ANOVA for diffusions and Ito processes

• 成果类型: Article
• 署名作者: Mykland, Per Aslak; Zhang, Lan
• 署名单位: University of Chicago; Carnegie Mellon University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053606000000452
• 发表日期: 2006
• 页码: 1931-1963
• 关键词: STOCHASTIC VOLATILITY MODELS; discretely observed diffusions; asymptotic expansions; term structure; coefficient; martingales; likelihood

摘要

U processes are the most common form of continuous semimartingales, and include diffusion processes. This paper is concerned with the nonparametric regression relationship between two such U processes. We are interested in the quadratic variation (integrated volatility) of the residual in this regression, over a unit of time (such as a day). A main conceptual finding is that this quadratic variation can be estimated almost as if the residual process were observed, the difference being that there is also a bias which is of the same asymptotic order as the mixed normal error term. The proposed methodology, ANOVA for diffusions and Ito processes, can be used to measure the statistical quality of a parametric model and, nonparametrically, the appropriateness of a one-regressor model in general. On the other hand, it also helps quantify and characterize the trading (hedging) error in the case of financial applications.