Bayesian analysis of nonlinear and non-Gaussian time series models

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http://urn.fi/URN:ISBN:978-952-10-8747-9
Title: Bayesian analysis of nonlinear and non-Gaussian time series models
Author: Yin, Ming
Contributor: University of Helsinki, Faculty of Social Sciences, Department of Political and Economic Studies
Doctoral Programme in Economics
Publisher: Helsingin yliopisto
Date: 2018-12-19
Belongs to series: URN:ISSN:2323-9794
URI: http://urn.fi/URN:ISBN:978-952-10-8747-9
http://hdl.handle.net/10138/267611
Thesis level: Doctoral dissertation (article-based)
Abstract: This thesis is a collection of three self-contained essays on using sequential Bayesian methods together with efficient parallel computing strategies, to estimate nonlinear and non-Gaussian econometric/financial time series models. In the past few decades, Bayesian inference has played an increasingly important role in time series econometrics, which, in my opinion, is the consequence of the continuous availability of new efficient algorithms and more powerful computing infrastructures. Concurrent with the fast developments in the semiconductor industry, most previously challenging non-linear and non-Gaussian time series models can now be readily estimated through simulation-based Bayesian methods. In addition, using posterior odds, Bayesian theory also provides a formal framework of conducting model comparison. The first topic of this thesis is the Gaussian mixture autoregressive (GMAR) model. Comparing to other nonlinear autoregressive type models, the GMAR model is unique in several respects: For example, the conditional distribution of each observation is a mixture of several Gaussian distributed components. In particular, this mixture is governed by endogenously determined mixing weights, which are functions of past observations. In addition, the GMAR model is defined in a sensible way that its stationarity and ergodicity conditions are straightforward to establish. It is even possible to obtain the explicit expression of the stationary distribution. These appealing properties make the GMAR model an ideal modeling alternative for the (Markov switching autoregressive) MSAR model, which has been used extensively as the workhorse model to study many aggregate economic time series. In the first essay, I consider sequential Monte Carlo (SMC) algorithm as a novel solution to estimate the GMAR model. In contrary to conventional algorithms (like MCMC), the SMC is robust to multimodal posteriors, and can be used in high dimension scenarios. In addition, the SMC algorithm is based on the sequential importance sampling (SIS) strategy which admits a competitive linear computational complexity at each time, and therefore ready for parallelism. To produce a comprehensive comparison of the MSAR and the GMAR model, as well as to evaluate the evidence of different model specifications, in the second essay, I conduct the Bayesian model selection between these two models with different settings. In contrast to conventional information criteria-based methods, Bayesian model selection offers a simpler and more adaptive way to determine not only the right model, but also the right specification (for example, number of regimes and lags) of the model that better describes the real economy. The third essay is dedicateed to the second topic of this thesis, which focuses on tailoring the Particle Learning (PL) algorithm of Carvalho et al. (2010), to estimate the Markov switching stochastic volatility model with fat-tail innovations (MSSVt). The MSSVt model is not only capable of explaining volatility persistence, but also capable of capturing changes in volatility due to exogenous economic variables or unusual market events. More importantly, the fat-tailed innovations are designed to account for extreme variations in the observations. Despite its attractiveness, its multi-latent-layer structure makes it very difficult to estimate. To fill this research gap, I tailor the PL algorithm to estimate the MSSVt model.N/A
Subject: Economics, Econometrics
Rights: This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.


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