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Automatic Estimation of Arbitrary Trends

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Automatic trend estimation

Part of the book series: SpringerBriefs in Physics ((SpringerBriefs in Physics))

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Abstract

In this final chapter we transform the RCMA algorithm presented in Chap. 4 in an automatic algorithm. Instead of the two parameters controlling the RCMA we introduce a single parameter equal to the minimum distance between two successive local extrema of the smoothed time series. Its optimum value is determined as a function of the estimated serial correlation of the noise and of the estimated ratio between the amplitudes of the trend variations and noise fluctuations. The accuracy of the automatic RCMA is measured by Monte Carlo experiments and it is only slightly smaller than the maximum accuracy obtained by exhaustive search of all the RCMA trends. As an illustration we use the automatic RCMA to estimate the trend from a financial time series and by means of the partitioning algorithm presented in Chap. 6 we evaluate the significance of the local extrema of the estimated trend.

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Notes

  1. 1.

    The automatic RCMA algorithm supplemented with the identification of significant monotonic segments of the estimated trend is implemented by the MATLAB program trendrcma freely accessible on web.

References

  1. Hamilton, J.D.: Time series analysis. Princeton University Press, Princeton (1994)

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  2. Schumpeter, J.A.: Business cycles. A theoretical, historical and statistical analysis of the capitalist process. McGraw-Hill, New York (1939)

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  3. Voit, J.: The statistical mechanics of financial markets, 3rd edn. Springer, Berlin (2005)

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Authors and Affiliations

  1. “Tiberiu Popoviciu” Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, 400110, Romania

    Calin Vamos & Maria Craciun

Authors
  1. Calin Vamos
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  2. Maria Craciun
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Correspondence to Calin Vamos .

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© 2012 The Author(s)

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Vamos, C., Craciun, M. (2012). Automatic Estimation of Arbitrary Trends. In: Automatic trend estimation. SpringerBriefs in Physics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4825-5_7

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  • DOI: https://doi.org/10.1007/978-94-007-4825-5_7

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  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-4824-8

  • Online ISBN: 978-94-007-4825-5

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

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