Bootstrap Nonparametric Test for Trends in the Presence of ARCH/GARCH Effects
Bei Chen1, Yulia R. Gel1, Bovas Abraham1, Abdel H. El-Shaarawi2
1Statistics and Actuarial Science, University of Waterloo, ON, Canada; 2National Water Research Institute, Burlington, ON, Canada

Many hydrological time series, e.g. ice phenology and pollution measurements, show presence of conditional heteroscedasticity. Testing for possible trend of unknown functional form, i.e. including but not limited to a linear trend, while taking into account the dynamic variability of hydrological data, has a significant practical importance as it allows to better assess the climatic and other environmental changes. In this talk, we introduce a new bootstrap nonparametric trend test under ARCH/GARCH effects based on heteroscedastic Analysis of Variance (ANOVA) with a large number of factor levels, which enables to detect a wide range of smooth (non)-monotonic trends and also can serve as a goodness-of-fit method to check if the assumption of the hypothesized trend function is valid. The proposed algorithm is an extension of the Wang-Van Keilegom test, based on a nonparametric regression with serially correlated innovations with constant variance. The new test has considerably better performance compared to the widely applied test in hydrology, Kendall's Tau, particularly in the cases when both trend and seasonality are present and for small samples of observations. Under weak smoothness assumptions, we show that the test statistic is asymptotically normal. In addition, since our bootstrap procedure utilizes the linear form of ARCH/GARCH processes, the new approach considerably reduces computational costs, which makes the test useful for real-time modeling. We illustrate our methodology with an application to detection of trends in ice phenology time series and acidity levels of the Turkey Lakes Watershed.

Keywords: Bootstrap; Trend; GARCH; Nonparametric test

Biography: Bei Chen is a Ph.D. student in the Department of Statistics and Actuarial Science at the University of Waterloo. Her research interests lie in time series analysis and nonparametric statistics. Bei's Ph.D. dissertation is on linearization in nonlinear and nonstationary time series. Currently, a particular focus of her research is on bootstrap resampling method for dependent observations with environmental and financial applications.