Automatic trend estimation

Dordrecht : Springer Netherlands : Imprint : Springer, 2013

Abstract/Sommario: Discrete stochastic processes and time series -- Trend definition -- Finite AR(1) stochastic process -- Monte Carlo experiments. - Monte Carlo statistical ensembles -- Numerical generation of trends -- Numerical generation of noisy time series -- Statistical hypothesis testing -- Testing the i.i.d. property -- Polynomial fitting -- Linear regression -- Polynomial fitting -- Polynomial fitting of artificial time series -- An astrophysical example -- Noise smoothing -- Moving average -- ...; [leggi tutto] Discrete stochastic processes and time series -- Trend definition -- Finite AR(1) stochastic process -- Monte Carlo experiments. - Monte Carlo statistical ensembles -- Numerical generation of trends -- Numerical generation of noisy time series -- Statistical hypothesis testing -- Testing the i.i.d. property -- Polynomial fitting -- Linear regression -- Polynomial fitting -- Polynomial fitting of artificial time series -- An astrophysical example -- Noise smoothing -- Moving average -- Repeated moving average (RMA) -- Smoothing of artificial time series -- A financial example -- Automatic estimation of monotonic trends -- Average conditional displacement (ACD) algorithm -- Artificial time series with monotonic trends -- Automatic ACD algorithm -- Evaluation of the ACD algorithm -- A paleoclimatological example -- Statistical significance of the ACD trend -- Time series partitioning -- Partitioning of trends into monotonic segments -- Partitioning of noisy signals into monotonic segments -- Partitioning of a real time series -- Estimation of the ratio between the trend and noise -- Automatic estimation of arbitrary trends -- Automatic RMA (AutRMA) -- Monotonic segments of the AutRMA trend -- Partitioning of a financial time series. - Our book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics [comprimi]

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Dettagli

Campo	Valore
Descrizione	Automatic trend estimation / by C˘alin Vamos¸, Maria Cr˘aciun. - Dordrecht : Springer Netherlands : Imprint : Springer, 2013. - X, 131 p. 77 illus ; digital. - (SpringerBriefs in Physics)
Specifiche	[Supporto spec. Risorsa elettr.] Risorsa remota
Note	Springer eBooks. - Printed edition: 9789400748248
Collezione	[Fa parte di] SpringerBriefs in Physics [Vai al dettaglio]
Autori	Vamos¸, C˘alin - [Responsabilità principale] Cr˘aciun, Maria - [Responsabilità secondaria] SpringerLink (Online service) - [Responsabilità secondaria]
Soggetto	Computational Mathematics and Numerical Analysis Computer science - Mathematics Computer simulation Distribution (Probability theory) Numerical and Computational Physics Physics Probability Theory and Stochastic Processes Simulation and Modeling Statistical Physics, Dynamical Systems and Complexity
Classificazione	530.1 - Teorie della fisica e fisica matematica
Lingua	Inglese
Numeri	ISBN: 978-94-007-4825-5 DOI: 10.1007/978-94-007-4825-5 N. catalogo straniero: QC1-999 (Library of Congress Call Number)
ID scheda	130368
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