Fuzzy Time Series Model for Unequal Interval Length Using Genetic Algorithm

Abstract

Time series analysis and forecasting depend on the observed historical data. As it deals with numerous number of information, imprecision occurs due to many reasons like truncation error, mechanical fault, noise. In such cases, fuzzy concept works well to handle impreciseness. Fuzzy time series forecasting methodology consists of defining universe of discourse (UOD), fuzzification of time series data points, assigning relationships between consecutive data points and defuzzification to get back the forecasting results in real domain. In this paper, UOD of a time series has been defined, unequal partitions of the UOD are established and then relationship among consecutive data points is evaluated to get the forecasting models. Genetic algorithm has been used in partitioning the UOD unequally and establishing the relationship. Forecasting model is applied on enrollment of University of Alabama, BSE sensex time series, and Shenzhen stock exchange data. The results are compared with conventional fuzzy time series models.

6 Appendix

If $A_i$ is the ith actual value, $F_i$ is the ith forecasted value, and m denotes the number of historical data, then mean square error (MSE) is given below.

1.1 6.1 Mean Square Error (MSE)

If the actual and forecasted values are given, then MSE gives the average of the squares of the errors. Errors are the difference between forecasted and actual value.

$$\begin{aligned} MSE = \frac{1}{m}{\displaystyle \sum _{i=1}^m(\mathrm{F}_i - \mathrm{A}_i)^2} \end{aligned}$$

(7)