Bayes Factors for Discrete Observations from Diffusion Processes
针对精细时间尺度的时间序列数据，提出一种基于贝叶斯因子的模型选择方法，将数据生成过程建模为连续时间扩散过程，并用离散数据近似计算贝叶斯因子，适用于金融数据如S&P 500指数。
We present an approach to model selection for a time series of data on a fine time scale. The underlying process generating the data is modelled as a continuous time stochastic process. The underlying continuous processes are assumed to be diffusions with time varying drift and diffusion coefficient. Several approaches to modelling the diffusion coefficient are described. To perform model selection, we propose an approximation to the Bayes factor that uses only the discrete data. We illustrate our approach for several well-known processes including: Brownian motion with drift, the Ornstein-Uhlenbeck process, a mean reversion process with drift, exponential Brownian motion, and a logistic growth model. Finally, we apply our technique to data from the Standard & Poor's 500 stock index by comparing a random walk to a mean reversion model.