Characterizing and modelling cyclic behaviour in non-stationary time series through multi-resolution analysis

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@Article{2008Prama..71..459A,
  author =       "Dilip P. Ahalpara and Amit Verma and 
                 Jitendra C. Parikh and Prasanta K. Panigrahi",
  title =        "Characterizing and modelling cyclic behaviour in
                 non-stationary time series through multi-resolution
                 analysis",
  journal =      "Pramana",
  year =         "2008",
  month =        nov,
  volume =       "71",
  pages =        "459--485",
  publisher =    "Springer India, in co-publication with Indian Academy
                 of Sciences",
  keywords =     "genetic algorithms, genetic programming, finance,
                 Non-stationary time series, wavelet transform,
                 Characterizing and modelling cyclic behaviour in
                 non-stationary time series through multi-resolution
                 analysis",
  ISSN =         "0304-4289",
  DOI =          "doi:10.1007/s12043-008-0125-x",
  adsurl =       "http://adsabs.harvard.edu/abs/2008Prama..71..459A",
  adsnote =      "Provided by the SAO/NASA Astrophysics Data System",
  abstract =     "A method based on wavelet transform is developed to
                 characterise variations at multiple scales in
                 non-stationary time series. We consider two different
                 financial time series, S&P CNX Nifty closing index of
                 the National Stock Exchange (India) and Dow Jones
                 industrial average closing values. These time series
                 are chosen since they are known to comprise of
                 stochastic fluctuations as well as cyclic variations at
                 different scales. The wavelet transform isolates cyclic
                 variations at higher scales when random fluctuations
                 are averaged out; this corroborates correlated
                 behaviour observed earlier in financial time series
                 through random matrix studies. Analysis is carried out
                 through Haar, Daubechies-4 and continuous Morlet
                 wavelets for studying the character of fluctuations at
                 different scales and show that cyclic variations emerge
                 at intermediate time scales. It is found that
                 Daubechies family of wavelets can be effectively used
                 to capture cyclic variations since these are local in
                 nature. To get an insight into the occurrence of cyclic
                 variations, we then proceed to model these wavelet
                 coefficients using genetic programming (GP) approach
                 and using the standard embedding technique in the
                 reconstructed phase space. It is found that the
                 standard methods (GP as well as artificial neural
                 networks) fail to model these variations because of
                 poor convergence. A novel interpolation approach is
                 developed that overcomes this difficulty. The dynamical
                 model equations have, primarily, linear terms with
                 additive Pade-type terms. It is seen that the emergence
                 of cyclic variations is due to an interplay of a few
                 important terms in the model. Very interestingly GP
                 model captures smooth variations as well as bursty
                 behaviour quite nicely.",
  notes =        "(1) Institute for Plasma Research, Near Indira Bridge,
                 Bhat, Gandhinagar, 382 428, India (2) Physical Research
                 Laboratory, Navrangpura, Ahmedabad, 380 009, India (3)
                 Indian Institute of Science Education and Research,
                 Salt Lake City, Kolkata, 700 106, India",
}

Genetic Programming entries for Dilip P Ahalpara Amit Verma Jitendra C Parikh Prasanta K Panigrahi

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