SEMIMARTINGALE DETECTION AND GOODNESS-OF-FIT TESTS

• 成果类型: Article
• 署名作者: Bull, Adam D.
• 署名单位: University of Cambridge
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1484
• 发表日期: 2017
• 页码: 1254-1283
• 关键词: time financial models; INTEGRATED VOLATILITY; diffusion-coefficient; microstructure noise; parametric form; jumps

摘要

In quantitative finance, we often fit a parametric semimartingale model to asset prices. To ensure our model is correct, we must then perform goodnessof- fit tests. In this paper, we give a new goodness-of-fit test for volatilitylike processes, which is easily applied to a variety of semimartingale models. In each case, we reduce the problem to the detection of a semimartingale observed under noise. In this setting, we then describe a wavelet-thresholding test, which obtains adaptive and near-optimal detection rates.