BOSTON UNIVERSITY GRADUATE SCHOOL OF ARTS AND SCIENCES Dissertation APPLICATION OF STATISTICAL PHYSICS IN TIME SERIES ANALYSIS

This dissertation covers the two major parts of my PhD research: i) Modeling instantaneous correlation ii) Quantifying time-lag correlation iii) Modeling time-lag correlation iv) Modeling and application of heteroskedasticity. For modeling instantaneous correlation, we studied the limitations of random matrix theory (RMT), and proposed autoregressive random matrix theory (ARRMT) which take into account of the impact of autocorrelations in RMT. For quantifying time-lag correlation, we proposed time-lag random matrix theory (TLRMT) and found long-range crosscorrelations in financial, physiology and genomic data. For modeling time-lag correlation, we proposed global factor model (GFM) and built the relationship between the autocorrelation of the global factor and the time-lag crosscorrelation among individual time series. For modeling and application of heteroskedasticity, we proposed a high frequency trading model using two fractionally intergrated autoregressive conditional heteroskedasticity (FIARCH) processes, and explained the fat-tailed distribution of returns and the long memory in volatilities of financial data.