IDEAS home Printed from
   My bibliography  Save this paper

Parameter estimation for differential equations using fractal-based methods and applications to economics


  • Cinzia COLAPINTO


  • Matteo FINI


  • Herb E. KUNZE


  • Jelena LONCAR



Many problems from the area of economics and finance can be described using dynamical models. For them, in which time is the only independent variable and for which we work in a continuous framework, these models take the form of deterministic differential equations (DEs). We may study these models in two fundamental ways: the direct problem and the inverse problem. The direct problem is stated as follows: given all of the parameters in a system of DEs, find a solution or determine its properties either analytically or numerically. The inverse problem reads: given a system of DEs with unknown parameters and some observational data, determine the values of the parameters such that the system admits the data as an approximate solution. The inverse problem is crucial for the calibration of the model; starting from a series of data we wish to describe them using deterministic differential equations in which the parameters have to be estimated from data samples. The solutions of the inverse problems are the estimations of the unknown parameters and we use fractal-based methods to get them. We then show some applications to technological change and competition models.

Suggested Citation

  • Cinzia COLAPINTO & Matteo FINI & Herb E. KUNZE & Jelena LONCAR, 2008. "Parameter estimation for differential equations using fractal-based methods and applications to economics," Departmental Working Papers 2008-07, Department of Economics, Management and Quantitative Methods at Universit√† degli Studi di Milano.
  • Handle: RePEc:mil:wpdepa:2008-07

    Download full text from publisher

    File URL:
    Download Restriction: no

    More about this item


    Differential equations; collage methods; inverse problems; parameter estimation; Lotka Volterra models; technological change; boat-fishery model;

    NEP fields

    This paper has been announced in the following NEP Reports:


    Access and download statistics


    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:mil:wpdepa:2008-07. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (DEMM Working Papers). General contact details of provider: .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.