Three essays on Bayesian econometrics

Abstract

This thesis deals with the subject of Bayesian econometric methods in time-series analysis in the field of economics and finance. Each chapter constitutes an independent empirical application conducted in a Bayesian framework. In the first chapter, we employ a Bayesian time-varying parameter Vector Autoregressive (TVP-VAR) model to examine the relation between the price of oil and investor sentiment. To measure investor sentiment, we construct a new proxy based on the search patterns of individuals on the Google engine. Using this new proxy, oil prices as well as benchmark macroeconomic and financial variables, we estimate a TVP-VAR that takes into account the changes in the transmission of investors sentiment shocks to oil prices over time. The results indicate that an unexpected increase in investor attention yields a long-lasting increase both in the price of oil and the stock market returns. In the second chapter, we use alternative Bayesian Markov- witching Generalised Autoregressive Conditional Heteroscedasticity (MS-GARCH) models to analyse the behaviour of volatility of cryptocurrencies. In total, we consider 292 cryptocurrrencies for each of which we estimate the estimate 27 alternative MS-GARCH specifications. First, we evaluate the in-sample performance of each model using the information criteria. Next, we assess the ability of the models to perform one-day ahead conditional volatility and Value-at-Risk forecasts. The results indicate that for a wide range of cryptocurrencies (with different characteristics), Markov-switching models which two or more regimes outperform the ones with a sole regime. In addition, the findings suggest the presence of inverse leverage effect in the majority of the cryptocurrencies. In the third chapter, we propose a new a methodology to test examine for Grangercausality in a time-varying framework. Specifically, we combine the estimates from a TVP-VAR with the null hypothesis of no Granger-causality that allows us to track changes in the causal relationship of variables in each period. This methodology offers several advantages compared the existing ones which mostly rely on rolling window algorithms. The performance (size and power) of the proposed methodology is evaluated through Monte Carlo simulations. As an empirical application, we examine the evolution of Granger-causal relationship between bitcoin returns and alternative variables. According to the results, other cryptocurrency returns, stock market returns and uncertainty Granger cause bitcoin returns during periods when bitcoin prices burst and bitcoin’s trading volume Granger causes bitcoin returns during periods when bitcoin prices remain relatively steady.