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Modified Local Whittle Estimation of the Memory Parameter in the Nonstationary Case

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Author Info
Katsumi Shimotsu
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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Abstract

Semiparametric estimation of the memory parameter is studied in models of fractional integration in the nonstationary case, and some new representation theory for the discrete Fourier transform of a fractional process is used to assist in the analysis. A limit theory is developed for an estimator of the memory parameter that covers a range of values of d commonly encountered in applied work with economic data. The new estimator is called the modified local Whittle estimator and employs a version of the Whittle likelihood based on frequencies adjacent to the origin and modified to take into account the form of the data generating mechanism in the frequency domain. The modified local Whittle estimator is shown to be consistent for 0 < d <2 and is asymptotically normally distributed with variance 1/4 for 1/2 < d < 7/4. The approach allows for likelihood-based inference about d in a context that includes nonstationary data, is agnostic about short memory components and permits the construction of valid confidence regions for d that extend into the nonstationary region.

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File URL: http://cowles.econ.yale.edu/P/cd/d12b/d1265.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1265.

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Length: 54 pages
Date of creation: Jul 2000
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Handle: RePEc:cwl:cwldpp:1265

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Discrete Fourier transform; fractional Brownian motion; fractional integration; long memory; nonstationarity; semiparametric estimation; Whittle likelihood;

Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions

References listed on IDEAS
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  1. Peter C.B. Phillips & Victor Solo, 1989. "Asymptotics for Linear Processes," Cowles Foundation Discussion Papers 932, Cowles Foundation, Yale University. [Downloadable!]
  2. Peter C.B. Phillips, 1999. "Discrete Fourier Transforms of Fractional Processes," Cowles Foundation Discussion Papers 1243, Cowles Foundation, Yale University. [Downloadable!]
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. John Galbraith & Victoria Zinde-Walsh, 2001. "Autoregression-Based Estimators for ARFIMA Models," CIRANO Working Papers 2001s-11, CIRANO. [Downloadable!]
  2. Arielle Beyaert, 2004. "Fractional Output Convergence, with an Application to Nine Developed Countries," Econometric Society 2004 Australasian Meetings 280, Econometric Society. [Downloadable!]
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This page was last updated on 2009-11-9.

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