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

By C˘alin Vamos¸, Maria Cr˘aciun

Our publication introduces a mode to judge the accuracy of pattern estimation algorithms below stipulations just like these encountered in genuine time sequence processing. this technique is predicated on Monte Carlo experiments with synthetic time sequence numerically generated by way of an unique set of rules. the second one a part of the publication includes a number of automated algorithms for pattern estimation and time sequence partitioning. The resource codes of the pc courses imposing those unique computerized algorithms are given within the appendix and may be freely on hand on the net. The booklet includes transparent assertion of the stipulations and the approximations lower than which the algorithms paintings, in addition to the right kind interpretation in their effects. We illustrate the functioning of the analyzed algorithms through processing time sequence from astrophysics, finance, biophysics, and paleoclimatology. The numerical scan approach commonly utilized in our ebook is already in universal use in computational and statistical physics.

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D. It can be shown that in this case Bartlett’s theorem remains valid and one can practically apply the same tests as for the initial time series. In accordance with Bartlett’s theorem, ρ(h) has a normal distribution with mean zero and variance N −1 . d. 96N −1/2 . A more complex test is the Box–Pierce test [2] for ARMA residuals which is based on the statistic h ρ 2 ( j) Q=N j=1 that is approximately chi-squared distributed. These tests and their versions impose only the condition that the sample autocorrelation function should not have too large values, but in numerical processing it is possible that the sample autocorrelation function becomes too small.

8(18), 1–4 (2003) 9. : The Monte Carlo method. J. Am. Stat. Assoc. 44, 335–341 (1949) 10. : Numerical Recipes in C. The Art of Scientific Computing, 2nd edn. Cambridge University Press, Cambridge (1992) 11. : Serial correlation of detrended time series. Phys. Rev. E 78, 036707 (2008) Chapter 3 Polynomial Fitting In this chapter we analyze the well-known polynomial fitting method by means of the Monte Carlo experiments with artificial time series generated by the algorithm presented in the previous chapter.

The results in the previous section are not applicable because in this case the noise is a mixture of a white noise and an AR(1) strongly correlated noise. In order to establish the statistical significance of the estimated trend we resort to a Monte Carlo experiment. 666. From the average value of the horizontal part of the periodogram in Fig. 262. For each of the 10000 artificial time series of the statistical ensemble we estimate by polynomial fitting with q = 2 a perturbed trend and we compute its resemblance index with respect to the parabolic trend in Fig.

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