Bayesian Model Selection for Beta Autoregressive Processes

We deal with Bayesian inference for Beta autoregressive processes. We restrict our attention to the class of conditionally linear processes. These processes are particularly suitable for forecasting purposes, but are difficult to estimate due to the constraints on the parameter space. We provide a full Bayesian approach to the estimation and include the parameter restrictions in the inference problem by a suitable specification of the prior distributions. Moreover in a Bayesian framework parameter estimation and model choice can be solved simultaneously. In particular we suggest a Markov-Chain Monte Carlo (MCMC) procedure based on a Metropolis-Hastings within Gibbs algorithm and solve the model selection problem following a reversible jump MCMC approach

Monte carlo within simulated annealing for integral constrained optimizations

For years, Value-at-Risk and Expected Shortfall have been well established measures of market risk and the Basel Committee on Banking Supervision recommends their use when controlling risk. But their computations might be intractable if we do not rely on simplifying assumptions, in particular on distributions of returns. One of the difficulties is linked to the need for Integral Constrained Optimizations. In this article, two new stochastic optimization-based Simulated Annealing algorithms are proposed for addressing problems associated with the use of statistical methods that rely on extremizing a non-necessarily differentiable criterion function, therefore facing the problem of the computation of a non-analytically reducible integral constraint. We first provide an illustrative example when maximizing an integral constrained likelihood for the stress-strength reliability that confirms the effectiveness of the algorithms. Our results indicate no clear difference in convergence, but we favor the use of the problem approximation strategy styled algorithm as it is less expensive in terms of computing time. Second, we run a classical financial problem such as portfolio optimization, showing the potential of our proposed methods in financial applications

Hierarchical Species Sampling Models

This paper introduces a general class of hierarchical nonparametric prior distributions. The random probability measures are constructed by a hierarchy of generalized species sampling processes with possibly non-diffuse base measures. The proposed framework provides a general probabilistic foundation for hierarchical random measures with either atomic or mixed base measures and allows for studying their properties, such as the distribution of the marginal and total number of clusters. We show that hierarchical species sampling models have a Chinese Restaurants Franchise representation and can be used as prior distributions to undertake Bayesian nonparametric inference. We provide a method to sample from the posterior distribution together with some numerical illustrations. Our class of priors includes some new hierarchical mixture priors such as the hierarchical Gnedin measures, and other well-known prior distributions such as the hierarchical Pitman-Yor and the hierarchical normalized random measures

Endogeneity in Interlocks and Performance Analysis: A Firm Size Perspective

This paper contributes to the literature on interlocking directorates (ID) by providing a new solution to the two econometric issues arising in the joint analysis of interlocks and firm performance which are the endogenous nature of ID and sample selection bias due to the exclusion of isolated firms. Some key determinants of ID network formation are identified and used to check for endogeneity. We analyze the impact of the positioning in the network on firms’ performance and inspect how the impact varies across firms of different sizes drawing on information relating to 37,324 firms in the interlocking network which, to our knowledge, is the widest dataset ever used in approaching the study of ID. Our results, made robust for endogeneity and sample selection bias, suggest that eigenvector centrality and the clustering coefficient have a positive and significant impact on all the performance measures and that this effect is more pronounced for small firms

Generalized Poisson difference autoregressive processes

This paper introduces a novel stochastic process with signed integer values. Its autoregressive dynamics effectively captures persistence in conditional moments, rendering it a valuable feature for forecasting applications. The increments follow a Generalized Poisson distribution, capable of accommodating over- and under-dispersion in the conditional distribution, thereby extending standard Poisson difference models. We derive key properties of the process, including stationarity conditions, the stationary distribution, and conditional and unconditional moments, which prove essential for accurate forecasting. We provide a Bayesian inference framework with an efficient posterior approximation based on Markov Chain Monte Carlo. This approach seamlessly incorporates inherent parameter uncertainty into predictive distributions. The effectiveness of the proposed model is demonstrated through applications to benchmark datasets on car accidents and an original dataset on cyber threats, highlighting its superior fitting and forecasting capabilities compared to standard Poisson model

COVID-19 spreading in financial networks: A semiparametric matrix regression model

Network models represent a useful tool to describe the complex set of financial relationships among heterogeneous firms in the system. A new Bayesian semiparametric model for temporal multilayer networks with both intra- and inter-layer connectivity is proposed. A hierarchical mixture prior distribution is assumed to capture heterogeneity in the response of the network edges to a set of risk factors including the number of COVID-19 cases in Europe. Two layers, defined by stock returns and volatilities are considered and within and between layers connectivity is investigated. The financial connectedness arising from the interactions between two layers is measured. The model is applied in order to compare the topology of the network before and after the spreading of the COVID-19 disease

Bayesian Dynamic Tensor Regression

High- and multi-dimensional array data are becoming increasingly available. They admit a natural representation as tensors and call for appropriate statistical tools. We propose a new linear autoregressive tensor process (ART) for tensor-valued data, that encompasses some well-known time series models as special cases. We study its properties and derive the associated impulse response function. We exploit the PARAFAC low-rank decomposition for providing a parsimonious parametrization and develop a Bayesian inference allowing for shrinking effects. We apply the ART model to time series of multilayer networks and study the propagation of shocks across nodes, layers and time

A Matrix-Variate t Model for Networks

Networks represent a useful tool to describe relationships among financial firms and network analysis has been extensively used in recent years to study financial connectedness. An aspect, which is often neglected, is that network observations come with errors from different sources, such as estimation and measurement errors, thus a proper statistical treatment of the data is needed before network analysis can be performed. We show that node centrality measures can be heavily affected by random errors and propose a flexible model based on the matrix-variate t distribution and a Bayesian inference procedure to de-noise the data. We provide an application to a network among European financial institutions