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GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform

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  • Fryzlewicz, Piotr
  • Delouille, V´eronique
  • Nason, Guy P.

Abstract

We consider the stochastic mechanisms behind the data collected by the solar X-ray sensor (XRS) on board the the GOES-8 satellite. We discover and justify a non-trivial mean-variance relationship within the XRS data. Transforming such data so that its variance is stable and its distribution is taken closer to the Gaussian is the aim of many techniques (e.g. Anscombe, Box-Cox). Recently, new techniques based on the Haar-Fisz transform have been introduced that use a multiscale method to transform and stabilize data with a known meanvariance relationship. In many practical cases, such as the XRS data, the variance of the data can be assumed to increase with the mean, but other characteristics of the distribution are unknown. We introduce a method, the data-driven Haar-Fisz transform (DDHFT), which uses Haar-Fisz but also estimates the mean-variance relationship. For known noise distributions, the DDHFT is shown to be competitive with the fixed Haar-Fisz methods. We show how our DDHFT method denoises the XRS series where other existing methods fail.

Suggested Citation

  • Fryzlewicz, Piotr & Delouille, V´eronique & Nason, Guy P., 2007. "GOES-8 X-ray sensor variance stabilization using the multiscale data-driven Haar-Fisz transform," LSE Research Online Documents on Economics 25221, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:25221
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    References listed on IDEAS

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    1. Linton, O. B. & Chen, R. & Härdle, Wolfgang, 1995. "An Analysis of Transformations for Additive Nonparanetric Regression," SFB 373 Discussion Papers 1995,68, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Piotr Fryzlewicz & Guy P. Nason, 2006. "Haar–Fisz estimation of evolutionary wavelet spectra," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(4), pages 611-634, September.
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    4. Piotr Fryzlewicz & Theofanis Sapatinas & Suhasini Subba Rao, 2006. "A Haar--Fisz technique for locally stationary volatility estimation," Biometrika, Biometrika Trust, vol. 93(3), pages 687-704, September.
    5. Johnstone, Iain & Silverman, Bernard W., 2005. "EbayesThresh: R Programs for Empirical Bayes Thresholding," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i08).
    6. Fryzlewicz, Piotr & Sapatinas, Theofanis & Subba Rao, Suhasini, 2006. "A Haar-Fisz technique for locally stationary volatility estimation," LSE Research Online Documents on Economics 25225, London School of Economics and Political Science, LSE Library.
    7. Fryzlewicz, Piotr & Nason, Guy P., 2006. "Haar-Fisz estimation of evolutionary wavelet spectra," LSE Research Online Documents on Economics 25227, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Antonis A. Michis & Guy P. Nason, 2015. "Estimation and Prediction of Shipping Trends with the Data-Driven Haar-Fisz Transform," Working Papers 2015-1, Central Bank of Cyprus.
    2. Antonis A. Michis & Guy P. Nason, 2017. "Case study: shipping trend estimation and prediction via multiscale variance stabilisation," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(15), pages 2672-2684, November.
    3. Guy P. Nason & Daniel Bailey, 2008. "Estimating the intensity of conflict in Iraq," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(4), pages 899-914, October.
    4. Antonis A. Michis, 2021. "Wavelet Multidimensional Scaling Analysis of European Economic Sentiment Indicators," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 443-480, October.

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    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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