Thesis
Essays on variational Bayes in Econometrics
- Creator
- Rights statement
- Awarding institution
- University of Strathclyde
- Date of award
- 2023
- Thesis identifier
- T16730
- Person Identifier (Local)
- 201982490
- Qualification Level
- Qualification Name
- Department, School or Faculty
- Abstract
- The first essay (Chapter 1) presents a Variational Bayes (Vb) algorithm for Vector Autoregression (reduced-form VAR). The algorithm is derived based on the evidence lower bound, which is demonstrated to be tight, ensuring efficient convergence. The optimization is carried through the Coordinate descent optimization. To validate the proposed method, its accuracy and computational costs are compared with existing Vb approaches that approximate VAR using a one equation at a time technique (Choleskytransformed VAR), and a more computationally intensive Markov Chain Monte Carlo (MCMC) method using Gibbs sampling. In applications using both US macroeconomic data and artificial data, our Vb for VAR outperforms Vb in Cholesky-transformed VAR in terms of VAR covariance accuracy. Furthermore, compared to the MCMC method, our proposed Vb algorithm for reduced form VAR achieves comparable accuracy while significantly reducing computation time. The second essay (Chapter 2) takes the Variational Bayes (Vb) approach to the next level by extending it to the challenging domain of Mixed Frequency Vector Autoregression (MF-VAR) models. These models tackle the complexities of dealing with multiple frequency data in a single estimation, including the issue of missing lower frequency observations in a higher frequency system. To overcome these challenges, we introduce a robust and innovative Vb method known as the Variational Bayes-Expectation Maximization algorithm (Vb-EM). Our Vb-EM algorithm offers several key contributions to approximate Bayesian inference in the MF-VAR model. We derive an evidence lower bound to the log marginal likelihood, accounting for missing observations, and optimize it with respect to the variational parameters. In doing so, we surpass existing Vb methods in the literature by achieving a tighter evidence lower bound, ensuring optimal convergence. To further validate our approach, we compare it to the more computationally demanding Markov Chain Monte Carlo (MCMC) method using Gibbs sampling. Through extensive empirical evaluations and out-of-sample forecasts of eleven US macroeconomic series, we demonstrate that our Vb EM algorithm performs on par with MCMC in terms of point forecasts. Furthermore, when assessing predictive density, we find no significant empirical evidence to distinguish between the two methods. Notably, our Vb-EM algorithm offers the distinct advantage of significantly lower computational costs, making it an appealing choice for researchers and practitioners alike. The third essay (Chapter 3) begins by emphasizing that the spike of volatilities of macroeconomic variables during the surge of Covid-19 pandemic, which led to poor performance of the workhorse Bayesian VAR with stochastic volatility in terms of forecasting. This has attracted considerable attention from economists towards alternative models, including non-parametric models such as Gaussian process VAR. The approach to estimate VAR one equation at a time, namely Cholesky-transformed VARs, enables the application of more advanced regression models in VAR. In this chapter I explore several advanced Gaussian process VARs, including GP-VAR, GP-DNN-VAR (which incorporates a deep neural network as the mean function in the GP prior), and Heteroscedastic-GP-VAR (HGP-VAR) where the likelihood variance is assumed to be time-varying and parameterized by another latent-GP function. In this chapter the variational inference is utilized to be the approximating method for HGP-VAR. The forecasting results suggest that during non pandemic periods, HGP-VAR and GP-VAR perform similarly to BVAR-SV. However, during the Covid-19 pandemic, the advantage of having time-variant likelihood variance in HGP-VAR becomes more pronounced for predicting macroeconomic variables in a highly turbulent period.
- Advisor / supervisor
- Koop, Gary
- Resource Type
- DOI
- Funder
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