Reliable estimation of long-range dependence (LRD) parameters, such as the Hurst exponent, is a well-studied problem in the statistical literature. However, many time series observed in practice present missingness or are naturally irregularly-sampled. In these settings, current literature is sparse; most approaches require heavy modifications to deal with the irregular observations.
In this talk we present a technique for estimating the Hurst exponent of a long memory time series. The method is based on a flexible wavelet transform built via the lifting scheme, and is naturally suitable for series exhibiting time domain irregularity. The technique provides good estimation for regularly- as well as irregularly-spaced series.
We illustrate the technique through a time series application in climatology.
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