A Nonparametric Approach to Detecting Parametric Nonmonotonic Trends in Environmental Processes

• Activity Number: 306
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Vyacheslav Lyubchich and Yulia R. Gel*+ and Abdel El-Shaarawi
• Companies: University of Waterloo, Canada and University of Waterloo and The American University in Cairo
• Keywords: trend detection ; nonmonotonic trends ; change points and regime shifts ; bootstrap ; climate studies ; high-dimensional statistical inference

Abstract

We propose a new testing procedure for detecting smooth (non)monotonic trends embedded into a linear noise that possibly does not degenerate to a finite dimensional representation, or into a conditionally heteroscedastic (G)ARCH noise. The proposed nonparametric trend test is local regression-based, and we develop a flexible and computationally efficient hybrid bootstrap procedure to approximate its finite sample behavior. Since the proposed trend test does not assume prior knowledge on the dependence structure and probability distribution of the observed process, the new testing procedure is fully data-driven and robust to misspecification of dependence structure and distributional assumptions. Moreover, since the proposed methodology allows to test for monotonic vs. nonmonotonic trends and, hence, to assess existence of extremums in the hypothesized trend function, the developed approach may be also employed for preliminary detection of regime shifts and change points in the observed environmental data series. Our simulation studies indicate competitive performance of the proposed nonparametric procedure for detection of (non)monotonic trends against conventional trend tests.