Long memory estimation for complex-valued time series

Marina I. Knight, Matthew A. Nunes

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)


Long memory has been observed for time series across a multitude of fields, and the accurate estimation of such dependence, for example via the Hurst exponent, is crucial for the modelling and prediction of many dynamic systems of interest. Many physical processes (such as wind data) are more naturally expressed as a complex-valued time series to represent magnitude and phase information (wind speed and direction). With data collection ubiquitously unreliable, irregular sampling or missingness is also commonplace and can cause bias in a range of analysis tasks, including Hurst estimation. This article proposes a new Hurst exponent estimation technique for complex-valued persistent data sampled with potential irregularity. Our approach is justified through establishing attractive theoretical properties of a new complex-valued wavelet lifting transform, also introduced in this paper. We demonstrate the accuracy of the proposed estimation method through simulations across a range of sampling scenarios and complex- and real-valued persistent processes. For wind data, our method highlights that inclusion of the intrinsic correlations between the real and imaginary data, inherent in our complex-valued approach, can produce different persistence estimates than when using real-valued analysis. Such analysis could then support alternative modelling or policy decisions compared with conclusions based on real-valued estimation.
Original languageEnglish
Pages (from-to)517-536
Number of pages20
JournalStatistics and Computing
Issue number3
Early online date4 Jul 2018
Publication statusPublished - 31 May 2019


  • Complex-valued time series
  • Hurst exponent
  • Irregular sampling
  • Long-range dependence
  • Wavelets

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics


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