An Algorithm Forecasting Time Series Using Wavelet

In this paper we used the technique of wavelets with fuzzy logic to forecast enrollment of Alabama university from 1971 to 1994 where data were taken and analyzed by using wavelets, then logic , and we used the mean square error (MSE) to compare the forecasting results with previous different forecasting methods. The results were acceptable compared with the results of previous research. 1Introduction Time series forecasting are widely used in many areas, Such as economics, inventory, systems, statistics, etc. Forecasting is one of the important activities in business Enrollment, finance, etc. that helps in decision making. The Classical time series methods can not deal with forecasting problems in which the values of time series are linguistic terms represented by using wavelet and fuzzy logic. Wavelets turned out to be very useful when applied to many Problems including analysis and synthesis of time series in both time and scale [13]. Foundations of wavelet based analysis method were laid in the beginning of the 20 th century. Back then, in the year 1909 Hungarian mathematician Alfred haar introduced his two-state function in appendix to his doctoral thesis published later on [6] lately a very fast development of wavelet-based data mining [18] techniques may be observed. Fuzzy set theory is first presented by Zadeh (1965) for treatment of uncertain environment inseveral fields. Particularly fuzzy logic designs are well accepted and established for electronic devices and later fuzzy sets found a broad application potential on various studyfields [5]. Song and Chissom [15] introduced a theory for fuzzy time Series and applied fuzzy time series methods [16], [17] that modeled the enrollments of the university of Alabama, in recent years a number of techniques have been proposed for forecasting based on fuzzy set theory methods. Chen presented a method to forecast the enrollments of the university of Alabama based on fuzzy time series [1] . In [8] Huang extended Chen’s work presented in [1] and used simplified calculations with the addition of heuristic rules to forecast the enrollments. The rest of this paper is organized as follows. In section (2) we briefly review wavelet transform, in section (3) we deal with Definitions of the fuzzy time series. In section (4) we use the theory of wavelet transform and An Algorithm Forecasting Time Series Using Wavelet Kais Ismail Ibraheem 1 ,Eman Bacheer Abdelahad 2 1 Department of Computer, University of Mosul, Mosul, Iraq 2 Department of Mathematic, University of Mosul, Mosul, Iraq IJCSI International Journal of Computer Science Issues, Vol. 11, Issue 1, No 1, January 2014 ISSN (Print): 1694-0814 | ISSN (Online): 1694-0784 www.IJCSI.org 160 Copyright (c) 2014 International Journal of Computer Science Issues. All Rights Reserved. fuzzy time series to propose a new method to forecast the enrollment of the university of Alabama. In section (5) we compare the forecasting result of the forecasting result of the proposed method with the existing methods, and the conclusions are discussed in this section . 2-Wavelet Transform According to Fourier theory, a signal can be expressed as the sum of a series of sines and cosines. This sum is also called a Fourier expansion (see Eq. (1)).However, a serious drawback of the Fourier transform is that it only has frequency resolution and no time resolution. Therefore, we can identify all the frequencies present in a signal, but we do not know when they are present. The wavelet theory is proposed [12]