1,721,009 research outputs found
Basics of optimization theory with applications in MATLAB and R
Full text linkThis document is the result of a reorganization of lecture notes used by the author during the Teaching Assistantship of the Optimization course at the M.Sc. in Economics program at the University of Venice. It collects a series of results in Static and Dynamic Optimization, Differential and Difference Equations useful as a background for the main courses in Mathematics, Finance and Economics both at the M.Sc. and at the Ph.D. level. In addition, it offers a brief critical summary
of the power of programming and computational tools for applied mathematics, with an overview of some useful functions of the softwares MATLAB and R. All the codes used are available upon request to the author
Measuring sovereign bond fragmentation in the Eurozone
No full textFragmentation in the sovereign bond market of the Eurozone involves divergences in borrowing costs and undermines the stability of the monetary union. In this paper, we propose an indicator of fragmentation between government bonds of the core and peripheral European countries. Using a regime-switching cointegration model, we identify the absence of fragmentation as periods where the bond yields of the two groups share a common stochastic trend in the long-run. The results show that the indicator of fragmentation is responsive to systemic stress events and is negatively related to the ECB’s monetary policy actions
Essays on the econometric modelling of temporal networks
Full text linkGraph theory has long been studied in mathematics and probability as a tool for describing dependence between nodes. However, only recently it has been implemented on data, givin birth to the statistical analysis of real networks.
The topology of economic and financial networks is remarkably complex: it is generally unobserved, thus requiring adequate inferential procedures for it estimation, moreover not only the nodes, but the structure of dependence itself evolves over time. Statistical and econometric tools for modelling the dynamics of change of the network structure are lacking, despite their increasing requirement in several fields of research. At the same time, with the beginning of the era of “Big data” the size of available datasets is becoming increasingly high and their internal structure is growing in complexity, hampering traditional inferential processes in multiple cases.
This thesis aims at contributing to this newborn field of literature which joins probability, economics, physics and sociology by proposing novel statistical and econometric methodologies for the study of the temporal evolution of network structures of medium-high dimension
A discussion on: Sparse graphs using exchangeable random measures by F. Caron and E. B. Fox
No full textStatistical network modelling has focused on representing the graph as a discrete structure, namely the adjacency matrix. When assuming exchangeability of this arraywhich can aid in modelling, computations and theoretical analysisthe Aldous-Hoover theorem informs us that the graph is necessarily either dense or empty. We instead consider representing the graph as an exchangeable random measure and appeal to the Kallenberg representation theorem for this object. We explore using completely random measures (CRMs) to define the exchangeable random measure, and we show how our CRM construction enables us to achieve sparse graphs while maintaining the attractive properties of exchangeability. We relate the sparsity of the graph to the Levy measure defining the CRM. For a specific choice of CRM, our graphs can be tuned from dense to sparse on the basis of a single parameter. We present a scalable Hamiltonian Monte Carlo algorithm for posterior inference, which we use to analyse network properties in a range of real data sets, including networks with hundreds of thousands of nodes and millions of edges
Bayesian Markov-Switching Tensor Regression for Time-Varying Networks
Full text linkModeling time series of multilayer network data is challenging due to the peculiar characteristics of real-world networks, such as sparsity and abrupt structural changes. Moreover, the impact of external factors on the network edges is highly heterogeneous due to edge- and time-specific effects. Capturing all these features results in a very high-dimensional inference problem. A novel tensor-on-tensor regression model is proposed, which integrates zero-inflated logistic regression to deal with the sparsity, and Markov-switching coefficients to account for structural changes. A tensor representation and decomposition of the regression coefficients are used to tackle the high-dimensionality and account for the heterogeneous impact of the covariate tensor across the response variables. The inference is performed following a Bayesian approach, and an efficient Gibbs sampler is developed for posterior approximation. Our methodology applied to financial and email networks detects different connectivity regimes and uncovers the role of covariates in the edge-formation process, which are relevant in risk and resource management. Code is available on GitHub. Supplementary materials for this article are available online
Bayesian SAR Model with Stochastic Volatility and Multiple Time-Varying Weights
Full text linkA novel spatial autoregressive model with time-varying structural variance for panels of time series data is introduced. It incorporates multilayer networks and accounts for dynamic relationships, thus enabling the analysis of shock propagation through time-varying spillover effects. The proposed method outperforms alternative spatial model benchmarks in an empirical application investigating the impact of cooperative and conflictual geopolitical relationships on G7 stock markets. The results indicate that cooperative interactions have a greater influence on stock markets than conflictual ones, highlighting the collaborative nature of the G7. They also reveal heterogeneous network exposures and distinct patterns of direct and indirect spillover effects
Visualizing and comparing distributions with half-disk density strips
Full text linkWe propose a user-friendly graphical tool, the half-disk density strip (HDDS), for visualizing and comparing probability density functions. The HDDS exploits color shading for representing a distribution in an intuitive way. In univariate settings, the half-disk density strip allows to immediately discern the key characteristics of a density, such as symmetry, dispersion, and multi-modality. In the multivariate settings, we define HDDS tables to generalize the concept of contingency tables. It is an array of half-disk density strips, which compactly displays the univariate marginal and conditional densities of a variable of interest, together with the joint and marginal densities of the conditioning variables. Moreover, HDDSs are by construction well suited to easily compare pairs of densities. To highlight the concrete benefits of the proposed methods, we show how to use HDDSs for analyzing income distribution and life-satisfaction, conditionally on continuous and categorical controls, from survey data. The code for implementing HDDS methods is made available through a dedicated R package
Bayesian Markov-Switching Tensor Regression for Time-Varying Networks
Full text linkModeling time series of multilayer network data is challenging due to the peculiar characteristics of real-world networks, such as sparsity and abrupt structural changes. Moreover, the impact of external factors on the network edges is highly heterogeneous due to edge- and time-specific effects. Capturing all these features results in a very high-dimensional inference problem. A novel tensor-on-tensor regression model is proposed, which integrates zero-inflated logistic regression to deal with the sparsity, and Markov-switching coefficients to account for structural changes. A tensor representation and decomposition of the regression coefficients are used to tackle the high-dimensionality and account for the heterogeneous impact of the covariate tensor across the response variables. The inference is performed following a Bayesian approach, and an efficient Gibbs sampler is developed for posterior approximation. Our methodology applied to financial and email networks detects different connectivity regimes and uncovers the role of covariates in the edge-formation process, which are relevant in risk and resource management. Code is available on GitHub. Supplementary materials for this article are available online
Extreme time-varying spillovers between high carbon emission stocks, green bond and crude oil: Comment
Full text linkIn this article, we provide a comment on the work of Dai et al. (2023), who introduced the Time-Varying Parameters Quantile Vector Auto Regressive model (TVP-QVAR) to analyze the spillovers between high carbon emission stocks, green bonds, and crude oil. We argue that some peculiar results provided in the study cited above are due to a mismatch between the methodology presented by the authors and the code used to conduct the empirical analysis. We empirically support our claims by applying an approximate methodology to the data shared by Dai et al. (2023)
Bayesian Markov switching tensor regression for time-varying networks
Full text linkWe propose a new Bayesian Markov switching regression model for multi-dimensional arrays (tensors) of binary time series. We assume a zero-inflated logit dynamics with time-varying parameters and apply it to multi-layer temporal networks. The original contribution is threefold. First, in order to avoid over-fitting we propose a parsimonious parametrization of the model, based on a low-rank decomposition of the tensor of regression coefficients. Second, the parameters of the tensor model are driven by a hidden Markov chain, thus allowing for structural changes. The regimes are identied through prior constraints on the mixing probability of the zero-inflated model. Finally, we model the jointly dynamics of the network and of a set of variables of interest. We follow a Bayesian approach to inference, exploiting the Polya-Gamma data augmentation scheme for logit models in order to provide an efficient Gibbs sampler for posterior approximation. We show the effectiveness of the sampler on simulated datasets of medium-big sizes, nally we apply the methodology to a real dataset of nancial networks
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