Modeling and Forecasting of Time Series Data Set using Fuzzy Set

Abstract

Forecasting future outcomes has always been a subject of keen interest in real world. In the present era various government and private sectors uses time series data which requires forecasting the future outcome within time using past and present information. To do so there is a need of efficient forecasting model which can predict future outcome with high accuracy. Conventional time series model failed to provide accurate forecasting result if time series data consist of linguistic variables like high, low, and medium, etc., because of vagueness. The concept of soft computing was introduced to deals with imprecise and vague data. A new time series model was introduced to overcome the problem of conventional time series model using an important element of soft computing, i.e., fuzzy set. In this thesis, we have introduced a new time series model. The concept of high-order fuzzy time series is used to develop forecasting model. Historical data set is partitioned in to effective interval lengths using an existing Re-Partitioning Discretization (RPD) approach and a novel defuzzification technique based on weighted-mean defuzzification approach is introduced to obtain forecasting outcome. Historical temperature data set of Taipei, student enrollment data set of Alabama University and stock price of TAIFEX (Taiwan Future Exchange) is used to evaluate the forecasting accuracy of proposed model. Statistical parameters like mean, Standard Deviation, Root Mean Square Error (RMSE) and Average Forecasting Error Rate (AFER) are used to calculate the accuracy of proposed model. RMSE and AFER obtained using proposed model over different data set are compared with other existing models. This comparison shows that proposed model outperform over existing models. Forecasting accuracy of proposed model over historical temperature data set of Taipei is better than other existing model, i.e., model based upon Artificial Neural Network and Multi-variant Markov Chain Model. Also forecasting accuracy of proposed model over student enrollment data set of Alabama University is better than Song and Chissom’s 4th order model. Forecasting accuracy of proposed model over stock price of TAIFEX is as good as Chen’s method.