Statistical Analysis of Long-Memory Continuous-Time Processes

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The investigator studies the continuous-time fractionally-integrated Auto-Regressive Moving-Average processes and their variants, based onrecent advances in stochastic calculus of fractional Brownian motion.Such models provide a general framework for analyzing univariate or multivariate discrete-time data sampled from an underlying strongly-dependent continuous-time process. In particular, the investigator develops methods for studying volatility, fractional co-integration and temporal aggregation of long-memory timeseries data. Time series data are data collected sequentially over time, and they abound in science and other fields, e.g., finance.The investigator studies new methods for analyzing time series datawith long-memory temporal patterns. The developed methodologies furnish general tools for analyzing changes in the volatility pattern in the data, exploring structural relationships within a set of time series data, and assessing effects of aggregating the data over longer observational periods.These methods have applications in various fields, e.g., pricing of financialderivatives.