New Directions in Fractal Modeling: Estimation, Filtering, and Applications

分形建模的新方向：估计、过滤和应用

• 批准号: RGPIN-2015-06749
• 负责人: Fisher, Adlai
• 金额: $ 1.02万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=650786
• 关键词: New; Directions; Fractal; Modeling; Estimation

Fractals and multifractals are of major importance in mathematics and many areas of engineering and the natural sciences. The first multifractal measures were developed and applied in geology (de Wijs, 1951) and the modelling of turbulence (Kolmogorov, 1962; Mandelbrot, 1972, 1974). Subsequent applications include astronomy, genetics, hydrology, meteorology, medicine, network traffic modeling, and seismology.  In finance, my own research developed the first multifractal stochastic processes, based on time-deformed Brownian motions (Calvet, Fisher, and Mandelbrot, 1997). Subsequent research provides moment-based inference (Calvet and Fisher, 2002), exact filtering and maximum-likelihood estimation (Calvet and Fisher, 2001); particle filtering (Calvet, Fisher, and Thompson, 2006); extensions using equilibrium theory, including multifractal jump-diffusions (Calvet and Fisher, 2007, 2008); and applications to interest rates (Calvet, Fisher, and Wu, 2013) and option pricing (Calvet, Fisher, Fearnley, and Leippold, 2014).***The proposed research advances multifractal tools and develops new applications. To date, the Markov-switching Multifractal (MSM), based on discrete-valued state variables, has been a key building block for multifractal applications in finance.  Recent particle filtering techniques permit consideration of a broader set of models with diffusive components. This should in particular prove advantageous in option pricing applications, which show good results relative to standard benchmarks.  Application and further development of these particle filtering methods will be a key area of research. The research program will also develop simpler computational methods by adaptating Mixed Data Sampling methods ("MIDAS", Ghysels, Santa-Clara, and Valkanov, 2006) to multifractal processes.***The research program will also seek to determine the causes of multifractality in financial data by investigating the transmission of information across stocks, where stocks are modeled as a network. Coauthors and I have shown evidence of slow information diffusion, best captured by a hyperbolic decay, in daily stock returns (Boguth, Carlson, Fisher, and Simutin, 2014). The proposed research will examine information transmission at much higher frequencies, using a relatively recent news database called RavenPack. News are sourced from professional blogs, newspapers and newswires time stamped to the milliseconds. To process this news database such as extracting news for a specific firm on multiple years requires parallel data processing because of the size of the data. This research will permit precise tracking of the transmission of news across stocks, identification of the relevant transmission network, identification of the link to volatility, and to fractal properties in asset returns. **

分形和多重分子在数学，工程和自然科学领域至关重要。第一个多重分子测量是在地质学（De Wijs，1951年）和湍流建模（Kolmogorov，1962; Mandelbrot，1972，1974）中开发和应用的。随后的应用包括天文学，遗传学，水文学，气象，医学，网络交通建模和地震学。在金融方面，我自己的研究基于时间呈现的布朗动作（Calvet，Fisher和Mandelbrot，1997）开发了第一个多重分子随机过程。随后的研究提供了基于力矩的推断（Calvet and Fisher，2002），精确的过滤和最大似然估计（Calvet and Fisher，2001）；粒子过滤（Calvet，Fisher和Thompson，2006年）；使用等效理论的扩展，包括多重跳跃式延伸（Calvet and Fisher，2006年）； Fisher，2007，2008）；以及对利率（Calvet，Fisher和Wu，2013年）和期权定价（Calvet，Fisher，Fearnley和Leippold，2014年）的应用。迄今为止，基于离散的状态变量的马尔可夫开关多型（MSM）一直是金融中多重分数应用程序的关键构建块。最近的粒子过滤技术允许考虑一组具有不同组件的模型。在期权定价应用程序中，这尤其应该被证明是有利的，这些应用程序相对于标准基准显示出良好的结果。这些粒子过滤方法的应用和进一步开发将是研究的关键领域。该研究计划还将通过调整混合数据采样方法（“ Midas”，Ghysels，Santa-Clara和Valkanov，2006年）来开发更简单的计算方法。我和合着者已经显示了每日股票回报中最好由双曲线衰变捕获的信息缓慢扩散的证据（Boguth，Carlson，Fisher和Simutin，2014年）。拟议的研究将使用一个名为RavenPack的新闻数据库以更高的频率检查信息传输。新闻来自专业博客，报纸和新闻刻在毫秒到毫秒的时间。为了处理此新闻数据库，例如在多年内为特定公司提取新闻需要并行数据处理，因为数据的大小。这项研究将允许精确跟踪跨股票的新闻传输，相关传输网络的识别，识别与波动率的链接以及资产回报中的分形属性。 **