By C˘alin Vamos¸, Maria Cr˘aciun

ISBN-10: 9400748248

ISBN-13: 9789400748248

ISBN-10: 9400748256

ISBN-13: 9789400748255

Our ebook introduces a style to guage the accuracy of development estimation algorithms lower than stipulations just like these encountered in actual time sequence processing. this technique is predicated on Monte Carlo experiments with synthetic time sequence numerically generated through an unique set of rules. the second one a part of the publication comprises numerous computerized algorithms for development estimation and time sequence partitioning. The resource codes of the pc courses enforcing those unique automated algorithms are given within the appendix and should be freely to be had on the internet. The publication includes 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 by way of processing time sequence from astrophysics, finance, biophysics, and paleoclimatology. The numerical scan strategy greatly utilized in our booklet is already in universal use in computational and statistical physics.

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D. d. series with mean zero and variance N −1 . d. 8) √ where G(x) = Φ(x)/ N and Φ(x) is the normal cdf. 11 shows the average ε over statistical ensembles with S = 100 for the autocorrelation function of the 30 0 10 xn |xn| ln|xn| 〈ε〉 Fig. d. white noise (o), of its absolute values (*), and of the logarithm of its absolute values (∇) 2 Monte Carlo Experiments −1 10 −2 10 1 10 2 3 10 10 4 10 N Gaussian white noises {xn }, for their absolute values {|xn |}, and for the logarithm of their absolute values {ln |xn |}.

Hence the accuracy of the polynomial fitting is mainly controlled by the number of the monotonic segments. In conclusion, the polynomial fitting is recommended for time series with simple trends. , many monotonic segments, then the degree of the estimated polynomial trend rapidly increases and the order of magnitude of its coefficients becomes very large. The accuracy also worsens if the trend has very steep segments where the resolution of the time series is small. 3 An Astrophysical Example In this section we estimate the polynomial trend of a time series describing the variability of the X-ray flux from a Seyfert galaxy.

Vamo¸s and M. 1007/978-94-007-4825-5_4, © The Author(s) 2012 43 44 4 Noise Smoothing with the weighting coefficients wk ≥ 0 K+ wk = 1. k=K − The length of the averaging window [n + K − , n + K + ] is T = K + − K − + 1. We implicitly consider that w K − > 0 and w K + > 0, otherwise new limits K ± can be found such that the coefficients w K − and w K + should be nonvanishing. The summation limits can also be infinite or zero. If K − ≥ 0 (K + ≤ 0), then only future (past) values of the time series are included in the MA.

### Automatic trend estimation by C˘alin Vamos¸, Maria Cr˘aciun

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