comparing the accuracy of the model meta heuristic and econometric in forecasting of financial time series with long-term memory (case study, stock index of cement industry in iran)

data with high frequency have a particular type of none stationary that is called fractional none stationary. this property causes the emergence of long-term memory in financial time series with high frequency. the existence of long-term memory in cement industry time-series is studied in this paper at first and its presence will be confirmed in a high confidence level by two tests r/s and gph. next, the accuracy of financial time-series forecast models such as arma and garch which don't consider the feature of long-term memory in time series modeling and models such as arfima and figarch that take this feature into account are compared with presented new meta heuristic that is composed of algorithm (harmony search) and weighted fuzzy time series by the way of rolling window and by the use of root mean square error criteria (rmse) in different time intervals. the results show that the presented meta heuristic method submits better result of common econometric models in all time intervals.