Characterizing and modelling cyclic behaviour in non-stationary time series through multi-resolution analysis
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- @Article{2008Prama..71..459A,
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author = "Dilip P. Ahalpara and Amit Verma and
Jitendra C. Parikh and Prasanta K. Panigrahi",
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title = "Characterizing and modelling cyclic behaviour in
non-stationary time series through multi-resolution
analysis",
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journal = "Pramana",
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year = "2008",
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month = nov,
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volume = "71",
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pages = "459--485",
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publisher = "Springer India, in co-publication with Indian Academy
of Sciences",
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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",
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ISSN = "0304-4289",
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DOI = "doi:10.1007/s12043-008-0125-x",
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adsurl = "http://adsabs.harvard.edu/abs/2008Prama..71..459A",
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adsnote = "Provided by the SAO/NASA Astrophysics Data System",
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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.",
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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
Citations