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Wavelet transform oriented methodologies with applications to time series analysis

Wavelet transform oriented methodologies with applications to time series analysis

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Wavelet transform oriented methodologies with applications to time series analysis

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  1. Bartosz Kozłowski, kozlow@iiasa.ac.at Wavelet transform oriented methodologies with applications to time series analysis Wavelet Analysis (WA) Filtration Approximation Periodicity Identification Forecasting International Institute for Applied Systems Analysis Institute of Control and Computation Engineering, WUT

  2. Wavelets’ Background • Foundations • Time and Frequency • Inversible

  3. Originalsignal Originalsignal WT WT Originalwaveletcoefficients Originalwaveletcoefficients Analysis Newsignal Newsignal Inverse WT Analysis Newwaveletcoefficients Analysis with WT

  4. Characteristics Fast Spatial Localization Frequency Localization Energy Applications Acoustics Economics Geology Health Care Image Processing Management Data Mining ... WA Background

  5. WaveShrink – 1Network Traffic

  6. WaveShrink – 1Network Traffic

  7. WaveShrink – 2Network Traffic

  8. WaveShrink – 2Network Traffic

  9. WaveShrink – 3Network Traffic

  10. WNS ApproachNetwork Traffic

  11. Trend ApproximationCrop Yields

  12. Trend ApproximationCrop Yields

  13. Periodicity Identification

  14. Periodicity IdentificationMeasures of Regularity

  15. Periodicity IdentificationSales

  16. Periodicity IdentificationWeather

  17. Forecasting Share Prices

  18. Forecasting Sales

  19. Forecasting Sales

  20. Evaluations

  21. 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%

  22. Summary • 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