Abstract
Reliable estimation of long-range dependence parameters is vital in time series. For example, in environmental and climate science such estimation is often key to understanding climate dynamics, variability and often prediction. The challenge of data collection in such disciplines means that, in practice, the sampling pattern is either irregular or blighted by missing observations. Unfortunately, virtually all existing Hurst parameter estimation methods assume regularly sampled time series and require modification to cope with irregularity or missing data. However, such interventions come at the price of inducing higher estimator bias and variation, often worryingly ignored. This article proposes a new Hurst exponent estimation method which naturally copes with data sampling irregularity. The new method is based on a multiscale lifting transform exploiting its ability to produce wavelet-like coefficients on irregular data and, simultaneously, to effect a necessary powerful decorrelation of those coefficients. Simulations show that our method is accurate and effective, performing well against competitors even in regular data settings. Armed with this evidence our method sheds new light on long-memory intensity results in environmental and climate science applications, sometimes suggesting that different scientific conclusions may need to be drawn.
Highlights
Time series that arise in many fields, such as climatology; finance, e.g. Jensen (1999) and references therein; geophysical science, such as sea level data analysis, Ventosa-Santaulària et al (2014) and network traffic (Willinger et al, 1997), to name just a few, often display persistent autocorrelations even over large lags
Motivated by the lack of suitable long-memory estimation methods that deal naturally with sampling irregularity or missingness, which often occur in climate science data collection and by the grave scientific consequences induced by misestimation, we propose a novel method for Hurst parameter estimation suitable for time series with regular or irregular observations
lifting one coefficient at a time (LOCAAT) is similar in spirit to the classical discrete wavelet transform (DWT) step which takes a signal vector of length 2 and through separate local averaging and differencing-like operations produces 2 −1 scaling and 2 −1 wavelet coefficients
Summary
Time series that arise in many fields, such as climatology (e.g. ice core data, Fraedrich and Blender 2003, atmospheric pollution, Toumi et al 2001); finance, e.g. Jensen (1999) and references therein; geophysical science, such as sea level data analysis, Ventosa-Santaulària et al (2014) and network traffic (Willinger et al, 1997), to name just a few, often display persistent (slow power-law decaying) autocorrelations even over large lags. Jensen (1999) and references therein; geophysical science, such as sea level data analysis, Ventosa-Santaulària et al (2014) and network traffic (Willinger et al, 1997), to name just a few, often display persistent (slow power-law decaying) autocorrelations even over large lags. This phenomenon is known as long memory or long-range dependence. We first describe two examples that are shown to benefit from long-memory parameter estimation for irregularly spaced time series or series subject to missing observations, our methods are, more widely applicable
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