| Summary: | The study of the effect of memory in different economic indices, especially inflation and money market, has high research attractiveness. In this paper, by using the data of consumer price index for Iran during 1990/04 – 2011/11, we investigate the characteristics of CPI’s long–run memory and regress its ARFIMA model. In addition, the amount of error terms in ARFIMA model are examined by FIGARCH model in order to determine what model the heteroscedasticity in inflation is following. The results indicate that monthly time series of inflation may have non-integer root. In other words, the degree of integration for inflation can be a non-integer number rather than an integer. To determine this, an Augmented Dikey-Fuller test, Philips–Prone test and KPSS are used and the results show that the degree of integration for inflation series should lie between zero and one. Thus, the hypothesis of inflation series with memory is proposed. By estimating the parameter of long run memory in the model it becomes evident that the inflation series has the degree of integration of 0.46 and one time differentiating leads to over-differentiation. Hence, inflation series has a long run memory in Iran and the effects of each shock on this variable exists for long periods.
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