Abstract—The prediction of meteorological parameters at a meteorological station is an interesting and open problem. A first- order linear dynamic model GM(1,1) is the main component of the grey system theory. The grey model requires only a few previous data points in order to make a real-time forecast. In this paper, we consider the daily average ambient temperature as a time series and the grey model GM(1,1) applied to local prediction (short-term prediction) of the temperature. In the same case study we use a fuzzy predictive model for global prediction. We conclude the paper with a comparison between local and global prediction schemes. Keywords—Fuzzy predictive model, grey model, local and global prediction, meteorological forecasting, time series. I. INTRODUCTION HE current weather forecasting tools, based on numerical techniques, are not always able to capture local variability in the weather. Local prediction is forecasting the future based only on a small set of the most recent data in time series. Forecasts of this kind are used to establish a curve for a most recent set of data, and then make predictions based on the established curve. In order to improve the current forecast system the ideas and algorithms of grey models are used [5]. Grey prediction can be considered as a curve fitting approach that has exceptionally good performance for real world data. The grey system theory, first proposed by J. Deng in 1982, avoids the inherent defects of conventional methods and only requires a limited amount of data to estimate the behavior of an uncertain system or a time series. Grey means incomplete or uncertain information. The grey system has been successfully applied to industrial, social, and ecological systems, economy, geography traffic, management and environmental sciences [6,7,8,15]. In this paper we represent a fuzzy predictive model (Wang- Mendel method) for global prediction which learns an input- output mapping [Chapter 5, 16], [5], [17]. The WM method was one of the first methods to design fuzzy systems from data. Manuscript received July 25, 2005. This work was supported by Archimedes I Program of the Greek Ministry of Education and E. U. A. I. Dounis is with the Technological Educational Institute of Piraeus, P. Ralli & Thivon 250, 12244, Aigaleo, Athens, Greece (phone: +30- 2106624541, e-mail: aidounis@otenet.gr). D. Tseles, G. Nikolaou are with the Technological Educational Institute of Piraeus, P. Ralli & Thivon 250, 12244, Aigaleo, Athens, Greece (phone: +30- 2105381200, e-mail: dtsel@teipir.gr). G. P. Syrcos, P. Tiropanis are with the Technological Educational Institute of Piraeus, P. Ralli & Thivon 250, 12244, Aigaleo, Athens, Greece (phone: +30-2105381188, e-mail: gsyrcos@otenet.gr). The WM method gives accurate prediction and at the same time is easy to explain to the non-expert. The method has been applied to a variety of problems [3,4,16]. The source of origin of the temperature data of the period from 1981 up to 2003 (8390 samples) was: National Observatory of Athens (NOA), Institute for Environmental Research and Sustainable Development (IERSD). The grey model and fuzzy model were implemented using MATLAB®. The paper is organised as follows. Section 2 presents the methodology to create a predictor. In section 3 the grey modelling approach that acts as the local prediction scheme is discussed. Section 4 presents the fuzzy predictive model acting as global prediction scheme. Simulation results and the comparison of two prediction schemes are then discussed in section 5. Conclusions are made in the final section. II. TIME SERIES PREDICTION In general, the predicted value of a variable in a future time is based on m previous values. The m is called the lag of the prediction. If we have the values of variable y for the moments from k-m to k-1, that is, y(k-1), y(k-2), …, y(k-m), we may predict y(k), and also the next time interval values y(k+1), …, y(k+p) where p is the time step. The methodology used to train a predictor is summarized as follows: 1. Pre-process data. 2. Decide the m lag values. 3. Separate the actual data set into a training data set and a test data set. 4. Create a local or global predictor based on the architectures that follow in the next sections. 5. Use the training data set to train the predictor. The training proceeds as follows. At time k, apply y(k- 1), y(k-2), …,y(k-m) to the predictor. Take the prediction output y(k+p). Calculate the output errors (criteria evaluation). 6. Evaluate the performance of the trained predictor with the test data set. The predictor uses a set of m-tuples as inputs and a single output as the target value of the predictor. This method is often called the sliding window technique as the m-tuples slides over the full training set. III. LOCAL PREDICTION AND GREY MODEL Local prediction is forecasting the future based only on a set of the most recent data in a time series. In order to improve the A. I. Dounis, P. Tiropanis, D. Tseles, G. Nikolaou, and G. P. Syrcos A Comparison of Grey Model and Fuzzy Predictive Model for Time Series T World Academy of Science, Engineering and Technology International Journal of Computer and Information Engineering Vol:2, No:6, 2008 2263 International Scholarly and Scientific Research & Innovation 2(6) 2008 scholar.waset.org/1307-6892/15438 International Science Index, Computer and Information Engineering Vol:2, No:6, 2008 waset.org/Publication/15438