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

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

Sampling distributions of local Whittle estimators

Availability:

Working Paper (updated December 16, 2025)
arXiv (updated December 15, 2025)
Replication Code

Abstract. Fractionally integrated time series, exhibiting long memory with slowly decaying autocorrelations, are frequently encountered in economics, finance, and related fields. Since the seminal work of Robinson (1995), a variety of semiparametric local Whittle estimators have been proposed for estimating the memory parameter $d$ . However, applied researchers must determine which estimator to use, and under what conditions. This paper compares several local Whittle estimators, first replicating key findings from the literature and then extending these with new Monte Carlo experiments and in-depth empirical studies. We compare how each estimator performs in the presence of short-run dynamics, unknown means, time trends, and structural breaks, and discuss how to interpret potentially conflicting results with real datasets. Based on the findings, we offer guidance to practitioners on estimator choice, bandwidth selection, and the potential diagnostic value of disagreements between estimators.

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

JEL Classification: C22, 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
}