This project aims to explore Bayesian estimation of stationary time series models for large datasets via Markov chain Monte Carlo (MCMC) methods. While first transforming the time series to the frequency domain has proved an effective method for reducing the computational cost of the likelihood function, the cost can be further reduced by employing subsampling MCMC methods. These methods estimate the likelihood based on a subsample of observations in the frequency domain, so-called periodogram observations. However, current subsampling MCMC methods assume that the periodogram observations do not depend on the model parameters. This assumption is violated when an exogenous variable is added to the time series model. This project aims to extend subsampling MCMC methods in the frequency domain to accommodate for models with exogenous variables.
University of Technology Sydney
Mark Youssef is an undergraduate student at the University of Technology Sydney completing a Bachelor of Science in analytics. He is majoring in financial mathematics and will be pursuing a career in data science, showing a keen interest in Bayesian methods and their ability to estimate complex models. Through his research, he aims to overcome some of the current limitations of these methods to expand their use to a wider range of models. He plans to further extend the research completed during this project through an honours degree and a PhD. Having also completed studies in audio engineering, Mark can often be found playing guitar or listening to his favourite bands.