Minimum distance estimation of stationary and non-stationary ARFIMA processes

A new parametric minimum distance time-domain estimator for ARFIMA processes is introduced in this paper. The proposed estimator minimizes the sum of squared correlations of residuals obtained after filtering a series through ARFIMA parameters. The estimator iseasy to compute and is consistent and asymptotically normally distributed for fractionallyintegrated (FI) processes with an integration order d strictly greater than -0.75. Therefore, it can be applied to both stationary and non-stationary processes. Deterministic components are also allowed in the DGP. Furthermore, as a by-product, the estimation procedure provides an immediate check on the adequacy of the specified model. This is so because the criterion function, when evaluated at the estimated values, coincides with the Box-Pierce goodness of fit statistic. Empirical applications and Monte-Carlo simulations supporting the analytical results and showing the good performance of the estimator in finite samples are also provided.

Strategies for sequential prediction of stationary time series

We present simple procedures for the prediction of a real valued sequence. The algorithms are based on a combinationof several simple predictors. We show that if the sequence is a realization of a bounded stationary and ergodic random process then the average of squared errors converges, almost surely, to that of the optimum, given by the Bayes predictor. We offer an analog result for the prediction of stationary gaussian processes.

A nonlinear threshold model for the dependence of extremes of stationary sequences

One of the main implications of the efficient market hypothesis (EMH) is that expected future returns on financial assets are not predictable if investors are risk neutral. In this paper we argue that financial time series offer more information than that this hypothesis seems to supply. In particular we postulate that runs of very large returns can be predictable for small time periods. In order to prove this we propose a TAR(3,1)-GARCH(1,1) model that is able to describe two different types of extreme events: a first type generated by large uncertainty regimes where runs of extremes are not predictable and a second type where extremes come from isolated dread/joy events. This model is new in the literature in nonlinear processes. Its novelty resides on two features of the model that make it different from previous TAR methodologies. The regimes are motivated by the occurrence of extreme values and the threshold variable is defined by the shock affecting the process in the preceding period. In this way this model is able to uncover dependence and clustering of extremes in high as well as in low volatility periods. This model is tested with data from General Motors stocks prices corresponding to two crises that had a substantial impact in financial markets worldwide; the Black Monday of October 1987 and September 11th, 2001. By analyzing the periods around these crises we find evidence of statistical significance of our model and thereby of predictability of extremes for September 11th but not for Black Monday. These findings support the hypotheses of a big negative event producing runs of negative returns in the first case, and of the burst of a worldwide stock market bubble in the second example. JEL classification: C12; C15; C22; C51 Keywords and Phrases: asymmetries, crises, extreme values, hypothesis testing, leverage effect, nonlinearities, threshold models

On Ito's formula for elliptic diffusion processes

Bardina and Jolis [Stochastic process. Appl. 69 (1997) 83-109] prove an extension of Ito's formula for F(Xt, t), where F(x, t) has a locally square-integrable derivative in x that satisfies a mild continuity condition in t and X is a one-dimensional diffusion process such that the law of Xt has a density satisfying certain properties. This formula was expressed using quadratic covariation. Following the ideas of Eisenbaum [Potential Anal. 13 (2000) 303-328] concerning Brownian motion, we show that one can re-express this formula using integration over space and time with respect to local times in place of quadratic covariation. We also show that when the function F has a locally integrable derivative in t, we can avoid the mild continuity condition in t for the derivative of F in x.

Selecting negotiation processes with Health Care

We address the question of how a third-party payer (e.g. an insurer) decides what providers to contract with. Three different mechanisms are studied and their properties compared. A first mechanism consists in the third-party payer setting up a bargaining procedure with both providers jointly and simultaneously. A second mechanism envisages the outcome of the same simultaneous bargaining but independently with every provider. Finally, the last mechanism is of different nature. It is the so-called "any willing provider" where the third-party payer announces a contract and every provider freely decides to sign it or not. The main finding is that the decision of the third-party payer depends on the surplus to be shared. When it is relatively high the third-party payer prefers the any willing provider system. When, on the contrary, the surplus is relatively low, the third-party payer will select one of the other two systems accor ing to how bargaining power is distributed.

On locally finite transitive two-ended digraphs

Projecte de recerca elaborat a partir d’una estada al Department de Matemàtica Aplicada de la Montanuniversität Leoben, Àustria, entre agost i desembre del 2006. L’ objectiu ha estat fer recerca sobre digrafs infinits amb dos finals, connexos i localment finits, i, en particular, en digrafs amb dos finals i altament arc-transitius. Malnic, Marusic et al. van introduir un nou tipus de relació d’equivalència en els vèrtexs d’un dígraf, anomenades relacions d’assolibilitat, que generalitzen i tenen el seu origen en un problema posat per Cameron et al., on les classes de la relació d’equivalència eren vèrtexs que pertanyien a un camí alternat del dígraf . Malnic et al. en el mencionat article van establir connexions ben estretes entre aquestes relacions d’assolibilitat i l'estructura de finals i creixement dels digrafs localment finits i transitius. En aquest treball, s’ha caracteritzat per complet aquestes relacions d’assolibitat en el cas de dígrafs localment finits i transitius amb exactament dos finals, en termes de la descomposició en números primers del número de línies que genera el digraf amb dos finals. A més, es nega la Conjectura 1 sostinguda per Seifter que afirmava que un digraf connex localment finit amb més d’un final era necessàriament o be 0-, 1- o altament arc-transitiu. Seifer havia donat una solució parcial a la conjectura pel cas de digrafs regulars amb grau primer que tinguin un conjunt de tall connex. En aquest treball, es descriu una família infinita de dígrafs regulars de grau dos, amb dos finals, exactament 2-arc transitius i no 3-arc transitius. Així, es nega la Conjectura de Seifter en el cas general, fins i tot per grau primer. Tot i així, la solució parcial donada per Seifter en el seu article és en cert sentit la millor possible i l'existència un conjunt de tall connex essencial.

Coupling and monotonicity of queueing processes

The main purpose of this work is to give a survey of main monotonicity properties of queueing processes based on the coupling method. The literature on this topic is quite extensive, and we do not consider all aspects of this topic. Our more concrete goal is to select the most interesting basic monotonicity results and give simple and elegant proofs. Also we give a few new (or revised) proofs of a few important monotonicity properties for the queue-size and workload processes both in single-server and multi- server systems. The paper is organized as follows. In Section 1, the basic notions and results on coupling method are given. Section 2 contains known coupling results for renewal processes with focus on construction of synchronized renewal instants for a superposition of independent renewal processes. In Section 3, we present basic monotonicity results for the queue-size and workload processes. We consider both discrete-and continuous-time queueing systems with single and multi servers. Less known results on monotonicity of queueing processes with dependent service times and interarrival times are also presented. Section 4 is devoted to monotonicity of general Jackson-type queueing networks with Markovian routing. This section is based on the notable paper [17]. Finally, Section 5 contains elements of stability analysis of regenerative queues and networks, where coupling and monotonicity results play a crucial role to establish minimal suficient stability conditions. Besides, we present some new monotonicity results for tandem networks.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

The role of attention in multisensory integration processes

Report for the scientific sojourn at the University of Queensland, Australia, between June to October 2007. The integration of sensory information coming from different modalities is a subjectively effortless and automatic process. However, recent findings converge on the idea that there might be some limitations on how much multisensory information can our brains integrate at a given moment. The overall objective of this research visit was to expand and reinforce our current line of research addressing the role that attention plays on the mechanisms responsible for multisensory integration. There is also a critical review of the literature as well as a list of research questions of potential interest in the area of the neuropsychology of multisensory attention.

Nano-electro-mechanical in dynamical cellular processes

Report for the scientific sojourn carried out at the Department of Structure and Constituents of Matter during 2007.The main focus of the work was on phenomena related to nano-electromechanical processes that take place on a cellular level. Additionally, it has also been performed independent work related to charge and energy transfer in bio molecules, energy transfer in coupled spin systems as well as electrodynamics of nonlinear metamaterials.

Desarrollo y aplicación de estrategias de control avanzado en procesos biológicos de tratamiento de efluentes contaminados

En este proyecto se ha desarrollado estrategias de control avanzadas para plantas de depuración de aguas residuales urbanas que eliminan conjuntamente materia orgánica, nitrógeno y fósforo. Las estrategias se han basado en el estudio multivariable del comportamiento del sistema, que ha producido subsidios para la utilización de lazos de control feedforward, de control predictivo y de un control de costes que automáticamente enviaba las consignas más adecuadas para los controladores de proceso. Para el desarrollo de las estrategias, se ha creado un sistema virtual de simulación (simulador) de plantas de depuradoras, basado en datos de literatura. Para el caso de una planta real, se ha desarrollado un simulador de la planta de Manresa (Catalunya). Sin embargo, el sistema de Manresa se ha utilizado exclusivamente para auxiliar los ingenieros de la planta en la tomada de decisiones de cambio de configuración para que la eliminación de fósforo se dé por la ruta biológica y no por la ruta química. La implementación de los simuladores ha permitido hacer muchas pruebas que en una planta real demandarían mucho tiempo y consumirían muchos recursos energéticos y financieros. Las estrategias de control más elaboradas han podido ahorrar hasta 150.000,00 Euros por año en relación a la operación de la planta sin el control automático. Cuanto a los estudios del modelo de la planta real, se concluyó que la eliminación biológica de fósforo puede sustituir el actual proceso químico de eliminación de fósforo, bajando los costes operacionales (costes del agente precipitante).

Stable stationary states of non-local interaction equations

"Vegeu el resum a l'inici del document del fitxer adjunt."

Locally univalent functions, VMOA, and the Dirichlet space

"Vegeu el resum a l'inici del document del fitxer adjunt."

A Schoenflies extension theorem for a class of locally bi-Lipschitz homeomorphisms

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