Meteorological Time Series Modeling Using an Adaptive Gene Expression Programming ALINA BĂRBULESCU and ELENA BĂUTU Department of Mathematics and Computers Science Ovidius University 124, Mamaia Blv., Constanţa, 900527 ROMANIA alinadumitriu@yahoo.com http://alina.ilinc.ro/ID_262/index.html ebautu@univ-ovidius.ro http://csam.univ-ovidius.ro/~ebautu Abstract: The precipitations are characterized by important spatial and temporal variation. Model determination for such series is of high importance for hydrological purposes (e.g. weather forecasting, agriculture, flood areas, administrative planning), even if discovering patterns in such series is a very difficult problem. The objective of the current study is to describe the use of an adaptive evolutionary technique that give promising results for the development of non-linear time series models. Key-Words: time series modeling, gene expression programming, adaptive algorithm, precipitation 1 Introduction Evolutionary techniques have been used successfully to solve various time series problems [1], [9]. The technique employed in this paper is an improved version of the Gene Expression Programming (GEP) algorithm. The studied time series consists of the mean annual precipitation registered between January 1965 and December 2005, at the Medgidia meteorological station, situated in the South – East of Romania, on the Black Sea coast. The complexity of the problem of modeling such meteorological time series derives from the diversity of phenomena that affect the climate, in general, and the precipitation, in particular (e.g. the greenhouse effect, human influences, solar influences, etc.). The problem is a topic of substantial interest in the literature [7], [8], [18]. Classical approaches, such as the linear model, rely on the assumption of a constant data generating process (whose characteristics do not vary with time). Often, they may fail to obtain adequate models due to the nonlinear dynamic behavior of time series, but also due to the lack of adaptation of the methods. This makes the problem very well suited for the use of heuristic methods, such as GEP. Our article has the following structure. In the next section, some considerations regarding the time series modeling problem are provided. We proceed by a brief presentation of the basic ideas on the evolutionary technique used to derive the models. Then, we perform a statistical analysis of studied time series, followed by the presentation of the experiments and the results. The final section concludes the paper with a discussion of our results and possible directions of future research. 2 Problem Formulation A time series model for the observed data is a specification of the joint distributions of a sequence of random variables of which is postulated to be a realization. ) ( t x ) ( t X ) ( t x In what follows we shall denote by n use the selection volume The problem that arises is to find a model that fits the time series as good as possible. In order to do it, the first step is to decide how many previous data points are used – the “window size”. One must also decide how the past data used by the model is sampled from the original time series. In this study, we denote the window size by w, and we sample the past data at a sampling lag k =1. This means that, for example, if w = 3, the model will predict the value at a moment t , , using the previous 3 values in the time series, namely . t x − t x 3 2 1 , , − − t t x x In a more formal manner, we are interested in finding a function that predicts the values of a time series as accurately as possible: f ( ) n t x x x f x w t t t t ≤ = − − − , ..., , , ˆ 2 1 . The accuracy of a model is measured in terms of prediction error: ( ) ∑ = − − = n i i i x x n error 1 2 ˆ 1 1 . Better models are those with smaller prediction error. We also can report the ratio of prediction error over standard deviation as a measure of the prediction quality in a model. Finding a function that fits the data is actually an inverse problem, since there may exist more than one Proceedings of the 10th WSEAS International Conference on EVOLUTIONARY COMPUTING ISSN: 1790-5109 17 ISBN: 978-960-474-067-3