- 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",
- volume = "71",
- number = "3",
- pages = "459--485",
- month = sep,
- publisher = "Springer India, in co-publication with Indian Academy of Sciences",
- keywords = "genetic algorithms, genetic programming, finance, Non-stationary time series, wavelet transform, SP, Characterizing and modelling cyclic behaviour in non-stationary time series through multi-resolution analysis",
- ISSN = "0304-4289",
-
URL = "
https://www.ias.ac.in/describe/article/pram/071/03/0459-0485",
-
URL = "https://www.ias.ac.in/article/fulltext/pram/071/03/0459-0485",
-
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",
- size = "27 pages",
- 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, Standard and Poor's 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 = "see also
\cite{physics/0612221}
https://www.ias.ac.in/listing/issues/pram
(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",
