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Poster Communications
SP2
Thursday, September 5th
19:45
Resampling Time Series using the Wavelet
Transform
Aline Edlaine de Medeiros
UEM
Márcia L. A. dos Santos
Eniuce M. de Souza
Brani Vidakovic
Among the techniques that allow the resampling in Time Series is the decomposition from the
Wavelet Transform. This technique is able to rewrite time series in terms of smooth and detail
wavelet coefficients with reduced serial autocorrelation. One of the classical methods of resampling
is the Parallel Bootstrap that uses the Decimated Discrete Wavelet Transform and the parallel
re-sampling of wavelet coefficients to generate replicas of a time series. The advantage of applying
the bootstrap is due to the possibility of estimating parameters as well as confidence intervals even
with small time series. In this paper, we propose to comparethe bootstrap method using a new
resampling methodology based on the Non-decimated Discrete Wavelet Transform (NDWT). Unlike
the decimated transform, the potential of the NDWT is to preserve the same number of wavelet
coefficients at each level of multiresolution. To evaluate the performance of both techniques,
confidence intervals were estimated for simulated time series and also for time series from the
number of Meninginte cases collected from the Brazilian DATASUS system. In addition, both
methods were evaluated for the preservation of the Hurst exponent, a measure used to evaluate
the intensity of autocorrelation inherent to time series, especially Higuchi’s estimation method is
being used due to its robustness. When assessing the Hurst exponent before and after resampling,
it is possible to analyze whether the autocorrection present in the time series was preserved by the
bootstrap. The obtained results indicate that both resampling methods are effective in preserving
the Hurst exponent, as well as generating satisfactory confidence intervals.
Keywords: Non-decimate Wavelet Transform; Bootstrap; Hurst Exponent
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