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A Self‐Normalized Semi‐Parametric Test to Detect Changes in the Long Memory Parameter

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  • Murad S. Taqqu
  • Ting Zhang

Abstract

We consider the problem of testing for change points in the long memory parameter. The test relies on semi‐parametric estimation of the long memory parameter, which does not require the complete parametric specification of the whole spectrum. A self‐normalizer utilizing a sequence of recursive semi‐parametric estimators is used to make the asymptotic distribution of the test statistic free of the nuisance scale parameter. We study the asymptotic behavior of the proposed test for situations when there is at most one change point and also when there are an unknown number of change points. Monte Carlo simulations are carried out to examine the finite‐sample performance of the proposed test.

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  • Murad S. Taqqu & Ting Zhang, 2019. "A Self‐Normalized Semi‐Parametric Test to Detect Changes in the Long Memory Parameter," Journal of Time Series Analysis, Wiley Blackwell, vol. 40(4), pages 411-424, July.
    • Handle: RePEc:bla:jtsera:v:40:y:2019:i:4:p:411-424
    DOI: 10.1111/jtsa.12444
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