Application of statistical physics in time series analysis

Abstract

This dissertation covers the four 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 study the limitations of random matrix theory (RMT) and investigate the impact of autocorrelations on the results 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 (TLRMT) and find long-range magnitude crosscorrelations in financial, physiological and genomic data. For modeling time-lag correlation, we propose a global factor model (GFM) and build the relationship between the autocorrelation of the global factor and the time-lag crosscorrelation among individual time series. We apply the method to equity indices data for 48 countries and find 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 (FIARCH) processes, and explained the fat-tailed distribution of returns and the long memory in volatilities of financial data.