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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711757
• 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).

该研究建议介绍了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，时间变化的波动率和/或级别的变化。方法包括：1）趋势和预测测试； 2）这些过程动态模型的测试和估计器。 趋势测试是为一种称为固定群岛的流程而设计的。通常，所有赛车都以趋势为特征，可以代表价格动态。固定的马利亚人展示了暂时的（本地）趋势，这可能会出乎意料地结束，而非统计的烈会（如随机步行）显示了全球，持久的趋势。在固定的观察期内，可能很难区分两种类型的趋势。在自然资源价格（例如原油或商品（例如小麦））的背景下，全球趋势代表了可持续增长，而当地趋势则代表了一种不可持续的临时增长。拟议的研究介绍了检测两种增长的测试，并有助于确定该增长是否可持续。区分这些模式对于自然资源管理和经济政策制定很重要。例如，原油价格的可持续增长将鼓励剥削新的油田，而临时价格增长则不会。最近的低油价发作对加拿大经济，加拿大美元和消费者价格指数产生了强烈影响。过去十年来的经验证据揭示了原油价格的当地趋势，并激发了我对石油价格动态的应用研究，这将有助于确定卑诗省的原油生产是否增加。 2016年，由于最近的石油发现，可以支持持久的经济增长。 对于固定的Martingale模型和其他脂肪尾部过程模型，提出了规格测试和新型的估计器。这些方法是强大的，即在弱假设下有效。它们适用于主管财务稳定委员会对银行系统引入极端风险的财务回报模型，例如，例如无观察到的全身风险因素模型。 拟议的方法将增强加拿大银行和金融机构总监办公室（OSFI）使用的经验分析工具。 从学术上讲，拟议的研究将通过排名最高的统计和计量经济学期刊的出版物来提高推论和估计的统计理论。从经验上讲，新方法满足了银行业和加拿大自然资源管理的需求。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决策者提供新的见解，这与加拿大政府对环境和监管程序的审查（2016）（www.canada.ca）。