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The reader will be able to reproduce the original automatic algorithms for trend estimation and time series partitioning
Teaches the essential characteristics of the polynomial fitting and moving averaging algorithms in the case of arbitrary non-monotonic trends
With examples of real time series from astrophysics, finance, biophysics, and paleoclimatology as encountered in practice
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.
Content Level »Research
Keywords »Automatic Estimation of Trends - Average Conditional Displacement - Discrete Stochastic Processes - Monte Carlo Experiment - Noise Smoothing - Noisy Time Series - Polynomial Fitting - Time Series Partitioning - Trend Estimation Algorithms