An automatic approach to the mean and covariance estima- tions of spatiotemporal nonstationary processes Hwa-Lung Yu 1 , Chih-Hsin Wang 1 , Yu-Zhang Wu 1 1 Dept of Bioenvironmental Systems Engineering, National Taiwan University hlyu@ntu.edu.tw Abstract. Modeling of nonstationary and nonhomogeneous enviromental processes has been among the major interests of geostatistical applications. In this study, a heurstic algorithm, i.e., particle swarm optimization, is used to automatically determine (1) the optimal nonparametric trend from kernel smoothing method, and (2) the nested spatiotemporal covariance models for the environmental process of interest. The proposed algorithm is not only included in parameter estimations but also in covariance model selection, i.e., selection of the number and the type of the structures of the fitted nested covariance model. A case study is shown by applying the pro- posed algorithm along with kriging method for the spatiotemporl modeling of particulate matter (PM10) in Taipei city (Taiwan). 1 INTRODUCTION Physical and environemntal processes are often considered as a mixture of low frequen- cy (trend) and high frequecy (residual) components, as shown in Eq. (1)， ) , ( ) , ( ) , ( t s t s m t s z ε + = (1) where is a continuous random process at spatial location s and time , and and ) , ( t s z ) t , ( t s m ) , ( t s ε are the trend function and spatiotemporal autocorrelated residual process, respectively. The functional forms for can generally be classified as nonparametric and parametric models. Parametric model is widely used in many geosta- tical approaches, e.g., universal kriging [1, 2] and regression kriging [3], and requires the prior knowledge of the functional form of general trend pattern which is not easily to be justified [4]. For the purposes of developing a general approach for the modeling of nonstationay processes, it is preferable to use nonparametric model which can be directly derived from the data without the necessity of extensive knowledge of data cha- ractereiscs. ) , ( t s m Several smoothing techniques have been applied for the nonparametric trend estimation, e.g., general additive model, spline, and kernel smoothing method [5]. Among them, kernel smoothing method is easily applied and generates the trend by averaging the data weighted with a certain predetermined kernel over each neighborhood within a speci- fied distance and can be easily extended into the multidimensional domain in space and time. The selection of neighborhood size is critical to the accuracy of nonparametric trend estimation. In addition, most smoothing techniques were primarily designed for the regression purposes, which assumes that a process decomposes into a smoothing trend and uncorrelated residuals. If correlated residuals are prevalent in the process, smoothing techniques may generate non-robust trend estimation [6, 7]. Therefore, pa-