Modelización de series temporales complejas: de las redes de telecomunicación a los mercados financieros

Este trabajo aborda el problema de modelizar sistemas din´amicos reales a partir del estudio de sus series temporales, usando una formulaci´on est´andar que pretende ser una abstracci´on universal de los sistemas din´amicos, independientemente de su naturaleza determinista, estoc´astica o h´ıbrida. Se parte de modelizaciones separadas de sistemas deterministas por un lado y estoc´asticos por otro, para converger finalmente en un modelo h´ıbrido que permite estudiar sistemas gen´ericos mixtos, esto es, que presentan una combinaci´on de comportamiento determinista y aleatorio. Este modelo consta de dos componentes, uno determinista consistente en una ecuaci´on en diferencias, obtenida a partir de un estudio de autocorrelaci´on, y otro estoc´astico que modeliza el error cometido por el primero. El componente estoc´astico es un generador universal de distribuciones de probabilidad, basado en un proceso compuesto de variables aleatorias, uniformemente distribuidas en un intervalo variable en el tiempo. Este generador universal es deducido en la tesis a partir de una nueva teor´ıa sobre la oferta y la demanda de un recurso gen´erico. El modelo resultante puede formularse conceptualmente como una entidad con tres elementos fundamentales: un motor generador de din´amica determinista, una fuente interna de ruido generadora de incertidumbre y una exposici´on al entorno que representa las interacciones del sistema real con el mundo exterior. En las aplicaciones estos tres elementos se ajustan en base al hist´orico de las series temporales del sistema din´amico. Una vez ajustados sus componentes, el modelo se comporta de una forma adaptativa tomando como inputs los nuevos valores de las series temporales del sistema y calculando predicciones sobre su comportamiento futuro. Cada predicci´on se presenta como un intervalo dentro del cual cualquier valor es equipro- bable, teniendo probabilidad nula cualquier valor externo al intervalo. De esta forma el modelo computa el comportamiento futuro y su nivel de incertidumbre en base al estado actual del sistema. Se ha aplicado el modelo en esta tesis a sistemas muy diferentes mostrando ser muy flexible para afrontar el estudio de campos de naturaleza dispar. El intercambio de tr´afico telef´onico entre operadores de telefon´ıa, la evoluci´on de mercados financieros y el flujo de informaci´on entre servidores de Internet son estudiados en profundidad en la tesis. Todos estos sistemas son modelizados de forma exitosa con un mismo lenguaje, a pesar de tratarse de sistemas f´ısicos totalmente distintos. El estudio de las redes de telefon´ıa muestra que los patrones de tr´afico telef´onico presentan una fuerte pseudo-periodicidad semanal contaminada con una gran cantidad de ruido, sobre todo en el caso de llamadas internacionales. El estudio de los mercados financieros muestra por su parte que la naturaleza fundamental de ´estos es aleatoria con un rango de comportamiento relativamente acotado. Una parte de la tesis se dedica a explicar algunas de las manifestaciones emp´ıricas m´as importantes en los mercados financieros como son los “fat tails”, “power laws” y “volatility clustering”. Por ´ultimo se demuestra que la comunicaci´on entre servidores de Internet tiene, al igual que los mercados financieros, una componente subyacente totalmente estoc´astica pero de comportamiento bastante “d´ocil”, siendo esta docilidad m´as acusada a medida que aumenta la distancia entre servidores. Dos aspectos son destacables en el modelo, su adaptabilidad y su universalidad. El primero es debido a que, una vez ajustados los par´ametros generales, el modelo se “alimenta” de los valores observables del sistema y es capaz de calcular con ellos comportamientos futuros. A pesar de tener unos par´ametros fijos, la variabilidad en los observables que sirven de input al modelo llevan a una gran riqueza de ouputs posibles. El segundo aspecto se debe a la formulaci´on gen´erica del modelo h´ıbrido y a que sus par´ametros se ajustan en base a manifestaciones externas del sistema en estudio, y no en base a sus caracter´ısticas f´ısicas. Estos factores hacen que el modelo pueda utilizarse en gran variedad de campos. Por ´ultimo, la tesis propone en su parte final otros campos donde se han obtenido ´exitos preliminares muy prometedores como son la modelizaci´on del riesgo financiero, los algoritmos de routing en redes de telecomunicaci´on y el cambio clim´atico. Abstract This work faces the problem of modeling dynamical systems based on the study of its time series, by using a standard language that aims to be an universal abstraction of dynamical systems, irrespective of their deterministic, stochastic or hybrid nature. Deterministic and stochastic models are developed separately to be merged subsequently into a hybrid model, which allows the study of generic systems, that is to say, those having both deterministic and random behavior. This model is a combination of two different components. One of them is deterministic and consisting in an equation in differences derived from an auto-correlation study and the other is stochastic and models the errors made by the deterministic one. The stochastic component is an universal generator of probability distributions based on a process consisting in random variables distributed uniformly within an interval varying in time. This universal generator is derived in the thesis from a new theory of offer and demand for a generic resource. The resulting model can be visualized as an entity with three fundamental elements: an engine generating deterministic dynamics, an internal source of noise generating uncertainty and an exposure to the environment which depicts the interactions between the real system and the external world. In the applications these three elements are adjusted to the history of the time series from the dynamical system. Once its components have been adjusted, the model behaves in an adaptive way by using the new time series values from the system as inputs and calculating predictions about its future behavior. Every prediction is provided as an interval, where any inner value is equally probable while all outer ones have null probability. So, the model computes the future behavior and its level of uncertainty based on the current state of the system. The model is applied to quite different systems in this thesis, showing to be very flexible when facing the study of fields with diverse nature. The exchange of traffic between telephony operators, the evolution of financial markets and the flow of information between servers on the Internet are deeply studied in this thesis. All these systems are successfully modeled by using the same “language”, in spite the fact that they are systems physically radically different. The study of telephony networks shows that the traffic patterns are strongly weekly pseudo-periodic but mixed with a great amount of noise, specially in the case of international calls. It is proved that the underlying nature of financial markets is random with a moderate range of variability. A part of this thesis is devoted to explain some of the most important empirical observations in financial markets, such as “fat tails”, “power laws” and “volatility clustering”. Finally it is proved that the communication between two servers on the Internet has, as in the case of financial markets, an underlaying random dynamics but with a narrow range of variability, being this lack of variability more marked as the distance between servers is increased. Two aspects of the model stand out as being the most important: its adaptability and its universality. The first one is due to the fact that once the general parameters have been adjusted , the model is “fed” on the observable manifestations of the system in order to calculate its future behavior. Despite the fact that the model has fixed parameters the variability in the observable manifestations of the system, which are used as inputs of the model, lead to a great variability in the possible outputs. The second aspect is due to the general “language” used in the formulation of the hybrid model and to the fact that its parameters are adjusted based on external manifestations of the system under study instead of its physical characteristics. These factors made the model suitable to be used in great variety of fields. Lastly, this thesis proposes other fields in which preliminary and promising results have been obtained, such as the modeling of financial risk, the development of routing algorithms for telecommunication networks and the assessment of climate change.

A personal data framework for exchanging knowledge about users in new financial services

Personal data is a key asset for many companies, since this is the essence in providing personalized services. Not all companies, and specifically new entrants to the markets, have the opportunity to access the data they need to run their business. In this paper, we describe a comprehensive personal data framework that allows service providers to share and exchange personal data and knowledge about users, while facilitating users to decide who can access which data and why. We analyze the challenges related to personal data collection, integration, retrieval, and identity and privacy management, and present the framework architecture that addresses them. We also include the validation of the framework in a banking scenario, where social and financial data is collected and properly combined to generate new socio-economic knowledge about users that is then used by a personal lending service.

Risk Allocation in Toll Highway Concessions in Spain: Lessons from Economic Recession

Spain has a long tradition of encouraging toll highways by granting concessions to private companies. Concessions in Spain have been characterized by a willingness to transfer considerable risk to the private sector. Traffic demand, acquisition of the right-of-way, and financial risk have often been allocated to the private sector. From 1996 to 2011, 16 toll highway concessions, covering a total distance of 835 km, were awarded by the central government of Spain with this approach. Some of those highways started their operations just before the economic recession began. The recession had negative consequences for Spain's economy. The gross domestic product per capita plummeted, and the unemployment rate increased from 9% to 20% of the working population in just 2 years. The recession also had severe consequences for the economic performance of toll highway concessions. Traffic levels declined at a much greater rate than did the gross domestic product. In addition, the conditions imposed by the financial markets on borrowers became much stricter because of the liquidity crisis. This study analyzes the impact that the economic recession ultimately had on the performance of toll highway concessions in Spain and the actions that the government adopted to avoid the bankruptcy of the concessionaires. It was found that the economic recession helped identify some deficiencies in how risk had been allocated in Spain. The measures that both Spain and the European Union are adopting so as to improve risk allocation are discussed.

Exploring the economic value of personal information from firms' financial statements

Currently personal data gathering in online markets is done on a far larger scale and much cheaper and faster than ever before. Within this scenario, a number of highly relevant companies for whom personal data is the key factor of production have emerged. However, up to now, the corresponding economic analysis has been restricted primarily to a qualitative perspective linked to privacy issues. Precisely, this paper seeks to shed light on the quantitative perspective, approximating the value of personal information for those companies that base their business model on this new type of asset. In the absence of any systematic research or methodology on the subject, an ad hoc procedure is developed in this paper. It starts with the examination of the accounts of a number of key players in online markets. This inspection first aims to determine whether the value of personal information databases is somehow reflected in the firms’ books, and second to define performance measures able to capture this value. After discussing the strengths and weaknesses of possible approaches, the method that performs best under several criteria (revenue per data record) is selected. From here, an estimation of the net present value of personal data is derived, as well as a slight digression into regional differences in the economic value of personal information.