Latent Yule-Simon Processes with Applications
Asher A. Hensley
May 8, 2018
Light Engineering room 250
Advisor: Prof. Petar Djuric
Time series data resulting from the latent dynamics of complex systems are ubiquitous in the modern world. Although the true mechanisms behind the data we observe may be beyond our grasp in many cases, there are statistical regularities that can help us better understand these latent processes. In this work, we present new hierarchical generative models based on latent Yule-Simon processes for modeling and predicting time series data with switching statistical properties. The Yule-Simon process is a type of urn process which imparts a preferential attachment law on regime durations leading to the formation of power-laws in the switching regime waiting time distribution. Such models act as flexible prior processes for explaining the creation of “bursty” time series data characterized by long runs of stable behavior punctuated by abrupt jumps. These models are nonparametric in the sense that the number of latent regimes is not only inferred from the data, but theoretically infinite. Given a set of time series measurements, we describe Bayesian inference procedures based on Markov Chain Monte Carlo sampling to invert the generative process and discover hidden structure within the data and gain insight into its dynamics. We then present several case studies using financial time series data to investigate the occurrence of events prior to market crashes, the volatility of cryptocurrency exchange rates, and the dynamics of price correlation.