Bayesian estimation of fractional difference parameter in ARFIMA models and its application

Recognizing and presenting the appropriate model is of particular importance to examine the statistical models for fitting time series data. Among time series models widely used in the analysis of economic, meteorological, geographical, and financial data is Auto Regressive Frac-tionally Integrated Moving Average (ARFIMA) model. In this model, and other time series models, the parameters of model are estimated by assuming that the average of data is constant. In this article, while investigating the behavior of ARFIMA model, Bayesian estimation of the fractional difference parameter (d) was presented considering the appropriate prior distribution. To check the efficiency of the proposed Bayesian estimation, using simulation and Akaike information criterion (AIC) it is shown that Bayesian estimation performs better compared to other methods. Finally, using a real data set and assuming a suitable prior distribution for the fractional differ-ence parameter (d), shows that ARFIMA (0, d,0) is a suitable model for these data. The goodness of fit of the ARFIMA model was evaluated according to the Bayesian estimation of parameters.