NDLI: Spectral estimation for locally stationary time series with missing observations

Content Provider	Springer Nature Link
Author	Knight, Marina I. Nunes, Matthew A. Nason, Guy P.
Copyright Year	2011
Abstract	Time series arising in practice often have an inherently irregular sampling structure or missing values, that can arise for example due to a faulty measuring device or complex time-dependent nature. Spectral decomposition of time series is a traditionally useful tool for data variability analysis. However, existing methods for spectral estimation often assume a regularly-sampled time series, or require modifications to cope with irregular or ‘gappy’ data. Additionally, many techniques also assume that the time series are stationary, which in the majority of cases is demonstrably not appropriate. This article addresses the topic of spectral estimation of a non-stationary time series sampled with missing data. The time series is modelled as a locally stationary wavelet process in the sense introduced by Nason et al. (J. R. Stat. Soc. B 62(2):271–292, 2000) and its realization is assumed to feature missing observations. Our work proposes an estimator (the periodogram) for the process wavelet spectrum, which copes with the missing data whilst relaxing the strong assumption of stationarity. At the centre of our construction are second generation wavelets built by means of the lifting scheme (Sweldens, Wavelet Applications in Signal and Image Processing III, Proc. SPIE, vol. 2569, pp. 68–79, 1995), designed to cope with irregular data. We investigate the theoretical properties of our proposed periodogram, and show that it can be smoothed to produce a bias-corrected spectral estimate by adopting a penalized least squares criterion. We demonstrate our method with real data and simulated examples.
Starting Page	877
Ending Page	895
Page Count	19
File Format	PDF
ISSN	09603174
Journal	Statistics and Computing
Volume Number	22
Issue Number	4
e-ISSN	15731375
Language	English
Publisher	Springer US
Publisher Date	2011-07-02
Publisher Place	Boston
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Missing data Nondecimated transform Spectral estimation Wavelet lifting Numeric Computing Mathematics Statistics and Computing/Statistics Programs Artificial Intelligence (incl. Robotics) Statistics
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Theoretical Computer Science Computational Theory and Mathematics Statistics, Probability and Uncertainty

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