LEADER 03936nam 2200601 a 450 001 9910741175103321 005 20200520144314.0 010 $a1-283-63415-5 010 $a9786613946607 010 $a94-007-4825-6 024 7 $a10.1007/978-94-007-4825-5 035 $a(CKB)2670000000256417 035 $a(EBL)994088 035 $a(OCoLC)810931919 035 $a(SSID)ssj0000766941 035 $a(PQKBManifestationID)11943486 035 $a(PQKBTitleCode)TC0000766941 035 $a(PQKBWorkID)10731660 035 $a(PQKB)11665174 035 $a(DE-He213)978-94-007-4825-5 035 $a(MiAaPQ)EBC994088 035 $a(PPN)168339110 035 $a(EXLCZ)992670000000256417 100 $a20120626d2012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAutomatic trend estimation /$fCalin Vamos, Maria Craciun 205 $a1st ed. 2013. 210 $aNew York $cSpringer$d2012 215 $a1 online resource (135 p.) 225 0$aSpringerBriefs in physics,$x2191-5423 300 $aDescription based upon print version of record. 311 $a94-007-4824-8 320 $aIncludes bibliographical references. 327 $aDiscrete 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. 330 $aOur book introduces a method to evaluate the accuracy of trend estimation algorithms under conditions similar to those encountered in real time series processing. This method is based on Monte Carlo experiments with artificial time series numerically generated by an original algorithm. The second part of the book contains several automatic algorithms for trend estimation and time series partitioning. The source codes of the computer programs implementing these original automatic algorithms are given in the appendix and will be freely available on the web. The book contains clear statement of the conditions and the approximations under which the algorithms work, as well as the proper interpretation of their results. We illustrate the functioning of the analyzed algorithms by processing time series from astrophysics, finance, biophysics, and paleoclimatology. The numerical experiment method extensively used in our book is already in common use in computational and statistical physics. 410 0$aSpringerBriefs in Physics,$x2191-5423 606 $aEstimation theory 615 0$aEstimation theory. 676 $a330.01 676 $a330.0151955 700 $aVamos$b Calin$01424815 701 $aCraciun$b Maria$01679423 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910741175103321 996 $aAutomatic trend estimation$94187032 997 $aUNINA