REALIZED LAPLACE TRANSFORMS FOR PURE-JUMP SEMIMARTINGALES

• 成果类型: Article
• 署名作者: Todorov, Viktor; Tauchen, George
• 署名单位: Northwestern University; Duke University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1006
• 发表日期: 2012
• 页码: 1233-1262
• 关键词: Levy processes; stable laws; volatility; parameters; models

摘要

We consider specification and inference for the stochastic scale of discretely-observed pure-jump semimartingales with locally stable Levy densities in the setting where both the time span of the data set increases, and the mesh of the observation grid decreases. The estimation is based on constructing a nonparametric estimate for the empirical Laplace transform of the stochastic scale over a given interval of time by aggregating high-frequency increments of the observed process on that time interval into a statistic we call realized Laplace transform. The realized Laplace transform depends on the activity of the driving pure-jump martingale, and we consider both cases when the latter is known or has to be inferred from the data.