One of the issues in reviewing the performance of a financial market is existence of long-term memory. Since for a financial time series, we may find this feature in the volatility. So reviewing in volatility has been considered by many economists. A common method for identification and modeling of long-term memory in the volatility is to use FIGARCH models. In this paper, we identify and model long-term memory in the data exchange rates volatility (EUR/IRR). According to the statistical properties of skewness, heavy tail and excess kurtosis of data, assuming normal residuals being rejected and therefore cannot identify model by using common methods. The data structure looks NIG distribution is a good choice for the distribution of residuals. Hence with this assumption, we again identify model. The results show a good selection for data is FIGARCH-NIG model.

In this paper, Bayesian fuzzy estimator is obtained first, for the fuzzy data based on the probability prior distribution and afterward based on the possible model and the possibility of a prior distribution. Considering the effect of the membership functions on the fuzzy and possibility Bayesian estimators, a membership function that gives the optimal fuzzy and possibility Bayesian estimators will be introduced for the data. The optimality of the new triangular-gaussian membership function is denoted by using the normal and exponential data sets.