A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations.

High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener-Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions.MR

Three Essays of Applied Bayesian Modeling: Financial Return Contagion, Benchmarking Small Area Estimates, and Time-Varying Dependence

This dissertation is composed of three chapters, each an application of Bayesian statistical models to particular research questions. In Chapter 1, we evaluate systemic risk exposure of financial institutions. Building upon traditional regime switching approaches, we propose a network model for volatility contagion to assess linkages between institutions in the financial system. Focusing empirical analysis on the financial sector, we find that network connectivity has dynamic properties, with linkages between institutions increasing immediately before the recent crisis. Out-of-sample forecasts demonstrate the ability of the model to predict losses during distress periods. We find that institutional exposure to crisis events depends upon the structure of linkages, not strictly the number of linkages. In Chapter 2, we develop procedures for benchmarking small area estimates. In sample surveys, precision can be increased by introducing small area models which "borrow strength" by incorporating auxiliary covariate information. One consequence of using small area models is that small area estimates at lower geographical levels typically will not aggregate to the estimate at the corresponding higher geographical levels. Benchmarking is the statistical procedure for reconciling these differences. Two new approaches to Bayesian benchmarking are introduced, one procedure based on Minimum Discrimination Information, and another for Bayesian self-consistent conditional benchmarking. Notably the proposed procedures construct adjusted posterior distributions whose moments all satisfy benchmarking constraints. In the context of the Fay-Herriot model, simulations are conducted to assess benchmarking performance. In Chapter 3, we exploit the Pair Copula Construction (PCC) to develop a flexible multivariate model for time-varying dependence. The PCC is an extremely flexible model for capturing complex, but static, multivariate dependency. We use a Bayesian framework to extend the PCC to account for time dynamic dependence structures. In particular, we model the time series of a transformation of parameters of the PCC as an autoregressive model, conducting inference using a Markov Chain Monte Carlo algorithm. We use financial data to illustrate empirical evidence for the existence of time dynamic dependence structures, show improved out-of-sample forecasts for our time dynamic PCC, and assess performance of dynamic PCC models for forecasting Value-at-Risk.Statistic

Assessing brain connectivity through electroencephalographic signal processing and modeling analysis

Brain functioning relies on the interaction of several neural populations connected through complex connectivity networks, enabling the transmission and integration of information. Recent advances in neuroimaging techniques, such as electroencephalography (EEG), have deepened our understanding of the reciprocal roles played by brain regions during cognitive processes. The underlying idea of this PhD research is that EEG-related functional connectivity (FC) changes in the brain may incorporate important neuromarkers of behavior and cognition, as well as brain disorders, even at subclinical levels. However, a complete understanding of the reliability of the wide range of existing connectivity estimation techniques is still lacking. The first part of this work addresses this limitation by employing Neural Mass Models (NMMs), which simulate EEG activity and offer a unique tool to study interconnected networks of brain regions in controlled conditions. NMMs were employed to test FC estimators like Transfer Entropy and Granger Causality in linear and nonlinear conditions. Results revealed that connectivity estimates reflect information transmission between brain regions, a quantity that can be significantly different from the connectivity strength, and that Granger causality outperforms the other estimators. A second objective of this thesis was to assess brain connectivity and network changes on EEG data reconstructed at the cortical level. Functional brain connectivity has been estimated through Granger Causality, in both temporal and spectral domains, with the following goals: a) detect task-dependent functional connectivity network changes, focusing on internal-external attention competition and fear conditioning and reversal; b) identify resting-state network alterations in a subclinical population with high autistic traits. Connectivity-based neuromarkers, compared to the canonical EEG analysis, can provide deeper insights into brain mechanisms and may drive future diagnostic methods and therapeutic interventions. However, further methodological studies are required to fully understand the accuracy and information captured by FC estimates, especially concerning nonlinear phenomena

Demand for money and the conduct of monetary policy in developing countries

Conventional error-correction and cointegration techniques are utilized to derive demand for money models for eleven developing countries. The performance of these models is assessed using a battery of statistical tests than is commonly reported in previous studies. We show that the cointegration equations outperform the conventional error-correction specifications in terms of statistical and theoretical considerations

Modelling and Testing Financial Risk

This dissertation centres on the modelling and testing of risk with the emphasis on gauging novel issues in finance. The first chapter models the stability of financial system using prominent systemic risk measures, and examines for various risk factors affecting financial stability including the risky practice of shadow insurance. The collected dataset suggests that shadow insurance has been increasingly exploited to reduce risk exposure and that entities exploiting shadow insurance are generally riskier and more interconnected with the financial system. Using panel analysis, I find statistical evidence that the practice of shadow insurance does affect financial stability based on two distinct systemic risk measures. In the second chapter, I propose a new multivariate econometric strategy for examining the spillover of volatility—the most fundamental risk measure. The asymptotic theory of the testing strategy is established under regularity conditions. The chapter includes an extensive simulation study to confirm the finite sample performance of the proposed econometric strategy and an empirical study based on the new test to examine volatility spillover between the North American and European financial markets before and after the Brexit referendum. In the third chapter, I consolidate the comprehensive literature on Granger causality methods, and I apply the unified methodology to examine different components of risk spillover between international crude oil and the Chinese equity markets that are fuel intensive. This unified analysis disentangles the complex oil-equity nexus to find that it has been nontrivially related to various factors such as demand and supply of oil, economic growth rate, government subsidies and the Chinese oil pricing reformation

Understanding the cost of carry in Nikkei 225 stock index futures markets: mispricing, price and volatility dynamics

This dissertation studies the cost of carry relationship and the international dynamics of mispricing, price and volatility in the three Nikkei futures markets - the Osaka Exchange (OSE), the Singapore Exchange (SGX) and the Chicago Mercantile Exchange (CME). Previous research does not fully consider the unique characteristics of the triple-listed Nikkei futures contracts, or the price and volatility dynamics in the three Nikkei futures exchanges at the same time. This dissertation makes a significant contribution to the existing literature. In particular, with a comprehensive new 19-year sample period, this dissertation helps deepen the understanding of the Nikkei spot-futures equilibrium and arbitrage behaviour, cross-border information transmission mechanism, and futures market integration. The first topic of the dissertation is to study the cost of carry relationship, mispricing and index arbitrage in the three Nikkei markets. The standard cost of carry model is adjusted for each Nikkei futures contract by allowing for the triple-listing nature and key institutional differences. Based on this, the economic significance of the Nikkei mispricing is explored in the presence of transaction costs. The static behaviour of the mispricing suggests that it is difficult especially for institutional investors to make arbitrage profits in the OSE and SGX, and that index arbitrage in the CME is not strictly risk-free due to the exchange rate effect. Smooth transition models are used to study the dynamic behaviour of the mispricing in the three markets. The results show that mean reversion in mispricing and limits to arbitrage are driven more by transaction costs than by heterogeneous arbitrageurs in the Nikkei markets. The second topic of the dissertation is to investigate the price discovery process in individual Nikkei markets and across the Nikkei futures markets. With smooth transition error correction models, this dissertation reports the leading role of the futures prices in the pre-crisis period and the leading role of the spot prices in the post-crisis period, in the first-moment information transmission process. Moreover, there is evidence of asymmetric adjustments in the Nikkei prices and volatilities. The cross-border dynamics suggest that the foreign Nikkei markets (the CME and SGX) act as the main price discovery vehicle, which implies the key functions of the equivalent, offshore markets in futures market globalisation. The third topic of the dissertation is to study the volatility transmission process in individual Nikkei markets and across the Nikkei futures markets, from the perspectives of the volatility interactions in and across the Nikkei markets and of the dynamic Nikkei market linkages. This dissertation finds bidirectional volatility spillover effects between the Nikkei spot and futures markets, and the information leadership of the foreign Nikkei markets (the CME and SGX) in the second-moment information transmission process across the border. It further examines the dynamic conditional correlations between the Nikkei markets. The results point to a dramatic integration process with strongly persistent and stable Nikkei market co-movements over time

Flexible estimation of temporal point processes and graphs

Handling complex data types with spatial structures, temporal dependencies, or discrete values, is generally a challenge in statistics and machine learning. In the recent years, there has been an increasing need of methodological and theoretical work to analyse non-standard data types, for instance, data collected on protein structures, genes interactions, social networks or physical sensors. In this thesis, I will propose a methodology and provide theoretical guarantees for analysing two general types of discrete data emerging from interactive phenomena, namely temporal point processes and graphs. On the one hand, temporal point processes are stochastic processes used to model event data, i.e., data that comes as discrete points in time or space where some phenomenon occurs. Some of the most successful applications of these discrete processes include online messages, financial transactions, earthquake strikes, and neuronal spikes. The popularity of these processes notably comes from their ability to model unobserved interactions and dependencies between temporally and spatially distant events. However, statistical methods for point processes generally rely on estimating a latent, unobserved, stochastic intensity process. In this context, designing flexible models and consistent estimation methods is often a challenging task. On the other hand, graphs are structures made of nodes (or agents) and edges (or links), where an edge represents an interaction or relationship between two nodes. Graphs are ubiquitous to model real-world social, transport, and mobility networks, where edges can correspond to virtual exchanges, physical connections between places, or migrations across geographical areas. Besides, graphs are used to represent correlations and lead-lag relationships between time series, and local dependence between random objects. Graphs are typical examples of non-Euclidean data, where adequate distance measures, similarity functions, and generative models need to be formalised. In the deep learning community, graphs have become particularly popular within the field of geometric deep learning. Structure and dependence can both be modelled by temporal point processes and graphs, although predominantly, the former act on the temporal domain while the latter conceptualise spatial interactions. Nonetheless, some statistical models combine graphs and point processes in order to account for both spatial and temporal dependencies. For instance, temporal point processes have been used to model the birth times of edges and nodes in temporal graphs. Moreover, some multivariate point processes models have a latent graph parameter governing the pairwise causal relationships between the components of the process. In this thesis, I will notably study such a model, called the Hawkes model, as well as graphs evolving in time. This thesis aims at designing inference methods that provide flexibility in the contexts of temporal point processes and graphs. This manuscript is presented in an integrated format, with four main chapters and two appendices. Chapters 2 and 3 are dedicated to the study of Bayesian nonparametric inference methods in the generalised Hawkes point process model. While Chapter 2 provides theoretical guarantees for existing methods, Chapter 3 also proposes, analyses, and evaluates a novel variational Bayes methodology. The other main chapters introduce and study model-free inference approaches for two estimation problems on graphs, namely spectral methods for the signed graph clustering problem in Chapter 4, and a deep learning algorithm for the network change point detection task on temporal graphs in Chapter 5. Additionally, Chapter 1 provides an introduction and background preliminaries on point processes and graphs. Chapter 6 concludes this thesis with a summary and critical thinking on the works in this manuscript, and proposals for future research. Finally, the appendices contain two supplementary papers. The first one, in Appendix A, initiated after the COVID-19 outbreak in March 2020, is an application of a discrete-time Hawkes model to COVID-related deaths counts during the first wave of the pandemic. The second work, in Appendix B, was conducted during an internship at Amazon Research in 2021, and proposes an explainability method for anomaly detection models acting on multivariate time series

A Parsimonious Granger Causality Formulation for Capturing Arbitrarily Long Multivariate Associations

High-frequency neuroelectric signals like electroencephalography (EEG) or magnetoencephalography (MEG) provide a unique opportunity to infer causal relationships between local activity of brain areas. While causal inference is commonly performed through classical Granger causality (GC) based on multivariate autoregressive models, this method may encounter important limitations (e.g., data paucity) in the case of high dimensional data from densely connected systems like the brain. Additionally, physiological signals often present long-range dependencies which commonly require high autoregressive model orders/number of parameters. We present a generalization of autoregressive models for GC estimation based on Wiener–Volterra decompositions with Laguerre polynomials as basis functions. In this basis, the introduction of only one additional global parameter allows to capture arbitrary long dependencies without increasing model order, hence retaining model simplicity, linearity and ease of parameters estimation. We validate our method in synthetic data generated from families of complex, densely connected networks and demonstrate superior performance as compared to classical GC. Additionally, we apply our framework to studying the directed human brain connectome through MEG data from 89 subjects drawn from the Human Connectome Project (HCP) database, showing that it is able to reproduce current knowledge as well as to uncover previously unknown directed influences between cortical and limbic brain regions