IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-7908-2413-1_1.html
   My bibliography  Save this book chapter

The Smooth Complex Logarithm and Quasi-Periodic Models

In: Statistical Modelling and Regression Structures

Author

Listed:
  • H. C. Eilers

    (Erasmus Medical Center, Department of Biostatistics)

Abstract

Quasi-periodic signals, which look like sine waves with variable frequency and amplitude, are common in nature and society. Examples that will be analyzed in this paper are sounds of crickets, counts of sunspots, movements of ocean currents, and brightness of variable stars. Euler’s formula for the complex logarithm, combined with smoothly changing real and imaginary components, provides a powerful model. It is highly non-linear and special care is needed to get starting values for an iterative estimating algorithm. The model is extended with a trend and harmonics. A cascaded link function allows modeling of quasi-periodic series of counts. The model and real-world applications are described in an expository style.

Suggested Citation

  • H. C. Eilers, 2010. "The Smooth Complex Logarithm and Quasi-Periodic Models," Springer Books, in: Thomas Kneib & Gerhard Tutz (ed.), Statistical Modelling and Regression Structures, pages 1-17, Springer.
    • Handle: RePEc:spr:sprchp:978-3-7908-2413-1_1
    DOI: 10.1007/978-3-7908-2413-1_1
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-3-7908-2413-1_1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.