Automatic trend estimation

Front Cover
Springer Science & Business Media, Sep 14, 2012 - Science - 131 pages
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.
 

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Contents

1 Introduction
1
2 Monte Carlo Experiments
14
3 Polynomial Fitting
31
4 Noise Smoothing
43
5 Automatic Estimation of Monotonic Trends
61
6 Estimation of Monotonic Trend Segments from a Noisy Time Series
81
7 Automatic Estimation of Arbitrary Trends
98
Appendix A Statistical Properties of the Linear Regression
111
Appendix B Spurious Serial Correlation Induced by MA
113
Appendix C Continuous Analogue of the ACD Algorithm
117
Appendix D Standard Deviation of a Noise Superposed over a Monotonic Trend
120
Appendix E Construction of a Partition of Scale Delta n
127
Appendix F Estimation of the Ratio Between the Trend and Noise Magnitudes
129
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About the author (2012)

Vamos is Scientific researcher II at "Tiberiu Popoviciu" Institute of Numerical Analysis (Romania). His interests are on time series theory and quantitative finance.

Craciun is Scientific researcher III at "Tiberiu Popoviciu" Institute of Numerical Analysis (Romania). Her interests are on time series theory and quantitative finance.