Inference Methods for Stationary Martingales and Other Non-Gaussian Processes

点击翻译按钮获取中文摘要

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).