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).

该研究提案引入了用于显示非线性模式的动态过程的新推理方法，例如轨迹中的尖峰、随时间变化的波动性和/或水平移动。方法包括：1）趋势检验和预测； 2）这些过程的动态模型的测试和估计。趋势测试是针对称为平稳鞅的过程类别而设计的。一般来说，所有鞅都具有趋势特征，并且可以代表价格动态。固定鞅显示临时（局部）趋势，可能会意外结束，而非固定鞅（例如随机游走）则显示全局的长期趋势。在固定的观察期内，可能很难区分这两种类型的趋势。在原油等自然资源或小麦等大宗商品价格的背景下，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上涨。拟议的研究引入了检测任一类型增长的测试，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新油田的开采，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当地趋势，并激发了我对油价动态的应用研究，这将有助于确定 BC 省原油产量的增加是否会增加。 2016 年，由于最近的石油发现可以支持长期的经济增长。对于固定鞅模型和其他厚尾过程模型，提出了规格测试和新型估计器。这些方法是稳健的，即在弱假设下有效。它们适用于监管金融稳定委员会引入银行体系进行压力测试的具有极端风险的财务回报模型，例如系统性风险的不可观测因子模型。 拟议的方法将增强加拿大银行和金融机构监管办公室（OSFI）使用的实证分析工具。在学术上，拟议的研究将通过在顶级统计和计量经济学期刊上发表论文，为推论和估计的统计理论做出贡献。从经验来看，新方法满足了银行业和加拿大自然资源管理的需求。根据加拿大政府的环境和监管流程审查 (2016) (www.canada.ca)，能源价格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。