Statistical Analysis of Long-Memory Continuous-Time Processes

研究者研究了连续时间分数积分自回归移动平均过程及其变体，基于分数布朗运动随机微积分的最新进展。这些模型为分析从潜在的强依赖连续过程中采样的单变量或多变量离散时间数据提供了一般框架。特别是，研究者开发了研究波动性的方法，分数协整和长记忆时间序列数据的时间聚合。时间序列数据是随时间顺序收集的数据，在科学和其他领域（如金融）中大量存在。研究者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测期内汇总数据的影响提供了通用工具。这些方法在许多领域都有应用，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.