The Generalized Pareto-Negative Binomial Model in Finding Relationships between Text Data and Quantitative Data

The Generalized Pareto-Negative Binomial (GP-NB) model was introduced to find the connections between text data and quantitative data. The assumptions for the model were word counts are Poisson distributed, quantitative financial variables are Gamma distributed and both are conditional on Gamma distributed latent variables. These assumptions resulted in a Negative Multinomial distribution for word counts and a Generalized Pareto distribution for the quantitative financial variables. Model parameters were estimated using Maximum Likelihood (MLE) and Quasi-Likelihood (QL) Estimation. Based on simulated data, we compared the bias and standard errors of the estimation methods and found no one method was best. We evaluated the model in predicting financial ratios, portfolio allocation and interpreting text data. In predicting financial ratios, the conditional MLE was better in terms of the Mean Square Prediction Error (MSPE) and Thiel\u27s coefficient compared to the random walk and Multivariate Generalized Linear Model - Quasi Likelihood (MGLM-QL) method. Then using the mean-variance analysis to find financial portfolios, we found that the Generalized Pareto (GP) distribution combined with Twitter data based on MGLM-QL model reduced the downside risk which was calculated based on the conditional Value-at-Risk (CVaR). Lastly, we used U.S state governors’ speeches and state economic data from Bikienga (2018) to evaluate the models’ interpretative ability and found that the model explained considerably more variation than a CCA-PCA approach and found that governors who spoke more about services for people tended to be associated with increased public welfare budgets