c m s 2005 workshop k s wavelet transform oriented methodologies with applications to time series...
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C MS
2005 WorkshopK S
Wavelet transform oriented methodologies with applications to time series analysis
Wavelet Analysis (WA)FiltrationApproximationPeriodicity IdentificationForecasting
Bartosz Kozłowski, [email protected]
International Institute for Applied Systems Analysis
Institute of Control and Computation Engineering, WUT
C MS2005 WorkshopK SWavelets’ Background
Foundations Time and Frequency Inversible
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C MS2005 WorkshopK SAnalysis with WT
Originalwavelet
coefficients
Newsignal
Originalsignal
Newwavelet
coefficients
WT
Inverse WT
Analysis
Originalwavelet
coefficients
Newsignal
Originalsignal
Analysis
WT
C MS2005 WorkshopK SWA Background
Characteristics Fast Spatial Localization Frequency Localization Energy
Applications Acoustics Economics Geology Health Care
Image Processing Management Data Mining ...
C MS2005 WorkshopK S
WaveShrink – 1Network Traffic
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WaveShrink – 2Network Traffic
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WaveShrink – 2Network Traffic
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C MS2005 WorkshopK S
WNS ApproachNetwork Traffic
C MS2005 WorkshopK S
Trend ApproximationCrop Yields
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Trend ApproximationCrop Yields
C MS2005 WorkshopK SPeriodicity Identification
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C MS2005 WorkshopK S
Periodicity IdentificationMeasures of Regularity
Measures
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Periodicity IdentificationSales
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Periodicity IdentificationWeather
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Original Time Series
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C MS2005 WorkshopK SForecasting Share Prices
C MS2005 WorkshopK SForecasting Sales
C MS2005 WorkshopK SForecasting Sales
C MS2005 WorkshopK SEvaluations
Direct Seasonal
Std. Dev. 5,815448996 37675615,83
Max. Err. 0,183306337 0,172322659
Min. Err. 0,004556636 0,000310097
Avg. Err. 0,056000513 0,036521327
C MS2005 WorkshopK S
Another Forecasts’ Accuracy Measure
How many times (%) the method correctly forecasted the raise / fall of the time series
Direct Wavelet Approach for Shares ~55%
Seasonal Wavelet Approach for Sales ~75%
C MS2005 WorkshopK SSummary
Allow to use standard approaches and combine them
Various application domains Open possibilities for new approaches Provide multiresolutional analysis Do not increase computational order of
complexity Improve results