Unbalanced Fractional Cointegration and the No-Arbitrage Condition on Commodity Markets

Technical abstract: A necessary condition for two time series to be nontrivially cointegrated is the equality of their respective integration orders. Nonetheless, in some cases, the apparent unbalance of integration orders of the observables can be misleading and the cointegration theory applies all the same. This situation refers to unbalanced cointegration in the sense that balanced long run relationship can be recovered by an appropriate filtering of one of the time series. In this paper, we suggest a local Whittle estimator of bivariate unbalanced fractional cointegration systems. Focusing on a degenerating band around the origin, it estimates jointly the unbalance parameter, the long run coefficient and the integration orders of the regressor and the cointegrating errors. Its consistency is demonstrated for the stationary regions of the parameter space and a finite sample analysis is conducted by means of Monte Carlo experiments. An application to the no-arbitrage condition between crude oil spot and futures prices is proposed to illustrate the empirical relevance of the developed estimator. Non-technical abstract: The no-arbitrage condition between spot and future prices implies an analogous condition on their underlying volatilities. Interestingly, the long memory behavior of the volatility series also involves a long-run relationship that allows to test for the no-arbitrage condition by means of cointegration techniques. Unfortunately, the persistent nature of the volatility can vary with the future maturity, thereby leading to unbalanced integration orders between spot and future volatility series. Nonetheless, if a balanced long-run relationship can be recovered by an appropriate filtering of one of the time series, the cointegration theory applies all the same and unbalanced cointegration operates between the raw series. In this paper, we introduce a new estimator of unbalanced fractional cointegration systems that allows to test for the no-arbitrage condition between the crude oil spot and futures volatilities

Qualitative Possibilistic Mixed-Observable MDPs

National audiencePossibilistic and qualitative POMDPs (pi-POMDPs) are counterparts of POMDPs used to model situations where the agent's initial belief or observation probabilities are imprecise due to lack of past experiences or insufficient data collection. However, like probabilistic POMDPs, optimally solving pi-POMDPs is intractable: the finite belief state space exponentially grows with the number of system's states. In this paper, a possibilistic version of Mixed-Observable MDPs is presented to get around this issue: the complexity of solving pi-POMDPs, some state variables of which are fully observable, can be then dramatically reduced. A value iteration algorithm for this new formulation under infinite horizon is next proposed and the optimality of the returned policy (for a specified criterion) is shown assuming the existence of a "stay" action in some goal states. Experimental work finally shows that this possibilistic model outperforms probabilistic POMDPs commonly used in robotics, for a target recognition problem where the agent's observations are imprecise

Structured Possibilistic Planning Using Decision Diagrams

National audienceQualitative Possibilistic Mixed-Observable MDPs (π-MOMDPs), generalizing π-MDPs and π-POMDPs, are well-suited models to planning under uncertainty with mixed-observability when transition, observation and reward functions are not precisely known and can be qualitatively described. Functions defining the model as well as intermediate calculations are valued in a finite possibilistic scale L, which induces a finite belief state space under partial observability contrary to its probabilistic counterpart. In this paper, we propose the first study of factored π-MOMDP models in order to solve large structured planning problems under qualitative uncertainty, or considered as qualitative approximations of probabilistic problems. Building upon the SPUDD algorithm for solving factored (probabilistic) MDPs, we conceived a symbolic algorithm named PPUDD for solving factored π-MOMDPs. Whereas SPUDD’s decision diagrams’ leaves may be as large as the state space since their values are real numbers aggregated through additions and multiplications, PPUDD’s ones always remain in the finite scale L via min and max operations only. Our experiments show that PPUDD’s computation time is much lower than SPUDD, Symbolic-HSVI and APPL for possibilistic and probabilistic versions of the same benchmarks under either total or mixed observability, while still providing high-quality policies

Planning in Partially Observable Domains with Fuzzy Epistemic States and Probabilistic Dynamics

International audienceA new translation from Partially Observable MDP into Fully Observable MDP is described here. Unlike the classical translation, the resulting problem state space is finite, making MDP solvers able to solve this simplified version of the initial partially observable problem: this approach encodes agent beliefs with possibility distributions over states, leading to an MDP whose state space is a finite set of epistemic states. After a short description of the POMDP framework as well as notions of Possibility Theory, the translation is described in a formal manner with semantic arguments. Then actual computations of this transformation are detailed, in order to highly benefit from the factored structure of the initial POMDP in the final MDP size reduction and structure. Finally size reduction and tractability of the resulting MDP is illustrated on a simple POMDP problem

International Conference “American Literature and the Philosophical”

The international conference “American Literature and the Philosophical” was held in Paris on March 23-25 and was organized by Richard Anker (Université Clermont Auvergne), Thomas Constantinesco (Université Paris Diderot / IUF), Mathieu Duplay (Université Paris Diderot), Cécile Roudeau (Université Paris Diderot), and Stéphane Vanderhaeghe (Université Paris Vincennes Saint-Denis). For three days, the forty-seven speakers examined how literature can be apprehended as a philosophical discourse i..

Sensor Data Fusion For Hazard Mapping And Piloting

International audienceAutonomous landing on Mars, Moon or asteroids may require a Hazard Detection and Avoidance (HDA) system on-board the lander. Past studies on HDA dealt with the use of camera or LiDARs separately to detect dangerous slopes, boulders and shadow areas. The present work, performed in the frame of an ESA TRP, proposes to use jointly a camera and a LiDAR to take advantage of each while mitigating their drawbacks, consequently improving the HDA performances. Various algorithmic solutions and sensor configurations are proposed and tested in the Mars and asteroid landing cases

Emergence and cosmic evolution of the Kennicutt-Schmidt relation driven by interstellar turbulence

The scaling relations between the gas content and star formation rate of galaxies provide useful insights into processes governing their formation and evolution. We investigate the emergence and the physical drivers of the global Kennicutt-Schmidt (KS) relation at $0.25 \leq z \leq 4$ in the cosmological hydrodynamic simulation NewHorizon capturing the evolution of a few hundred galaxies with a resolution of $\sim$ 40 pc. The details of this relation vary strongly with the stellar mass of galaxies and the redshift. A power-law relation $\Sigma_{\rm SFR} \propto \Sigma_{\rm gas}^{a}$ with $a \approx 1.4$, like that found empirically, emerges at $z \approx 2 - 3$ for the most massive half of the galaxy population. However, no such convergence is found in the lower-mass galaxies, for which the relation gets shallower with decreasing redshift. At the galactic scale, the star formation activity correlates with the level of turbulence of the interstellar medium, quantified by the Mach number, rather than with the gas fraction (neutral or molecular), confirming previous works. With decreasing redshift, the number of outliers with short depletion times diminishes, reducing the scatter of the KS relation, while the overall population of galaxies shifts toward low densities. Using pc-scale star formation models calibrated with local Universe physics, our results demonstrate that the cosmological evolution of the environmental and intrinsic conditions conspire to converge towards a significant and detectable imprint in galactic-scale observables, in their scaling relations, and in their reduced scatter.Comment: 26 pages, 22 figure

Emergence and cosmic evolution of the Kennicutt-Schmidt relation driven by interstellar turbulence

© 2024 The Author(s). Published by EDP Sciences. This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), https://creativecommons.org/licenses/by/4.0/The scaling relations between the gas content and star formation rate of galaxies provide useful insights into the processes governing their formation and evolution. We investigated the emergence and the physical drivers of the global Kennicutt–Schmidt (KS) relation at 0.25 ≤ z ≤ 4 in the cosmological hydrodynamic simulation NEWHORIZON, capturing the evolution of a few hundred galaxies with a resolution down to 34 pc. The details of this relation vary strongly with the stellar mass of galaxies and the redshift. A power-law relation ΣSFR ∝ Σgasa with a ≈ 1.4, like that found empirically, emerges at z ≈ 2 − 3 for the more massive half of the galaxy population. However, no such convergence is found in the lower-mass galaxies, for which the relation gets shallower with decreasing redshift. At galactic scales, the star formation activity correlates with the level of turbulence of the interstellar medium, quantified by the Mach number, rather than with the gas fraction (neutral or molecular), confirming the conclusions found in previous works. With decreasing redshift, the number of outliers with short depletion times diminishes, reducing the scatter of the KS relation, while the overall population of galaxies shifts toward low densities. Our results, from parsec-scale star formation models calibrated with local Universe physics, demonstrate that the cosmological evolution of the environmental (e.g., mergers) and internal conditions (e.g., gas fractions) conspire to shape the KS relation. This is an illustration of how the interplay of global and local processes leaves a detectable imprint on galactic-scale observables and scaling relations.Peer reviewe

Early diagnosis of Alzheimer's disease using cortical thickness: impact of cognitive reserve

Brain atrophy measured by magnetic resonance structural imaging has been proposed as a surrogate marker for the early diagnosis of Alzheimer's disease. Studies on large samples are still required to determine its practical interest at the individual level, especially with regards to the capacity of anatomical magnetic resonance imaging to disentangle the confounding role of the cognitive reserve in the early diagnosis of Alzheimer's disease. One hundred and thirty healthy controls, 122 subjects with mild cognitive impairment of the amnestic type and 130 Alzheimer's disease patients were included from the ADNI database and followed up for 24 months. After 24 months, 72 amnestic mild cognitive impairment had converted to Alzheimer's disease (referred to as progressive mild cognitive impairment, as opposed to stable mild cognitive impairment). For each subject, cortical thickness was measured on the baseline magnetic resonance imaging volume. The resulting cortical thickness map was parcellated into 22 regions and a normalized thickness index was computed using the subset of regions (right medial temporal, left lateral temporal, right posterior cingulate) that optimally distinguished stable mild cognitive impairment from progressive mild cognitive impairment. We tested the ability of baseline normalized thickness index to predict evolution from amnestic mild cognitive impairment to Alzheimer's disease and compared it to the predictive values of the main cognitive scores at baseline. In addition, we studied the relationship between the normalized thickness index, the education level and the timeline of conversion to Alzheimer's disease. Normalized thickness index at baseline differed significantly among all the four diagnosis groups (P < 0.001) and correctly distinguished Alzheimer's disease patients from healthy controls with an 85% cross-validated accuracy. Normalized thickness index also correctly predicted evolution to Alzheimer's disease for 76% of amnestic mild cognitive impairment subjects after cross-validation, thus showing an advantage over cognitive scores (range 63–72%). Moreover, progressive mild cognitive impairment subjects, who converted later than 1 year after baseline, showed a significantly higher education level than those who converted earlier than 1 year after baseline. Using a normalized thickness index-based criterion may help with early diagnosis of Alzheimer's disease at the individual level, especially for highly educated subjects, up to 24 months before clinical criteria for Alzheimer's disease diagnosis are met