Inference Methods for Stationary Martingales and Other Non-Gaussian Processes

本研究建议为动态过程引入新的推理方法，这些动态过程显示非线性模式，如轨迹中的峰值、时变波动和/或水平变化。方法包括：1)趋势检验和预测；2)这些过程的动态模型的检验和估计。******趋势测试是为一类称为平稳鞅的过程设计的。一般来说，所有鞅都具有趋势特征，可以表示价格动态。平稳鞅显示临时的（局部的）趋势，这种趋势可能会意外地结束，而非平稳鞅，如随机漫步，则显示全局的、持久的趋势。在一个固定的观测期内，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上涨。拟议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。区分这些模式对自然资源管理和经济政策制定很重要。例如，原油价格的持续增长将鼓励新油田的开发，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当地原油价格的趋势，并激发了我对油价动态的应用研究，这将有助于确定bc省2016年由于最近的石油发现而增加的原油产量是否可以支持长期的经济增长。******对于平稳鞅模型和其他厚尾过程模型，提出了一种规格检验和一种新的估计量。这些方法是稳健的，即在弱假设下是有效的。它们适用于监管机构金融稳定委员会（financial Stability Board）为压力测试向银行体系引入的具有极端风险的金融回报模型，例如系统性风险的未观察因子模型。拟议的方法将加强加拿大银行和金融机构监督办公室（OSFI）使用的实证分析工具。******在学术上，建议的研究将通过在顶级统计和计量经济学期刊上发表文章，为推断和估计的统计理论做出贡献。从经验上看，新方法解决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）（www.canada.ca）

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).**