Application of Statistical Physics in Time Series Analysis

Speaker: Duan Wang

When: April 8, 2015 (Wed), 11:00AM to 12:00PM (add to my calendar)
Location: SCI 352

This event is part of the PhD Final Oral Exams.

Dissertation Committee: H.E. Stanley, Robert Carey, William Klein, Boris Podobnik, Plamen Ivanov

ABSTRACT

This dissertation covers the four major parts of my PhD research: i) Modeling instanta- neous correlation ii) Quantifying time-lag correlation iii) Modeling time-lag correlation iv) Modeling and application of heteroskedasticity. For modeling instantaneous correlation, we study the limitations of random matrix theory (RMT) and analytically show autocorrelations would impact the result of RMT. We propose autoregressive random matrix theory (ARRMT) which takes into account the impact of autocorrelations on the study of crosscorrelations in multiple time series. We illustrate the method using air pressure data for 95 US cities. For quantifying time-lag correlation, we propose time-lag random matrix theory (TL-RMT) and nd long-range magnitude crosscorrelations in nancial, physiology and genomic data. For modeling time-lag correlation, we propose global factor model (GFM) and build the relationship between the autocorrelation of the global factor and the time-lag cross-correlation among individual time series. We applied the method to equity indices data for 48 countries and nd out that a single global factor can explain most of the time lag crosscorrelations among these indices. For modeling and application of heteroskedasticity, we propose a high frequency trading model using two fractionally intergrated autoregressive conditional heteroskedasticity (FI-ARCH) processes, and explained the fat-tailed distribution of returns and the long memory in volatilities of financial data.

Duan