By C˘alin Vamos¸, Maria Cr˘aciun
Our ebook introduces a style to judge the accuracy of pattern estimation algorithms below stipulations just like these encountered in actual time sequence processing. this technique relies on Monte Carlo experiments with man made time sequence numerically generated via an unique set of rules. the second one a part of the e-book comprises numerous automated algorithms for pattern estimation and time sequence partitioning. The resource codes of the pc courses enforcing those unique computerized algorithms are given within the appendix and should be freely to be had on the internet. The publication comprises transparent assertion of the stipulations and the approximations below which the algorithms paintings, in addition to the right kind interpretation in their effects. We illustrate the functioning of the analyzed algorithms via processing time sequence from astrophysics, finance, biophysics, and paleoclimatology. The numerical test strategy largely utilized in our ebook is already in universal use in computational and statistical physics.
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Additional resources for Automatic trend estimation
In order to study the influence of this property on the trend estimation accuracy we use statistical ensembles of numerically generated time series. 5, 1, 2, 4}. The other parameter of the artificial time series is ΔNmin = 20. For each artificial time series s ≤ S and each given value of K we determine the minimum of the resemblance index η(s) given by Eq. 6) by exhaustive search over the number of repetitions i ≤ 50. We use statistical ensembles of S = 100 artificial time series and we compute the average value of the minimum error ηmin and the average number of repetitions i min for which the minimum is obtained.
3), which must be analyzed with special methods . In addition we consider for φ only positive values because few of the phenomena of interest are characterized by an anticorrelated noise. 9]. When we choose the value of φ we have to take also into account the length of the time series. In Fig. 5 we present several noisy time series with N = 100 and N = 1000, different values of φ, and r = 1. 25 5 0 −10 −20 0 x x n n 10 −5 0 (c) 500 n 1000 0 (d) r=4 1000 r=10 3 3 2 2 1 1 x n xn 500 n 0 0 −1 −1 −2 0 500 n 1000 −2 0 500 n 1000 Fig.
9]. When we choose the value of φ we have to take also into account the length of the time series. In Fig. 5 we present several noisy time series with N = 100 and N = 1000, different values of φ, and r = 1. 25 5 0 −10 −20 0 x x n n 10 −5 0 (c) 500 n 1000 0 (d) r=4 1000 r=10 3 3 2 2 1 1 x n xn 500 n 0 0 −1 −1 −2 0 500 n 1000 −2 0 500 n 1000 Fig. 9 over the same trend but with different ratios r a stochastic trend appears (Fig. , the strongly correlated noise has variations that cannot be distinguished from those of the trend (see Sect.
Automatic trend estimation by C˘alin Vamos¸, Maria Cr˘aciun