In this paper, we apply a recursive method to financial data to determine their corresponding Hurst exponent and the optimal Autoregressive Fractionally Integrated Moving Average (ARFIMA) models. We begin by introducing the long-range dependence phenomenon and methods to address it in time series modeling. Then, a recursive algorithm, where the Hurst exponent is estimated by applying an autoregressive filter to the data repeatedly until it converges, is empirically tested with simulated data for stability and convergence. Finally, we apply this convergence approach to real commodity data sets. We identify the optimal ARFIMA models for each commodity studied and estimate the Hurst exponent as well as their corresponding ARFIMA parameters. Our results provide a stable method for estimating the Hurst index and fitting stationary long-memory processes to ARFIMA models.