Multiresolution analysis of S&P500 time series

S.I.: Advances of OR in Commodities and Financial Modelling

Abstract

Time series analysis is an essential research area for those who are dealing with scientific and engineering problems. The main objective, in general, is to understand the underlying characteristics of selected time series by using the time as well as the frequency domain analysis. Then one can make a prediction for desired system to forecast ahead from the past observations. Time series modeling, frequency domain and some other descriptive statistical data analyses are the primary subjects of this study: indeed, choosing an appropriate model is at the core of any analysis to make a satisfactory prediction. In this study Fourier and wavelet transform methods are used to analyze the complex structure of a financial time series, particularly, S&P500 daily closing prices and return values. Multiresolution analysis is naturally handled by the help of wavelet transforms in order to pinpoint special characteristics of S&P500 data, like periodicity as well as seasonality. Besides, further case study discussions include the modeling of S&P500 process by invoking linear and nonlinear methods with wavelets to address how multiresolution approach improves fitting and forecasting results.

Keywords

Time series analysis Frequency domain analysis Wavelets Multiresolution analysis Statistical analysis 

References

  1. Ababneh, F., Wadi, S. A., & Ismail, M. T. (2013). Haar and Daubechies wavelet methods in modeling banking sector. International Mathematical Forum, 8(12), 551–566.Google Scholar
  2. Addo, P. M., Billio, M., & Guegan, D. (2013). Nonlinear dynamics and recurrence plots for detecting financial crisis. The North American Journal of Economics and Finance, 26, 416–435.CrossRefGoogle Scholar
  3. Aloui, C., & Nguyen, D. K. (2014). On the detection of extreme movements and persistent behavior in Mediterranean stock markets: A wavelet-based approach. IPAG Business School, Working Paper Series, 66.Google Scholar
  4. Bayraktar, E., Poor, H. V., & Sircar, K. R. (2004). Estimating the fractal dimension of the S&P 500 Index using wavelet analysis. International Journal of Theoretical and Applied Finance, 7(5), 615–643.CrossRefGoogle Scholar
  5. Boggess, A., & Narcowich, F. J. (2009). A first course in wavelets with Fourier analysis. Hoboken, NJ: Wiley.Google Scholar
  6. Burke, B. (1994). The mathematical microscope: Waves, wavelets, and beyond. In M. Bartusiak (Ed.), Scientific discovery at the frontier (pp. 196–235). Washington: National Academy Press.Google Scholar
  7. Cabrelli, C. A., & Molter, U. M. (1989). Wavelet transform of the dilation equation. Journal of the Australian Mathematical Society, 37(4), 474–489.CrossRefGoogle Scholar
  8. Capobianco, E. (2004). Multiscale analysis of stock index return volatility. Computational Economics, 23(3), 219–237.CrossRefGoogle Scholar
  9. Crowley, P. M. (2005). An intuitive guide to wavelets for economists. Bank of Finland Research Discussion Paper, 1.Google Scholar
  10. Danielsson, J. (2011). Financial risk forecasting: The theory and practice of forecasting market risk with implementation in R and Matlab. Wiley-Blackwell.Google Scholar
  11. Eynard, J., Grieu, S., & Polit, M. (2011). Wavelet-based multi-resolution analysis and artificial neural networks for forecasting temperature and thermal power consumption. Engineering Applications of Artificial Intelligence, 24(3), 501–516.CrossRefGoogle Scholar
  12. Gençay, R., Selçuk, F., & Whitcher, B. (2001). An introduction to wavelets and other filtering methods in finance and economics. San Diego: San Diego Academic Press.Google Scholar
  13. Hazewinkel, M. (2013). Encyclopaedia of mathematics: Coproduct — Hausdorff — Young inequalities. Berlin: Springer.Google Scholar
  14. Huang, W., Yang, W., & Zhang, Y. (2013). Structural changes in Singapore private property market: A wavelet approach. In Singapore economic review conference 2013.Google Scholar
  15. In, F., & Kim, S. (2006). The hedge ratio and the empirical relationship between the stock and futures markets: A new approach using wavelet analysis. Journal of Business, 79(2), 799–820.CrossRefGoogle Scholar
  16. Kumar, A., Joshi, L. K., Pal, A. K., & Shukla, A. K. (2011). MODWT based time scale decomposition analysis of BSE and NSE indexes financial time series. International Journal of Mathematical Analysis, 5(27), 1343–1352.Google Scholar
  17. Lu, X., Wang, K., & Dou, H. J. (2001). Wavelet multifractal modeling for network traffic and queuing analysis. In: International Conference on computer networks and mobile computing (pp. 260–265). IEEE.Google Scholar
  18. Lyubushin, A. A. (2001). Multidimensional wavelet analysis of geophysical monitoring time series. Izvestiya, Physics of the Solid Earth, 37(6), 41–51.Google Scholar
  19. Mallat, S. (1989). A theory for multiresolution signal decomposition: The wavelet representation. IEEE Transactions on Pattern Analysis and Machine Intelligence, 11, 674–693.CrossRefGoogle Scholar
  20. Mandelbrot, B. B. (1997). Fractals and scaling in finance: Discontinuity, concentration, risk. New York: Springer.CrossRefGoogle Scholar
  21. Masset, P. (2008). Analysis of financial time-series using Fourier and wavelet methods. Fribourg: University of Fribourg.Google Scholar
  22. Meng, W. (2001). Wavelet coding with fractal for image sequences. In Intelligent multimedia, video and speech processing (pp. 514–517). IEEE.Google Scholar
  23. Molle, J. W. D., & Morrice, D. J. (1994). Initial transient detection in simulations using the second-order cumulant spectrum. Annals of Operations Research, 53(1), 443–470.CrossRefGoogle Scholar
  24. Murtagh, F., Starck, J. L., & Renaud, O. (2004). On neuro-wavelet modeling. Decision Support Systems, 37(4), 475–484.CrossRefGoogle Scholar
  25. Nouri, M., Oryoie, A. R., & Fallahi, S. (2012). Forecasting gold return using wavelet analysis. World Applied Sciences Journal, 19(2), 276–280.Google Scholar
  26. Osowski, S., & Garanty, K. (2007). Forecasting of the daily meteorological pollution using wavelets and support vector machine. Engineering Applications of Artificial Intelligence, 20(6), 745–755.CrossRefGoogle Scholar
  27. Percival, D. B., & Walden, A. T. (2000). Wavelet methods for time series analysis. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  28. Ramsey, J. B., Usikov, D., & Zaslavsky, G. M. (1995). An analysis of U.S. stock price behavior using wavelets. Fractals, 3, 377–389Google Scholar
  29. Sangbae, K., & Haeuck, I. F. (2003). The relationship between financial variables and real economic activity: Evidence from spectral and wavelet analyses. Studies in Nonlinear Dynamics and Econometrics, 7(4), 1–18.Google Scholar
  30. Sheikholeslami, G., Chatterjee, S., & Zhang, A. (2000). Wavecluster: A multi-resolution clustering approach for very large spatial databases. The VLDB Journal The International Journal on Very Large Data Bases, 8(3–4), 289–304.CrossRefGoogle Scholar
  31. Strang, G. (1989). Wavelets and dilation equations: A brief introduction. SIAM Review, 31(4), 614–627.CrossRefGoogle Scholar
  32. Torrence, C., & Compo, G. P. (1998). A practical guide to wavelet analysis. Bulletin of the American Meteorological Society, 79, 61–78.CrossRefGoogle Scholar
  33. Vuorenmaa, T. A. (2004). A multiresolution analysis of stock market volatility using wavelet methodology. Master’s thesis, Universtiy of Helsinki.Google Scholar
  34. Wadi, S. A., Ismail, M. T., Alkhahazaleh, M. H., & Karim, S. A. A. (2011). Selecting wavelet transforms model in forecasting financial time series data based on arima model. Applied Mathematical Sciences, 5(7), 315–326.Google Scholar
  35. Walden, A. T. (2001). Wavelet analysis of discrete time series. 3rd European Congress of Mathematics (3ECM), 2, 627–641.CrossRefGoogle Scholar
  36. Wong, H., Ip, W. C., Xie, Z., & Lui, X. (2003). Modelling and forecasting by wavelets, and the application to exchange rates. Journal of Applied Statistics, 30(5), 537–553.CrossRefGoogle Scholar
  37. Yousefi, S., Weinreich, I., & Reinarz, D. (2005). Wavelet-based prediction of oil prices. Chaos, Solitons and Fractals, 25(2), 265–275.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Applied MathematicsMiddle East Technical UniversityÇankaya, AnkaraTurkey

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