Multiplex Network Econometrics

MultiNetMetrics has been focused on dynamic behaviour of networks by the development of novel econometric techniques related to time series and multilayer networks. After the 2007-2009 global financial crisis and consequently 2010-2012 European sovereign debt crisis, the macroeconomic and financial literature has focused on novel methods to explain this crisis. In particular, they start linking network theory to economic and econometric topics since network analysis allows a better understanding of complex systems of interconnected financial institutions and markets. This analysis could be extended to the current Covid situation although the data are not available, but it will be interested in the future to use the proposed models and methods to study the movements in the financial and macroeconomic markets. The work performed during MultiNetMetrics research project is based on novel scientific contributions, in particular methodological issues that will lead to future research projects. The scientific
contributions originated in the research project cover novel methodology which can be used to study financial and macroeconomic networks. Moreover, the project has been presented in several conferences, workshops and seminars related to econometrics and statistics with an audience of academics and policy makers from university and central banks.

The research agenda developed and performed during the MultiNetMetrics project focused on novel methodologies for the extraction and the analysis of network in finance and macroeconomics, but also for a general use. Firstly, the project propose an innovative Bayesian nonparametric (BNP) time-varying graphical framework for making inference in high-dimensional time series. In particular, two different prior distributions for the transition matrix of a vector Autoregressive (VAR) model have been considered. The first is based on spike-and-slab prior with Dirichlet Process Mixture priors on the slab component and the second one on a time-series Dirichlet Process Prior. The proposed BNP time-varying VAR model allows to infer time-varying Granger causality networks from time series; to flexible model and cluster non-zero time-varying coefficients and to accomodate for potential non-linearities. The nice feature of this part of the MultiNetMetrics project is the possibility to work with both observed and latent networks, where in the second case, the network extraction is estimate a posteriori. Secondly, MultiNetMetrics deal with multilayer and multiplex networks and it can be related to the first part. As a second theoretical contribution, we deal with a Bayesian version of the Generalized Autoregressive Score (GAS) model, where the estimation is done via a Bayesian algorithm and not in a frequentist way. In this scenario, the methodology has been applied to CDS spread data from around the world and we deal with a Vector Autoregressive (VAR) model with GAS structure of the error matrix. The proposed methodology and algorithm has been used to study a posterior the network structure of the linkages between different CDS spread across countries and has been developed by using a two-step approach. The first step deals with the estimation of the model, while the second step works with a Signal adaptive Variable selector (SAVS) for the network extraction. In conclusion, the project has worked with different Bayesian techniques with a common denominator as the network extraction. In the project, all the codes have been self-written in MATLAB with the opportunity of using parallelization. The MultiNetMetrics website has been regularly updated with informations regarding publications, working papers and conference participations.

MultiNetMetrics project deals with novel econometrics techniques and in particular with time series modeling from a Bayesian perspective. Once the methodology has been introduced, the project investigated the topology of the networks and of the multiplex networks focusing on the discovery of importance paths (alias linkages) and of important variables (alias nodes) inside the time-varying structure of the network. The project proposes two different approaches to improve the estimation of the network structure, observed or latent, when the number of variables included increases to high-dimensionality. The Bayesian non-parametric time-varying parameter prior allows to extract network a posteriori from any kind of dataset available and could be easily applied to novel datasets related to the present health crisis (Covid-19). The same could be raised for the Bayesian Generalized Score models (GAS), which has been applied to financial data (5 years CDS spreads) to extract Granger causality and contagion transmission in financial network. MultiNetMetrics project has contributed to the literature by providing novel Bayesian methodology for the analysis of multivariate time series and then for the extraction of networks for high-dimensionality problems. This project has then opened novel perspective and future research lines for the network extraction inside the transition matrix of the VAR model or inside the covariance matrix.

Periodic Reporting for period 1 - MultiNetMetrics (Multiplex Network Econometrics)

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