Estimation of Nonstationary and Noninvertible ARFIMA Model Based on Sequential Detrending

When a differenced series is integrated to restore its original order of integration, the initial values are lost in the differencing process; integrating the series with any values other than the initial values yields a series with a spurious deterministic trend.

Therefore, we use sequential detrending to prevent the trend from affecting the estimation of the fractional integration order. This method provides a valid estimate for any fractional integration order, whether negative or positive. Simulation results show that many methods of fractional order estimation can be used for ARFIMA (p,d,q) with d∈(−∞,+∞) in the presence of an intercept, short-memory terms, and a deterministic trend.