Statistical Analysis of Long-Memory Continuous-Time Processes

基于分数布朗运动随机演算的最新进展，研究了连续时间分数积分自回归滑动平均过程及其变种，这些模型为分析从基本的强相依连续时间过程中抽取的单变量或多变量离散时间数据提供了一个通用的框架。特别是，研究人员开发了研究长记忆时间序列数据的波动性、分数协整和时间聚集的方法。时间序列数据是指在一段时间内按顺序收集的数据，广泛存在于科学和金融等领域。研究人员研究了分析具有长记忆时间模式的时间序列数据的新方法。所开发的方法为分析数据中波动模式的变化、探索一组时间序列数据中的结构关系以及评估在较长观察期内聚合数据的影响提供了通用工具。这些方法在各个领域都有应用，例如金融衍生品的定价。

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.