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Curato IV, Stelzer R, Ströh B. Central limit theorems for stationary random fields under weak dependence with application to ambit and mixed moving average fields. ANN APPL PROBAB 2022. [DOI: 10.1214/21-aap1722] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
| | | | - Bennet Ströh
- Institute of Mathematical Finance, Ulm University
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Courgeau V, Veraart AED. Likelihood theory for the graph Ornstein-Uhlenbeck process. STATISTICAL INFERENCE FOR STOCHASTIC PROCESSES 2021. [DOI: 10.1007/s11203-021-09257-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
AbstractWe consider the problem of modelling restricted interactions between continuously-observed time series as given by a known static graph (or network) structure. For this purpose, we define a parametric multivariate Graph Ornstein-Uhlenbeck (GrOU) process driven by a general Lévy process to study the momentum and network effects amongst nodes, effects that quantify the impact of a node on itself and that of its neighbours, respectively. We derive the maximum likelihood estimators (MLEs) and their usual properties (existence, uniqueness and efficiency) along with their asymptotic normality and consistency. Additionally, an Adaptive Lasso approach, or a penalised likelihood scheme, infers both the graph structure along with the GrOU parameters concurrently and is shown to satisfy similar properties. Finally, we show that the asymptotic theory extends to the case when stochastic volatility modulation of the driving Lévy process is considered.
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Sauri O. Pathwise Decompositions of Brownian Semistationary Processes. THEORY OF PROBABILITY AND ITS APPLICATIONS 2019. [DOI: 10.1137/s0040585x97t989404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Campese S. A limit theorem for moments in space of the increments of Brownian local time. ANN PROBAB 2017. [DOI: 10.1214/16-aop1093] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Benth FE, Eyjolfsson H. Simulation of volatility modulated Volterra processes using hyperbolic stochastic partial differential equations. BERNOULLI 2016. [DOI: 10.3150/14-bej675] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Chong C, Klüppelberg C. Integrability conditions for space–time stochastic integrals: Theory and applications. BERNOULLI 2015. [DOI: 10.3150/14-bej640] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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A Lévy-driven rainfall model with applications to futures pricing. ASTA ADVANCES IN STATISTICAL ANALYSIS 2015. [DOI: 10.1007/s10182-015-0246-8] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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