Network reconstruction is the process of recovering a unique structured representation of some dynamic system using input-output data and some additional knowledge about the structure of the system. Many network reconstruction algorithms have been proposed in recent years, most dealing with the reconstruction of strictly proper networks (i.e., networks that require delays in all dynamics between measured variables). However, no reconstruction technique presently exists capable of recovering both the structure and dynamics of networks where links are proper (delays in dynamics are not required) and not necessarily strictly proper.The ultimate objective of this dissertation is to develop algorithms capable of reconstructing proper networks, and this objective will be addressed in three parts. The first part lays the foundation for the theory of mathematical representations of proper networks, including an exposition on when such networks are well-posed (i.e., physically realizable). The second part studies the notions of abstractions of a network, which are other networks that preserve certain properties of the original network but contain less structural information. As such, abstractions require less a priori information to reconstruct from data than the original network, which allows previously-unsolvable problems to become solvable. The third part addresses our original objective and presents reconstruction algorithms to recover proper networks in both the time domain and in the frequency domain.

Exponential smoothing algorithms are very attractive for the practical world such as in industry. When considering bivariate exponential smoothing methods, in addition to the properties of univariate methods, additional properties give insight to relationships between the two components of a process, and also to the overall structure of the model. It is important to study these properties, but even with the merits the bivariate exponential smoothing algorithms have, exponential smoothing algorithms are nonstatistical/nonstochastic and to study the properties within exponential smoothing may be worthless. As an alternative approach, the (bivariate) ARIMA and the structural models which are classes of statistical models, are shown to generalize the exponential smoothing algorithms. We study these properties within these classes as they will have implications on exponential smoothing algorithms. Forecast properties are studied using the state space model and the Kalman filter. Comparison of ARIMA and structural model completes the study. / Mathematical Sciences / M. Sc. (Statistics)

This thesis studies bubbles in the U.S. stock market and how they are influenced by monetary policy pursued by the FED. Using Kalman filtering, the log-real price of S&P 500 is decomposed into a market-fundamentals component and a bubble component. The market-fundamentals component depends on the expected future dividends and the required rate of return, while the bubble component is treated as an unobserved state vector in the state-space model. The results suggest that, mainly in recent decades, the bubble has accounted for a substantial portion of S&P 500 price dynamics and might have played a significant role during major bull and bear markets. The innovation of this thesis is that it goes one step further and investigates the effects of monetary policy on both estimated components of S&P 500. For this purpose, the block- restriction VAR model is employed. The findings indicate that the decreasing interest rates have a significant short-term positive effect on the market-fundamentals component but not on the bubble. On the other hand, quantitative easing seems to have a positive effect on the bubble but not on the market-fundamentals component. Finally, the results suggest that the FED has not been successful at distinguishing between stock price movements due to fundamentals or the price misalignment.

[pt] Esta Dissertação procura, sob um enfoque freqüentista, discutir tecnologias para que se imponham restrições no processo de estimação de componentes não observáveis associadas a um modelo em Espaço de Estado (EE) arbitrário. O escopo do texto abrange desde procedimentos propostos pioneiramente por Howard Doran para restrições de igualdade, lineares e/ou não lineares, invariantes ou variantes no tempo, em modelos em EE lineares, até a adoção e o ajuste de estruturas mais delicadas, como os modelos em EE não lineares. Entende-se que estes últimos se constituem em uma alternativa relevante, caso seja requerida, por exemplo, a imposição de restrições de desigualdade. Técnicas e estratégias de implementação são apresentadas, debatidas e comparadas, incluindo-se também o processo de estimação de parâmetros desconhecidos e a questão de diagnósticos. Ao final, são apresentados exercícios empíricos com base nas tecnologias discutidas. Os modelos propostos para esta ilustração visam à realização da análise dinâmica de estilo baseado no retorno para carteiras de investimento brasileiras (a versão estática desses modelos fora introduzida por William Sharpe, para carteiras norte-americanas), os quais devem, eventualmente, abranger dois tipos de restrições nas componentes de interesse, quais sejam, um de igualdade e outro de desigualdade. / [en] This Dissertation aims, in a frequentist way, to discuss technologies for imposing restrictions in non-observable components associated with an arbitrary State Space (SS) model. The text scope ranges from procedures proposed originally by Howard Doran for equality, linear or non- linear, time invariant or time varying restrictions in a linear SS model, to adoption and estimation of more complicated structures like non-linear SS models. It is understood that these last ones are a relevant alternative, in cases of, for instance, inequality restrictions requirement. Implementation techniques and strategies are given, debated and compared, also including unknown parameters estimation and diagnostics analysis. At the end, empirical exercises are presented based on discussed methodologies. The proposed models for this illustration aim at dynamic return based style analysis for Brazilian investment portfolios (the static version of these models had been introduced by William Sharpe, for American portfolios), which shall eventually satisfy two kinds of restrictions on components of interest, namely one of equality and other of inequality.

Nous considérions des modèles à espace d'état où les observations sont multicatégorielles et longitudinales, et l'état est décrit par des modèles du type CHARN. Nous estimons l'état au moyen des récursivités de Kalman généralisées. Celles-ci reposent sur l'application d'une variété de filtres particulaires et de l’algorithme EM. Nos résultats sont appliqués à l'estimation du trait latent en qualité de vie. Ce qui fournit une alternative et une généralisation des méthodes existantes dans la littérature. Ces résultats sont illustrés par des simulations numériques et une application aux données réelles sur la qualité de vie des femmes ayant subi une opération pour cause de cancer du sein / We consider state space models where the observations are multicategorical and longitudinal, and the state is described by CHARN models. We estimate the state by generalized Kalman recursions, which rely on a variety of particle filters and EM algorithm. Our results are applied to estimating the latent trait in quality of life, and this furnishes an alternative and a generalization of existing methods. These results are illustrated by numerical simulations and an application to real data in the quality of life of patients surged for breast cancer

The aim of this thesis is to model the dynamics of international term structure of interest rates taking into consideration several dependence channels.Thanks to a new international Treasury yield curve database, we observe that the explained variability decision criterion, suggested by the literature, is not able to select the best combination of factors characterizing the joint dynamics of yield curves. We propose a new methodology based on the maximisation of the likelihood function of a Gaussian state-space model with common and local factors. The associated identification problem is solved in an innovative way. By estimating several sets of countries, we select two global (and three local) factors which are also useful to forecast macroeconomic variables in each considered economy.In addition, our method allows us to detect hidden factors in the international bond returns. They are not visible through a classical principal component analysis of expected bond returns but they are helpful to forecast inflation and industrial production. Keywords: International treasury yield curves, common and local factors, state-space models, EM algorithm, International bond risk premia, principal components.

Diss. (sammanfattning) Stockholm : Handelshögskolan, 2008 Sammanfattning jämte 3 uppsatser

This thesis consists of three distinct parts. Part I introduces the basic concepts and the notion of general quadratic term structures (GQTS) essential in some of the following chapters. Part II focuses on credit risk models and Part III studies forward price term structure models using both the classical and the geometrical approach.  Part I is organized as follows. Chapter 1 is divided in two main sections. The first section presents some of the fundamental concepts which are a pre-requisite to the papers that follow. All of the concepts and results are well known and hence the section can be regarded as an introduction to notation and the basic principles of arbitrage theory. The second part of the chapter is of a more technical nature and its purpose is to summarize some key results on point processes or differential geometry that will be used later in the thesis. For finite dimensional factor models, Chapter 2 studies GQTS. These term structures include, as special cases, the affine term structures and Gaussian quadratic term structures previously studied in the literature. We show, however, that there are other, non-Gaussian, quadratic term structures and derive sufficient conditions for the existence of these GQTS for zero-coupon bond prices. On Part II we focus on credit risk models.   In Chapter 3 we propose a reduced form model for default that allows us to derive closed-form solutions for all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and survival probabilities. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity of default is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds. Further on, we study a model for portfolio credit risk that considers both firm-specific and systematic risk. The model generalizes the attempt of Duffie and Garleanu (2001). We find that the model produces realistic default correlation and clustering effects. Next, we show how to price CDOs, options on CDOs and how to incorporate the link to currently proposed credit indices. In Chapter 4 we start by presenting a reduced-form multiple default type of model and derive abstract results on the influence of a state variable $X$ on credit spreads when both the intensity and the loss quota distribution are driven by $X$. The aim is to apply the results to a real life situation, namely, to the influence of macroeconomic risks on the term structure of credit spreads. There is increasing support in the empirical literature for the proposition that both the probability of default (PD) and the loss given default (LGD) are correlated and driven by macroeconomic variables. Paradoxically, there has been very little effort, from the theoretical literature, to develop credit risk models that would take this into account. One explanation might be the additional complexity this leads to, even for the ``treatable'' default intensity models. The goal of this paper is to develop the theoretical framework necessary to deal with this situation and, through numerical simulation, understand the impact of macroeconomic factors on the term structure of credit spreads. In the proposed setup, periods of economic depression are both periods of higher default intensity and lower recovery, producing a business cycle effect. Furthermore, we allow for the possibility of an index volatility that depends negatively on the index level and show that, when we include this realistic feature, the impacts on the credit spread term structure are emphasized. Part III studies forward price term structure models. Forward prices differ from futures prices in stochastic interest rate settings and become an interesting object of study in their own right. Forward prices with different maturities are martingales under different forward measures. This mathematical property implies that the term structure of forward prices is always linked to the term structure of bond prices, and this dependence makes forward price term structure models relatively harder to handle. For finite dimensional factor models, Chapter 5 applies the concept of GQTS to the term structure of forward prices. We show how the forward price term structure equation depends on the term structure of bond prices. We then exploit this connection and show that even in quadratic short rate settings we can have affine term structures for forward prices. Finally, we show how the study of futures prices is naturally embedded in the study of forward prices, that the difference between the two term structures may be deterministic in some (non-trivial) stochastic interest rate settings. In Chapter 6 we study a fairly general Wiener driven model for the term structure of forward prices. The model, under a fixed martingale measure, $\Q$, is described by using two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest rates, driven by a multidimensional Wiener process $W$. The second system is an infinite SDE for the term structure of forward prices on some specified underlying asset driven by the same $W$. Since the zero coupon bond volatilities will enter into the drift part of the SDE for these forward prices, the interest rate system is needed as input to the forward price system. Given this setup, we use the Lie algebra methodology of Bj\o rk et al. to investigate under what conditions, on the volatility structure of the forward prices and/or interest rates, the inherently (doubly) infinite dimensional SDE for forward prices can be realized by a finite dimensional Markovian state space model. / Diss. Stockholm : Handelshögskolan, 2006

This thesis provides more precise characterisation of patterns, causes and consequences of takeover activity in Australia over three decades spanning from 1972 to 2004. The first contribution of the thesis is to characterise the time series behaviour of takeover activity. It is found that linear models do not adequately capture the structure of merger activity; a non-linear two-state Markov switching model works better. A key contribution of the thesis is, therefore, to propose an approach of combining a State-Space model with the Markov switching regime model in describing takeover activity. Experimental results based on our approach show an improvement over other existing approaches. We find four waves, one in the 1980s, two in the 1990s, and one in the 2000s, with an expected duration of each wave state of approximately two years. The second contribution is an investigation of the extent to which financial and macro-economic factors predict takeover activity after controlling for the probability of takeover waves. A main finding is that while stock market boom periods are empirically associated with takeover waves, the underlying driver is interest rate level. A low interest rate environment is associated with higher aggregate takeover activity. This relationship is consistent with Shleifer and Vishny (1992)'s liquidity argument that takeover waves are symptoms of lower cost of capital. Replicating the analysis to the biggest takeover market in the world, the US, reveals a remarkable consistency of results. In short, the Australian findings are not idiosyncratic. Finally, the implications for target and bidder firm shareholders are explored via investigation of takeover bid premiums and long-term abnormal returns separately between the wave and non-wave periods. This represents the third contribution to the literature of takeover waves. Findings reveal that target shareholders earn abnormally positive returns in takeover bids and bid premiums are slightly lower in the wave periods. Analysis of the returns to bidding firm shareholders suggests that the lower premiums earned by target shareholders in the wave periods may simply reflect lower total economic gains, at the margin, to takeovers made in the wave periods. It is found that bidding firms earn normal post-takeover returns (relative to a portfolio of firms matched in size and survival) if their bids are made in the non-wave periods. However, bidders who announce their takeover bids during the wave periods exhibit significant under-performance. For mergers that took place within waves, there is no difference in bid premiums and nor is there a difference in the long-run returns of bidders involved in the first half and second half of the waves. We find that none of theories of merger waves (managerial, mis-valuation and neoclassical) can fully account for the Australian takeover waves and their effects. Instead, our results suggest that a combination of these theories may provide better explanation. Given that normal returns are observed for acquiring firms, taken as a whole, we are more likely to uphold the neoclassical argument for merger activity. However, the evidence is not entirely consistent with neo-classical rational models, the under-performance effect during the wave states is consistent with the herding behaviour by firms.

[pt] Esta tese apresente duas contribuições para a modelagem e previsão de sinistros já ocorridos e ainda não avisados (Incurred But Not Reported – IBNR), quando organizados numa estrutura de dados conhecida como triângulo de run-off. Ambas as contribuições são baseadas em arcabouços gerais para a construção de modelos para séries temporais com coeficientes variantes no tempo. Em nossa primeira contribuição desenvolvemos a extensão multivariada do modelo em espaço de estado proposto por Atherino em 2008. A partir dessa extensão é possível modelas simultaneamente um ou mais triângulos de run-off associados às diversas coberturas de uma seguradora, levando-se em consideração a dependência entre os distintos triângulos, capturada pela estrutura da matriz variância – covariância do modelo SUTSE e a dependência entre as células de cada triângulo de run-off, capturada pelas componentes de nível e de periodicidade, de acordo com a proposta de atherino et al. (2010). Em nossa segunda contribuição desenvolvemos um arcabouço geral para a modelagem univariada de triângulos de run-off a partir da estruturas dos modelos GAS (Generalized Autoregressive Score) desenvolvidos por Creal at al. (2013). Esse arcabouço, bastante flexível, permite a escolha de qualquer distribuição para as entradas do triângulo run-off, considerando que os seus parâmetros variem ao longo período de origem ou de desenvolvimento. Em particular consideramos as distribuições gama e log-normal. Nossos resultados foram comparados com os obtidos através do método chain ladder (Mack, 1993), utilizado como benchmark na indústria de seguros. O teste Diebold e Mariano (1995) evidenciou que os modelos propostos geram melhores previsões, comparadas as previsões do método chain ladder. / [en] This thesis presents two contributions to the modeling and prediction of a type of claims in the insurance industry known as IBNR (Incurred But Not Reported) when these are organized in a data structure known as the run-off triangle. Both contributions are based on general frameworks for building models for time series with time varying coefficients. In our first contribution we developed the multivariate extension of the state space model proposed by Atherino in 2008. From this extension it is possible to model simultaneously one or more run-off triangles associated with different coverages from an insurer, taking into account the dependence between different triangles, captured by the structure of the variance-covariance matrix of the SUTSE model, while the dependence between the cells of each triangle run-off is captured by the components of level and periodicity according to the model proposed by Atherino (2008). In our second contribution we developed a general framework for univariate modeling of run-off triangles using the structure of GAS models (Generalized Autoregressive Score) developed by Creal et al. (2013). This framework, very flexible, allows one to choose any distribution to the inputs of the triangle run-off, considering that its parameters can vary over the period of origin or period of development. In particular we have considered both gamma and lognormal distributions. Our results were compared with those obtained by the chain ladder method (Mack, 1993) used as a benchmark in the insurance industry. The Diebold and Mariano test (1995) showed that the proposed models produced better predictions compared to the predictions of the chain ladder method.