Description, modeling and forecasting of data with optimal wavelets

Autor: Conrad J. Pérez-Vicente, Antonio Turiel, Oriol Pont
Přispěvatelé: Institute of Marine Sciences / Institut de Ciències del Mar [Barcelona] (ICM), Consejo Superior de Investigaciones Científicas [Madrid] (CSIC), Universitat de Barcelona (UB), Fundamental Physics, Universitat de Barcelona, Pont, Oriol
Jazyk: angličtina
Rok vydání: 2008
Předmět:
Economics and Econometrics
Mathematical optimization
Markov kernel
Logarithm
Optimal wavelet
Cascade algorithm
02 engineering and technology
Machine learning
computer.software_genre
Microcanonical multifractal formalism
01 natural sciences
Wavelet
0103 physical sciences
0202 electrical engineering
electronic engineering
information engineering
Cascade processes
Business and International Management
Time series
010306 general physics
ComputingMilieux_MISCELLANEOUS
Mathematics
business.industry
Estimator
[MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA]
[SHS.ECO]Humanities and Social Sciences/Economics and Finance
Cascade
Time series forecasting
020201 artificial intelligence & image processing
Artificial intelligence
Volatility (finance)
business
computer
[MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Zdroj: International Conference on Economic Science with Heterogeneous Interacting Agents
International Conference on Economic Science with Heterogeneous Interacting Agents, Jun 2008, Warsaw, Poland
Journal of Economic Interaction and Coordination
Journal of Economic Interaction and Coordination, Springer Verlag, 2009, 4 (1), pp.39-54. ⟨10.1007/s11403-009-0046-x⟩
Digital.CSIC. Repositorio Institucional del CSIC
instname
ISSN: 1860-711X
1860-7128
Popis: 16 pages, 4 figures
Cascade processes have been used to model many different self-similar systems, as they are able to accurately describe most of their global statistical properties. The so-called optimal wavelet basis allows to achieve a geometrical representation of the cascade process-named microcanonical cascade- that describes the behavior of local quantities and thus it helps to reveal the underlying dynamics of the system. In this context, we study the benefits of using the optimal wavelet in contrast to other wavelets when used to define cascade variables, and we provide an optimality degree estimator that is appropriate to determine the closest-to-optimal wavelet in real data. Particularizing the analysis to stock market series, we show that they can be represented by microcanonical cascades in both the logarithm of the price and the volatility. Also, as a promising application in forecasting, we derive the distribution of the value of next point of the series conditioned to the knowledge of past points and the cascade structure, i.e., the stochastic kernel of the cascade process
This work is a contribution toOCEANTECH(PIF 2006 Project) and FIS2006-13321-CO2-01. O. Pont is funded by a Ph.D. contract from Generalitat de Catalunya
Databáze: OpenAIRE
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