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 (draft coming soon)

Abstract. Fractionally integrated time series exhibiting long memory are common in economic and financial data. Semiparametric methods for estimating the memory parameter $d$ have proven to be effective and robust, but practitioners face difficulties selecting and implementing appropriate methods for their applications. 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, we replicate key Monte Carlo and empirical results from the literature, validating both the original findings and the software implementation. Extended empirical applications to economic time series demonstrate how method choice can affect substantive conclusions about persistence. 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-selw,
    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
}