Semiparametric Estimation of Fractional Integration: An Evaluation of Local Whittle Methods

Jason R. Blevins.
The Ohio State University, Department of Economics
Working Paper.

Availability:

• Working Paper (updated September 23, 2025)

Abstract. Fractionally integrated time series exhibiting long memory are commonly in economics, finance, and related fields. Semiparametric methods for estimating the memory parameter $d$ have proven to be effective and robust, but practitioners face difficulties arising from the availability multiple estimators with different valid parameter ranges and the choice of bandwidth parameter $m$. This paper provides a comprehensive evaluation of local Whittle methods from Robinson’s (1995, Annals of Statistics) foundational estimator through the exact local Whittle approaches of Shimotsu and Phillips (2005, Annals of Statistics) and Shimotsu (2010, Econometric Theory), where theoretical advances have expanded the feasible range of memory parameters and improved efficiency. Using a new implementation in Python, PyELW, we replicate key empirical and Monte Carlo results from the literature, providing external validation for both the original findings and the software implementation. We extend these empirical applications to demonstrate how method choice can affect substantive conclusions about persistence. Based on comprehensive simulation comparisons and empirical evidence, we provide practical guidance for applied researchers on how and when to use each method.

Keywords: fractional integration, fractional differencing, nonstationarity, long memory, local Whittle estimation.

JEL Classification: C22, C63, C87.

BibTeX Record:

@TechReport{blevins-2025-lws,
    author      = {Jason R. Blevins},
    title       = {Semiparametric Estimation of Fractional Integration: An Evaluation of Local {Whittle} Methods},
    type        = {Working Paper},
    institution = {The Ohio State University},
    year        = 2025
}