Automatic Trend Estimation

By Maria Crăciun and Calin Vamos

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.

• Format: Paperback
• Language: English
• ISBN: 9400748248
• ISBN13: 9789400748248
• Release Date: September 2012
• Publisher: Springer
• Length: 131 Pages
• Weight: 0.55 lbs.
• Dimensions: 0.4" x 6.0" x 9.0"