Inference Methods for Stationary Martingales and Other Non-Gaussian Processes

稳态鞅和其他非高斯过程的推理方法

• 批准号: RGPIN-2017-05657
• 负责人: Jasiak, Joann
• 金额: $ 0.68万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=751464
• 关键词: Inference; Methods; Stationary; Martingales; Other

This research proposal introduces new inference methods for dynamic processes that display nonlinear patterns, such as spikes in the trajectory, time varying volatility and/or level shifts. The methods include: 1) tests of trend and forecasts; 2) tests and estimators for dynamic models of these processes.The tests of trend are designed for a category of processes, called stationary martingales. In general, all martingales are characterized by trends and can represent price dynamics. The stationary martingales display temporary (local) trends, which can end unexpectedly, while the non-stationary martingales, such as the random walks display global, long-lasting trends. Over a fixed observational period, it may be hard to distinguish between the two types of trend. In the context of prices of natural resources, such as crude oil, or commodities, such as wheat, a global trend represents sustainable growth, while a local trend represents an unsustainable, temporary upswing. The proposed research introduces tests that detect growth of either type, and help determine if that growth is sustainable or not. Distinguishing between these patterns is important for natural resource management and economic policy making. For example, sustainable growth of crude oil prices would encourage exploitation of new oil fields whereas temporary price growth does not. Recent episode of low oil prices has strongly impacted Canadian economy, the Canadian Dollar and consumer price indexes. The empirical evidence from the past ten years reveals the local trends in crude oil prices and motivates my applied research on oil price dynamics, which will help determine if increased crude oil production in B.C. in 2016 due to recent oil discovery can support long-lasting economic growth.For the stationary martingale models and other models of fat-tailed processes, a specification test and a new type of estimators are proposed. These methods are robust, i.e valid under weak assumptions. They are applicable to models of financial returns with extreme risks introduced to the banking system by the supervisory Financial Stability Board for stress testing, such as the unobserved factor models of systemic risk. The proposed methods will enhance the tools of empirical analysis used by Canadian banks and the Office of the Superintendent of Financial Institutions (OSFI). Academically, the proposed research will contribute to the statistical theory of inference and estimation through publications in top ranked statistical and econometric journals. Empirically, the new methods address the needs of the banking sector and of the Canadian natural resource management. The trend analysis of energy prices will provide new insights for policy makers who seek to protect the environment and support economic growth, in line with the Government of Canada's Review of Environmental and Regulatory Processes (2016) (www.canada.ca).

这项研究建议介绍了新的推理方法的动态过程，显示非线性模式，如尖峰的轨迹，随时间变化的波动性和/或电平变化。这些方法包括：1）趋势和预测的检验; 2）这些过程的动态模型的检验和估计。趋势的检验是为一类称为平稳鞅的过程设计的。一般来说，所有的鞅都具有趋势的特征，并且可以代表价格动态。平稳鞅显示临时（局部）趋势，可能会意外结束，而非平稳鞅，如随机游走显示全局，长期趋势。在一个固定的观察期内，可能很难区分这两种趋势。就原油等自然资源或小麦等商品的价格而言，全球趋势代表可持续增长，而局部趋势则代表不可持续的暂时性上涨。拟议中的研究引入了检测两种类型增长的测试，并帮助确定这种增长是否可持续。区分这些模式对于自然资源管理和经济政策制定非常重要。例如，原油价格的可持续增长将鼓励开发新油田，而暂时的价格增长则不会。最近的低油价严重影响了加拿大经济，加元和消费者价格指数。过去十年的经验证据揭示了原油价格的本地趋势，并激励了我对油价动态的应用研究，这将有助于确定由于最近的石油发现而增加的2016年不列颠哥伦比亚省原油产量是否能够支持长期的经济增长。提出了一种规格检验和一类新的估计量。这些方法是鲁棒的，即在弱假设下有效。它们适用于金融稳定委员会为压力测试而引入银行系统的极端风险的金融回报模型，例如系统性风险的未观察因素模型。 拟议的方法将加强加拿大银行和金融机构监督办公室使用的经验分析工具。在学术上，拟议的研究将有助于通过在顶级统计和计量经济学期刊上发表文章的推断和估计的统计理论。从经验上看，新方法满足了银行部门和加拿大自然资源管理的需要。能源价格的趋势分析将为寻求保护环境和支持经济增长的政策制定者提供新的见解，符合加拿大政府的环境和监管程序审查（2016年）（www.canada.ca）。