Long memory estimation for complex-valued time series

Knight, Marina and Nunes, Matthew Alan (2019) Long memory estimation for complex-valued time series. Statistics and Computing, 29 (3). 517–536. ISSN 0960-3174

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Long memory has been observed for time series across a multitude of fields and the accurate estimation of such dependence, e.g. 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.

Item Type:
Journal Article
Journal or Publication Title:
Statistics and Computing
Additional Information:
The final publication is available at Springer via http://dx.doi.org/10.1007/s11222-018-9820-8
Uncontrolled Keywords:
?? computational theory and mathematicstheoretical computer sciencestatistics and probabilitystatistics, probability and uncertainty ??
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Deposited On:
25 Jun 2018 09:30
Last Modified:
28 Jun 2024 01:03