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Bayesian Markov switching tensor regression for time-varying networks

We 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 d...

Bayesian dynamic tensor regression

Multidimensional arrays (i.e. tensors) of data are becoming increasingly available and call for suitable econometric tools. We propose a new dynamic linear regression model for tensor-valued response variables and covariates that encompasses some well known multivariate models such as SUR, VAR, VECM, panel VAR and matrix regression models as special cases. For dealing with the over-parametrization and over-fitting issues due to the curse of dimensionality, we exploit a suitable parametrizatio...

Nonparametric forecasting of multivariate probability density functions

The study of dependence between random variables is the core of theoretical and applied statistics. Static and dynamic copula models are useful for describing the dependence structure, which is fully encrypted in the copula probability density function. However, these models are not always able to describe the temporal change of the dependence patterns, which is a key characteristic of nancial data. We propose a novel nonparametric framework for modelling a time series of copula probability ...

Visualizing and comparing distributions with half-disk density strips

We 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. I...

Basics of optimization theory with applications in MATLAB and R

This 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 powe...

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