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   -> Volume 7, Issue 6


Preprint: Two Preprints on Scale Analysis of Non-Gaussian Time Series
 
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a.walden@ic.ac.uk (A Walden)
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PostPosted: Mon Jun 22, 1998 10:58 am    
Subject: Preprint: Two Preprints on Scale Analysis of Non-Gaussian Time Series
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#7 Preprint: Two Preprints on Scale Analysis of Non-Gaussian Time Series

Two preprints are available on the scale analysis of non-Gaussian time series

1.
Authors: A. Serroukh (Imperial College, London, UK)
A.T. Walden (Imperial College, London, UK)

Title: The Scale Analysis of Bivariate Non-Gaussian Time Series via Wavelet
Cross-covariance

Statistics Section, Imperial College, Technical Report TR-98-02

Abstract:

Many scientific studies require a thorough understanding of the
scaling characteristics of observed processes. We derive and justify a
decomposition of the usual cross-covariance in terms of scale-by-scale
wavelet cross-covariances, and provide an estimator of the wavelet
cross-covariance at specified lag. For jointly stationary but
generally non-Gaussian linear processes, asymptotic results are given
for this wavelet cross-covariance estimator. The variance of the
esimator can in each case be expressed as a spectrum value at zero
frequency, a convenient form for practical estimation. A detailed
scale analysis of the surface albedo and temperature of pack ice in
the Beaufort Sea ably demonstrates the usefulness of wavelet analysis
in decomposing structures at different scales hidden in time series
data.

2.
Authors: A. Serroukh (Imperial College, London, UK)
A.T. Walden (Imperial College, London, UK)
D.B. Percival (University of Washington and Mathsoft Inc)

Title: Statistical Properties of the Wavelet Variance Estimator
for Non-Gaussian/Non-Linear Time Series

Statistics Section, Imperial College, Technical Report TR-98-03

Abstract:

The wavelet variance decomposes the variance of a time series into
components associated with different scales, and is widely used in
scientific and engineering studies. We consider an estimator of the
wavelet variance based on the maximal-overlap (or stationary, or
undecimated) discrete wavelet transform. The asymptotic distribution
of this wavelet variance estimator is derived for a wide class of
stochastic processes, not necessarily Gaussian or linear. We show how
to estimate the variance of this distribution using spectral methods.
Simulations confirm the theoretical results. At small scales,
estimates of the variance of the wavelet variance estimate for the
surface albedo of pack ice, a strongly non-Gaussian series, are much
larger than those obtained under a Gaussian assumption.

Preprints are available from:

http://www.ma.ic.ac.uk/~atw/
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