Automatic trend estimation

1. Front Matter

   Pages i-x

   PDF

2. Introduction

   • Calin Vamos, Maria Craciun

   Pages 1-13

3. Monte Carlo Experiments

   • Calin Vamos, Maria Craciun

   Pages 15-30

4. Polynomial Fitting

   • Calin Vamos, Maria Craciun

   Pages 31-42

5. Noise Smoothing

   • Calin Vamos, Maria Craciun

   Pages 43-59

6. Automatic Estimation of Monotonic Trends

   • Calin Vamos, Maria Craciun

   Pages 61-80

7. Estimation of Monotonic Trend Segments from a Noisy Time Series

   • Calin Vamos, Maria Craciun

   Pages 81-97

8. Automatic Estimation of Arbitrary Trends

   • Calin Vamos, Maria Craciun

   Pages 99-110

9. Back Matter

   Pages 111-131

   PDF

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.

• 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

• Institute of Numerical Analysis, Tiberiu Popoviciu, Cluj-Napoca, Romania

  C˘alin Vamos¸, Maria Cr˘aciun

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.

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