Economics - Theses
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ItemDevelopment of Bayesian dynamic nonparametric models and inferences( 2023-06)Dynamic econometric models play an important role in the analysis of economics and finance. Motivated by this significance, this thesis presents novel Bayesian nonparametric models and inferences, offering fast and accurate approaches for analysing large data sets and gaining more insightful understanding in empirical studies. Chapter 2 proposes a new dynamic Bayesian nonparametric model designed to capture time varying distributions, with each distribution being a mixture of an infinite number of Normal distributions. Our model builds on the work of Gutierrez, Mena, and Ruggiero (2016) and Mena and Ruggiero (2016). We improve their algorithm by incorporating a break indicator and a hierarchical prior structure that govern the parameters of all components within the mixture. Using the Australian banking statistics from 1925 to 2019, we apply the model to estimate the time-varying bank size and growth distributions. Our results reveal that the skewness of the weighted bank growth distribution is procyclical to business and financial cycles. Furthermore, we find that different quantiles of the weighted bank growth distribution exhibit different correlations with financial cycles. Chapter 3 proposes two new inferences, a variational inference (VI) and a stochastic variational inference (SVI), which are employed to approximate the Bayesian dynamic nonparametric model with large data sets. We apply these new inferences to the dynamic Dirichlet process mixture (DDPM) model. The DDPM model has a dependence structure with a break indicator. The prior of this indicator is a slab-or-spike prior, which includes a degenerate distribution. The presence of this degenerate distribution and dependence structure causes difficulties when applying VI and SVI techniques because they assume exponential conjugacy and independence within the variational density family. To address these challenges, our paper proposes a novel VI and SVI algorithm that maintains the conditional conjugate prior and preserves the dependence structure. It reduces the computational cost of estimating the model with large data sets while maintaining reasonable precision. Using the data of US banking from 1954 to 2014, we apply the approach to approximate the model and find a significant reduction in estimation time. Chapter 4 proposes a new variational inference (VI) algorithm to estimate a large dimensional Markov switching model fast and accurately. Although the multivariate Markov switching model captures useful information, the Markov chain Monte Carlo algorithm's computational cost increases significantly with its dimension. My contributions are threefold. First, while taking substantially less time to compute, this method achieves comparable in-sample and out-of-sample results to its MCMC counterpart. Second, this inference allows for the inclusion of important restrictions to identify hidden states. Third, my novel VI forward filtering backward smoothing algorithm is comparable to the well-known algorithm in economic literature from Chib (1996). As a result, this new strategy is simple and accessible to implement. My paper presents several results derived from multiple simulations, illustrating the accuracy and timely benefit of the new technique. For example, identifying the bull and bear states, detecting regime switching, and providing forecasts for investment strategies. In addition, applications to three sets of stock returns that are listed in the S&P 500 and one set of industry portfolios provide similar insights.