Semi-parametric estimation of the long-range dependence parameter was a subject of major interest in recent y ears. The purpose of this paper is to put in a common framework several recent contributions of that topic. We will focus in particular on spectral methods, w h i c h consist in estimating the exponent of the singularity of the spectral density function at zero frequency and on time-domain methods, which are based on the estimation on the rate of convergence to zero of the autocovariance coe cients and/or on the scaling of the variance of processes deduced from the original process by generalized aggregation. R esum e. L'estimation du coe cient de longue port ee dans un contexte semiparam etrique est un sujet dont l'importance s'est consid erablement d evelopp e au cours des derni eres ann ees. L'objet de cet article est de synth etiser un certain nombre de d eveloppement r ecents dans ce domaine. Nous nous concentrons en particulier sur les m ethodes spectrales, qui consistent a estimer l'exposant de la singularit e de la densit e spectrale a l a f r equence nulle, et les m ethodes temporelles, bas ees sur l'exposant d e d ecroissance de la fonction d'autocorr elation a l'in ni, ou de fa con similaire, sur la loi d' echelle de la variance de processus d eduits du processus initial par aggr egation (g en eralis ee). c Soci et e de Math ematiques Appliqu ees et Industrielles.

A limit order book provides information on available limit order prices and their volumes. Based on these quantities, we give an empirical result on the relationship between the bid-ask liquidity balance and trade sign and we show that the liquidity balance on the best bid/best ask is quite informative for predicting the future market order's direction. Moreover, we define price jump as a sell (buy) market order arrival which is executed at a price which is smaller (larger) than the best bid (best ask) price at the moment just after the precedent market order arrival. Features are then extracted related to limit order volumes, limit order price gaps, market order information and limit order event information. Logistic regression is applied to predict the price jump from the features of a limit order book. LASSO logistic regression is introduced to help us make variable selection from which we are capable to highlight the importance of different features in predicting the future price jump. In order to get rid of the intraday data seasonality, the analysis is based on two separated datasets: morning dataset and afternoon dataset. Based on an analysis on forty largest French stocks of CAC40, we find that trade sign and market order size as well as the liquidity on the best bid (best ask) are consistently informative for predicting the incoming price jump.

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This paper highlights some fundamental issues involved in the study of large-scale dynamical systems. Two particular topics are discussed in some detail, one dealing with the management of active sensors via partially observable Markov decision processes, and the other dealing with the modeling, recognition and tracking of multi-function radars in an electronic warfare environment. I. INTRODUCTIONAll dynamical systems share a basic feature: the state of the system, be it scalar or vector, varies with time. Typically, the state is not measurable directly. Rather, in an indirect manner, it makes its effect measurable through a set of observables. As such, the characterization of dynamical systems is described by a state-space model, which, in general, embodies two equations: (i) State-evolution equation, which describes the evolution of the state as a function of time:where t denotes discrete time, x t denotes the state vector at time t, f(.) is a vector-valued function of its argument, and the vector w t denotes dynamic noise.(ii) Measurement equation, which takes one of two forms, depending on whether the system is passive or active: (a) Passive dynamical system, described by (2a) where the vector y t denotes the set of observables, g(.) denotes another vector-valued function, and the vector v t denotes measurement noise.where the additional vector a t denotes action taken by the system at time t. According to (2a) and (2b), it is the action a t that distinguishes an active dynamical system from a passive one. Most important, an active dynamical system explores its environment by taking action a t whenever the environment resides in state x t ; we may therefore think of (x t ,a t ) as a state-action pair. Just as the environment state x t spans a state space, the action a t spans a space of its own called the action space. The constituents of the action space may be different modalities, waveforms, functions, etc., over which the system is able to operate. On this basis, we say an active dynamical system is of a largescale kind due to a combination of three factors: (i) high dimensionality of the environment state space; (ii) high computational complexity of the nonlinear predictive model used in tracking the state of the environment; and (iii) high search complexity of the action space. In contrast, a passive dynamical system merely listens to its environment; and through observables produced by the environment, it infers the state of the environment. Accordingly, a passive dynamical system is said to be of a large-scale kind solely on the basis of factors (i) and (ii).The availability of an action space or its absence has serious implications for the specific functions which a dynamical system can perform. Specifically, an active dynamical system is capable of interacting with its environment; hence, through searching over the action space for an optimal policy, it has a natural capability to perform optimal control. On the other hand, a passive dynamical system is well positioned to model its environm...