The Ornstein-Uhlenbeck (OU) process, a mean-reverting stochastic process, has been widely applied as a time series model in various domains. This paper describes the design and implementation of a model-based synthetic time series model based on a multivariate OU process and the Arbitrage Pricing Theory (APT) for generating synthetic pricing data for a complex market of interacting stocks. The objective is to create a group of synthetic stock price time series that reflects the correlation between individual stocks and clusters of stocks in how a real market behaves. We demonstrate the method using the Standard and Poor's (S&P) 500 universe of stocks as an example.

翻译：奥恩斯坦-乌伦贝克（OU）过程作为一种均值回归随机过程，已被广泛用作各领域的时间序列模型。本文描述了基于多变量OU过程与套利定价理论（APT）的模型驱动型合成时间序列框架的设计与实现，该框架用于生成复杂交互股票市场中的人工价格数据。其目标在于创建一组能够反映真实市场中个股与股票簇之间相关性的合成股票价格时间序列。我们以标准普尔500指数（S&P 500）成分股为例演示该方法。