifetime. These are predicting an out-of-sample unit's latent state even from non-series data, deciding when to start and stop learning about the state variable, and choosing models from important trade-offs. States evolve from linear dynamics with time-varying predictors and coefficients (drift) and generalized continuous noise (diffusion). Coefficients must address misprediction costs, data complexity, and distributional uncertainty (ambiguity) about the state's diffusion and stopping time. I exactly solve a stochastic dynamic program robust to worst-case costs from both uncertainties. The Bellman optimal coefficients extend generalized ridge regression by out-of-sample components impacting value changes given state changes. Performance issues trigger sequential analysis whether learning alternative models, given the effort, is better than keeping baseline. Learning is method-general and stops in fewest average attempts within decision errors. I derive preference functions for comparing models with state and cost-change constraints to decide a model, joint-time state and value distributions, and other properties beneficial to modelers.

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Section: Introductionmentioning

confidence: 99%

Robust Bellman State Prediction with Learning and Model Preferences

Estey

2024

Preprint

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“…In this context, diffusion models have been extensively used in numerous areas, namely, in economics, physics, the life sciences and engineering. However, inference on diffusion models for discretely observed data is challenging because a closed-form expression of the transition density of the process, and thus, of the likelihood, is often unavailable, see [1] for a survey on available inference methods for diffusion models, or [2] for a more recent review.…”

Section: Introductionmentioning

confidence: 99%

Unbiased likelihood-based estimation of Wright-Fisher diffusion processes

García-Pareja¹,

Nobile²

2023

Preprint

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In this paper we propose an unbiased Monte Carlo maximum likelihood estimator for discretely observed Wright-Fisher diffusions. Our approach is based on exact simulation techniques that are of special interest for diffusion processes defined on a bounded domain, where numerical methods typically fail to remain within the required boundaries. We start by building unbiased maximum likelihood estimators for scalar diffusions and later present an extension to the multidimensional case. Consistency results of our proposed estimator are also presented and the performance of our method is illustrated through a numerical example.

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“…The parameter estimation theory for SDE driven by Brownian motions are well know in the literature. Some traditional methods are the maximum likelihood estimator (MLE) or or the least squares estimator (LSE) techniques, [33,13,27,11], based on the Girsanov density. The consitency and the asymptotic distribution are well studied, see for instance [13,27], [21], [45], [1].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation for a Class of Stable Driven Stochastic Differential Equations

Manou-Abi

2023

Preprint

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In this paper, we consider parameter estimation for a stochastic process observed at some discrete times that is a solution of a given class of stochastic differential equations driven by α-stable processes, α ∈ (1, 2). Firstly, we consider the diffusion coefficients parameters estimation problem such as the scaling parameter and the driving stable process parameters. Secondly, we address the question of the joint estimation with the drift coefficients for Stable driven Cox–Ingersoll–Ross and Ornstein-Uhlenbeck processes. Our methodology which is based on the use of Nadaraya-Watson estimator is new according to the literature of such estimation problem. Indeed it is based on a combination of the characteristic sample function and the (linear or weighted) regression methods. We discuss the validity and efficiency of the numeric implementation of the estimators on synthetic data and real financial data as indexes and exchange rates. As a forthcoming work, we intend to provide a package (in the R programming language) for this type of estimation problem.

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Statistical inference for stochastic differential equations

Cited by 11 publications

References 120 publications

Robust Bellman State Prediction with Learning and Model Preferences

Robust Bellman State Prediction with Learning and Model Preferences

Unbiased likelihood-based estimation of Wright-Fisher diffusion processes

Parameter Estimation for a Class of Stable Driven Stochastic Differential Equations

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