04822nam a22005895i 4500 978-94-007-4825-5 DE-He213 20210625073210.0 cr nn 008mamaa 120914s2013 ne | s |||| 0|eng d 9789400748255 978-94-007-4825-5 10.1007/978-94-007-4825-5 doi QC1-999 PHU bicssc SCI040000 bisacsh PHU thema 530.1 23 Vamos¸, C˘alin. author. aut http://id.loc.gov/vocabulary/relators/aut Automatic trend estimation [electronic resource] / by C˘alin Vamos¸, Maria Cr˘aciun. 1st ed. 2013. Dordrecht : Springer Netherlands : Imprint: Springer, 2013. X, 131 p. 77 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda SpringerBriefs in Physics, 2191-5423 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. Physics. Statistical physics. Dynamical systems. Probabilities. Computer mathematics. Computer simulation. Numerical and Computational Physics, Simulation. https://scigraph.springernature.com/ontologies/product-market-codes/P19021 Complex Systems. https://scigraph.springernature.com/ontologies/product-market-codes/P33000 Probability Theory and Stochastic Processes. https://scigraph.springernature.com/ontologies/product-market-codes/M27004 Computational Mathematics and Numerical Analysis. https://scigraph.springernature.com/ontologies/product-market-codes/M1400X Simulation and Modeling. https://scigraph.springernature.com/ontologies/product-market-codes/I19000 Statistical Physics and Dynamical Systems. https://scigraph.springernature.com/ontologies/product-market-codes/P19090 Cr˘aciun, Maria. author. aut http://id.loc.gov/vocabulary/relators/aut SpringerLink (Online service) Springer Nature eBook Printed edition: 9789400748262 Printed edition: 9789400748248 SpringerBriefs in Physics, 2191-5423 https://doi.org/10.1007/978-94-007-4825-5 ZDB-2-PHA ZDB-2-SXP Physics and Astronomy (SpringerNature-11651) Physics and Astronomy (R0) (SpringerNature-43715)