On detecting non‐monotonic trends in environmental time series: a fusion of local regression and bootstrap

Abstract

Abstract In this paper, 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 (autoregressive conditionally heteroscedastic/generalized autoregressive conditionally heteroscedastic (ARCH/GARCH)) 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. Because 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, which is of particular importance for noisy environmental measurements. Moreover, because the proposed methodology allows to test for monotonic versus non‐monotonic 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. Copyright © 2013 John Wiley & Sons, Ltd.