TY  - BOOK
AU  - Vamos¸,C˘alin
AU  - Cr˘aciun,Maria
ED  - SpringerLink (Online service)
TI  - Automatic trend estimation
T2  - SpringerBriefs in Physics,
SN  - 9789400748255
AV  - QC1-999 
U1  - 530.1 23
PY  - 2013///
CY  - Dordrecht
PB  - Springer Netherlands, Imprint: Springer
KW  - Physics
KW  - Computer simulation
KW  - Computer mathematics
KW  - Probabilities
KW  - Statistical physics
KW  - Dynamical systems
KW  - Numerical and Computational Physics
KW  - Statistical Physics, Dynamical Systems and Complexity
KW  - Probability Theory and Stochastic Processes
KW  - Computational Mathematics and Numerical Analysis
KW  - Simulation and Modeling
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-94-007-4825-5
ER  -