WAVELET FILTRATION FOR FINANCIAL DATA ANALYSIS

1. WAVELET FILTRATION FOR FINANCIAL DATA ANALYSIS Stanislav Zaitsev

3. TECHNICAL INDICATOR – MOVING AVERAGE Market Price Movement Analysis FUNDAMENTAL ANALYSIS TECHNICAL ANALYSIS analysis of price dynamic based on the price history and volumes CHAOS THEORY Bill Williams, Malkiel Elliot Waves Theory Ralph N. Elliot Multifractal Analysis Benoit B. Mandelbrot CYCLES THEORY J.M. Hurst Trend-Following Analysis Including Frequency Filtration approaches Harmonic Analysis GRAPHICAL ANALYSIS

4. TECHNICAL INDICATOR – MOVING AVERAGE Simple Moving Average (SMA) SMA = SUM (CLOSE (i), N) / N Exponential Moving Average (EMA) EMA = (CLOSE (i) * P) + (EMA (i - 1) * (100 - P)) Smoothed Moving Average (SMMA) SMMA (i) = (SUM1 - SMMA (i - 1) + CLOSE (i)) / N Linear Weighted Moving Average (LWMA) LWMA = SUM (CLOSE (i) * i, N) / SUM (i, N)

5. COMPARING JMA (Jurik Research) with EMA Jurik Research www.jurikres.com

6. TREND FOLLOWING EFFICIENCY • According to Jurik research(http://www.jurikres.com/), the best MAfilter indicator should have: • 1) Minimal distance between price line and • filter line. This will impact the speed for decision making. • 2) Minimal gap between price and filter lines when uptrend is being changed to downtrend. If not, the prediction of the price will not be precise • 3) Minimal distance when there is uptrend. Otherwise it will take a time for convergence. • 4) Maximal smoothness. Otherwise, there will be too many false signals generated.

7. COMPARING DIFFERENT TYPES OF MA Jurik Research www.jurikres.com

8. WAVELET TRANSFORM (CONTINUOUS) Wavelet”Mexican Hat” and normalized wavelet family 1 Continuous wavelet transform: Decomposition 2 Reconstruction 3 , where

9. ORTHOGONAL DISCRETE WAVELET TRANSFORM 1 3 2

10. WAVELET FILTRATION ALGORYTHM INPUT DATA LOADING TIME SERIES Choose Wavelet PARAMETERS HANDLE COEFFICIENTS REMOVING DETALIZATION Choose Transform Type MAKE DETALIZATION COEFFICIENTS LOWER OR EQUAL TO 0 CHOOSE COEFFICIENTS HANDLING ALGORYTHM RECONSTRUCT THE TIME SERIES BY REVERSE WAVELET TRANSFORM USING MODIFIED COEFFICIENTS OUTPUT DATA

11. “WAVELET FILTRATION STUDIO” TOOL

12. CREATE WAVELET BY ENTERING COEFFICIENTS

13. CREATE FILTER

14. IMPORT FINANCIAL DATA

15. APPLY FILTER TO TIME SERIES

16. CLASSES HIERARCHY AND STORAGE

17. OPEN SOURCE PROJECT Wavelet Filtration Studio is available for free on Google Code with all sources as a open source project http://code.google.com/p/wavelet-filtration-studio/

18. TO IMPLEMENT IN FUTURE… COMPARISION OF THE DIFFERENT FILTERS BY THE KNOWN 4 CRITERIA Make Wavelet Filtration Studio to support any input data (1d, 2d etc), not only financial DIFFERENT WAVELET TRANSFORMS CONTINUOUS DISCRETE REDUNDANT W. T. (FRAMES) Implement support for 2D (and possibly nD) transformations and include all types of prices Open/Close/Hi/Low to allow analyzing financial data by 2 dimmentional wavelet transforms (including support for directional wavelets) MULTIRESOLUTIONAL ANALYSIS (MRA) THIS IS DONE NON-STATIONARY WAVELET TRANSFORM BIORTAGONAL WAVELET TRANSFORM