The present PhD dissertation consists of two independent job-market papers, therefore each chapter represents an article with its own conclusions. In both studies I introduce innovative statistical models aimed to be applied to the economic and financial data. A detailed description of the related inference and applications is provided. In the first paper, under the supervision of Professor Brunero Liseo (Sapienza University of Rome), I consider situations where a model for ordered categorical response variable is necessary. In this case the interest of the analysis lies in the shift of the predicted discrete ordered outcome distribution as one or more of the regressors change, i.e., marginal probability effects. Therefore the questions to be addressed are focused not on the scale of each variable, but rather on the association between variables themselves. Standard ordered response models may not be very suited to perform this analysis, being these effects to a large extent predetermined by the rigid parametric structure of the model. More specifically, in the case of normally distributed data, it is possible to address these issues by the multivariate normal and linear regression models. In this work I use the rank likelihood in non Gaussian situations and show how additional flexibility can be gained by modeling individual heterogeneity by means of a latent class structure. I extend the rank likelihood approach to Generalized Linear Mixed Effects models' framework which is therefore suitable for longitudinal data applications. The Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted. The performance of the model is illustrated in the context of sovereign credit ratings and Corruption Perception Index modeling and forecasting. The second study is entitled A Mixture of Heterogeneous Models with Time Dependent Weights. This part of dissertation has been developed and done while I was spending a visiting period at the Statistical and Applied Mathematical Institute, under the supervision of Professor Brunero Liseo and Dr Christian Macaro (SAS Institute). Understanding stock market volatility is a major task for market analysts, policy makers, economists and investors. However, inference in financial and economic models can be challenging due to the fact that an explicit dependence order between observations is added: a time dimension. Some of the existing approaches aim to address these challenges by using ARMA, GARCH, Dynamic Linear Models and many others. In this work, I provide an alternative way to model and predict these data using a mixture of heterogeneous models with mixing weights characterized by an autoregressive structure. In comparison to the static mixture, the models I introduce are based on time-dependent weights which allows one to learn how the data-generating mechanism changes over time. The resulting dynamic mixtures aim to model the composition of the stock market data. A Bayesian approach is adopted and the Metropolis-Hastings within Gibbs sampling technique is used. Through extensive analysis in both observed and simulated data settings, I show all the benefits the dynamic mixture model has over its static counterpart. I illustrate this performance in the context of the stock market expectation of a 30-day forward-looking volatility expressed by the volatility index VIX.

Contributions to Bayesian inference for economic and financial applications / Doroshenko, Lyubov. - (2021 Oct 07).

Contributions to Bayesian inference for economic and financial applications

DOROSHENKO, LYUBOV
07/10/2021

Abstract

The present PhD dissertation consists of two independent job-market papers, therefore each chapter represents an article with its own conclusions. In both studies I introduce innovative statistical models aimed to be applied to the economic and financial data. A detailed description of the related inference and applications is provided. In the first paper, under the supervision of Professor Brunero Liseo (Sapienza University of Rome), I consider situations where a model for ordered categorical response variable is necessary. In this case the interest of the analysis lies in the shift of the predicted discrete ordered outcome distribution as one or more of the regressors change, i.e., marginal probability effects. Therefore the questions to be addressed are focused not on the scale of each variable, but rather on the association between variables themselves. Standard ordered response models may not be very suited to perform this analysis, being these effects to a large extent predetermined by the rigid parametric structure of the model. More specifically, in the case of normally distributed data, it is possible to address these issues by the multivariate normal and linear regression models. In this work I use the rank likelihood in non Gaussian situations and show how additional flexibility can be gained by modeling individual heterogeneity by means of a latent class structure. I extend the rank likelihood approach to Generalized Linear Mixed Effects models' framework which is therefore suitable for longitudinal data applications. The Bayesian approach using Markov Chain Monte Carlo (MCMC) is adopted. The performance of the model is illustrated in the context of sovereign credit ratings and Corruption Perception Index modeling and forecasting. The second study is entitled A Mixture of Heterogeneous Models with Time Dependent Weights. This part of dissertation has been developed and done while I was spending a visiting period at the Statistical and Applied Mathematical Institute, under the supervision of Professor Brunero Liseo and Dr Christian Macaro (SAS Institute). Understanding stock market volatility is a major task for market analysts, policy makers, economists and investors. However, inference in financial and economic models can be challenging due to the fact that an explicit dependence order between observations is added: a time dimension. Some of the existing approaches aim to address these challenges by using ARMA, GARCH, Dynamic Linear Models and many others. In this work, I provide an alternative way to model and predict these data using a mixture of heterogeneous models with mixing weights characterized by an autoregressive structure. In comparison to the static mixture, the models I introduce are based on time-dependent weights which allows one to learn how the data-generating mechanism changes over time. The resulting dynamic mixtures aim to model the composition of the stock market data. A Bayesian approach is adopted and the Metropolis-Hastings within Gibbs sampling technique is used. Through extensive analysis in both observed and simulated data settings, I show all the benefits the dynamic mixture model has over its static counterpart. I illustrate this performance in the context of the stock market expectation of a 30-day forward-looking volatility expressed by the volatility index VIX.
7-ott-2021
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1577923
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