Goodness‐of‐fit tests for Lévy‐driven Ornstein‐Uhlenbeck processes

Abdelrazeq, Ibrahim; Ivanoff, B. Gail; Kulik, Rafał

doi:10.1002/cjs.11352

Cited by 4 publications

(5 citation statements)

References 14 publications

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“…Indeed, there exists a family of Poisson processes N (j) t with elementwise intensity λ = (λ (1) , . .…”

Section: Finite Jump Activity Casementioning

confidence: 99%

“…Remark 5.3. The parametric bootstrap used in the following sections is supported by the theoretical guarantees presented in [48,1]: consistent parameter estimators for the driving Lévy noise distribution are enough to replicate the true dynamics of the GrOU process. Although those results are proved for distributions characterised by their first two moments [1, Th.…”

Section: Generalised Hyperbolic Distributionmentioning

confidence: 99%

“…Finally, under the finite jump activity assumption (Assumption 8), remark that J t is a compound Poisson process. Indeed, there are Poisson processes N (j) t with elementwise finite intensities λ (j) such that (λ (1) , . .…”

Section: D2 Finite Jump Activitymentioning

confidence: 99%

“…Finally, the technical lemmas and propositions are stated in Appendix D whilst the proofs are relegated to Appendix E & F for a clearer layout of the argument. Finally, implementation details, R code and reproducible plots are available on GitHub (numerical routines 1 , end-to-end scripts 2 ).…”

Section: Introductionmentioning

confidence: 99%

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High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2022

Electron. J. Statist.

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We consider the Graph Ornstein-Uhlenbeck (GrOU) process observed on a non-uniform discrete timegrid and introduce discretised maximum likelihood estimators with parameters specific to the whole graph or specific to each component of the graph. Under a high-frequency sampling scheme, we study the asymptotic behaviour of those estimators as the mesh size of the observation grid goes to zero. We prove two stable central limit theorems to the same distribution as in the continuously-observed case under both finite and infinite jump activity for the Lévy driving noise. In addition to providing the consistency of the estimators, the stable convergence allows us to consider probabilistic sparse inference procedures on the edges themselves when a graph structure is not explicitly available. It also preserves its asymptotic properties. In particular, we also show the asymptotic normality and consistency of an Adaptive Lasso scheme. We apply the new estimators to wind capacity factor measurements, i.e. the ratio between the wind power produced locally compared to its rated peak power, across fifty locations in Northern Spain and Portugal. We compare those estimators to the standard least squares estimator through a simulation study extending known univariate results across graph configurations, noise types and amplitudes.

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“…Indeed, there exists a family of Poisson processes N (j) t with elementwise intensity λ = (λ (1) , . .…”

Section: Finite Jump Activity Casementioning

confidence: 99%

Section: Generalised Hyperbolic Distributionmentioning

confidence: 99%

Section: D2 Finite Jump Activitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Courgeau

Veraart

2022

Electron. J. Statist.

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“…The Ornstein–Uhlenbeck (OU) process has a wide array of applications in modelling the stochastic dynamics of various processes in the natural and social sciences including those in the economic and financial markets; see Chen, Mamon & Davison () for a survey, and Abdelrazeq, Ivanoff & Kulik () for some recent statistical developments involving this process. The classical OU model typically assumes that the drift component remains the same for the entire modelling‐time horizon and thus, it may not perform well when the mean level of the process varies with time.…”

Section: Introductionmentioning

confidence: 99%

Inference for a change‐point problem under an OU setting with unequal and unknown volatilities

2019

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An Ornstein–Uhlenbeck (OU) process is employed as a versatile model to capture the mean‐reverting and stochastic evolution of many variables in various fields of applications including finance and economics. Within the OU setting, we develop a new estimation method to determine the unknown change‐point location under the assumption that the volatilities before and after the change point in a time series are unequal. Our method hinges on the concept of a weighted least sum of squared errors approach and enhanced by a fusion of an iterative algorithm. The consistency of the change‐point estimator is established. This article highlights a numerical implementation on simulated and observed financial market data demonstrating the significant flexibility and accuracy of our proposed modelling and estimation method. The Canadian Journal of Statistics 48: 62–78; 2020 © 2019 Statistical Society of Canada

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Optimal trading strategies for Lévy-driven Ornstein–Uhlenbeck processes

Endres

Stübinger

2019

Applied Economics

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This study derives an optimal pairs trading strategy based on a Lévy-driven Ornstein-Uhlenbeck process and applies it to high-frequency data of the S&P 500 constituents from 1998 to 2015. Our model provides optimal entry and exit signals by maximizing the expected return expressed in terms of the first-passage time of the spread process. An explicit representation of the strategy's objective function allows for direct optimization without Monte Carlo methods. Categorizing the data sample into 10 economic sectors, we depict both the performance of each sector and the efficiency of the strategy in general. Results from empirical back-testing show strong support for the profitability of the model with returns after transaction costs ranging from 31.90 percent p.a. for the sector "Consumer Staples" to 278.61 percent p.a. for the sector "Financials". We find that the remarkable returns across all economic sectors are strongly driven by model parameters and sector size. Jump intensity decreases over time with strong outliers in times of high market turmoils. The value-add of our Lévy-based model is demonstrated by benchmarking it with quantitative strategies based on Brownian motion-driven processes.

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Goodness‐of‐fit tests for Lévy‐driven Ornstein‐Uhlenbeck processes

Cited by 4 publications

References 14 publications

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

High-frequency estimation of the Lévy-driven Graph Ornstein-Uhlenbeck process

Inference for a change‐point problem under an OU setting with unequal and unknown volatilities

Optimal trading strategies for Lévy-driven Ornstein–Uhlenbeck processes

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