Advanced Search
MyIDEAS: Login

A characterization of self-affine processes in finance through the scaling function

Contents:

Author Info

  • Marina Resta

    ()
    (DIEM sez. Matematica Finanziaria, via Vivaldi 5, 16126, Genova)

  • Davide Sciutti

Abstract

This work focuses on a method to characterize stochastic processes by way of their scaling function tau(·). The kernel idea is that, notwithstanding the properties of the stochastic generating process of raw data, a minimum set of conditions is required to provide empirical estimation of the corresponding scaling function. Additionally, if the generating process belongs to the class of self-affine processes it is possible to express tau in a very simple and elegant way. Starting from the defnition of self-affinity (self-similarity) given By Castaing in the feld of fully developed turbulence, a general closed Form for the scaling function of self-similar processes will be derived, using the relationships between the probability density functions of the increments of self-similar processes at finer and coarser scales through a self-affinity kernel. In particular, the attention will be focused onto two main aspects of Castaing’s formalism: a) Starting from the the Castaing’s formula it is possible to find the scaling function as the Laplace transform of a proper self–affinity kernel; b)conversely, if the functional form of function tau is already known, it is possible to uniquely find the corresponding self-affinity kernel. In order to prove the generality of the results obtained, two examples will be provided (in the mono-fractal and in the multi-fractal case). The latter result is quite interesting, for its practical (econometric) applications, when the behaviour of real data can be replicated by means of self-affine processes. In such case, the generalization provided to the Castaing’s formula makes possible to link through a closed form the (given) probability density function of the increments at some larger time scale together to the (ungiven) probability density function at a smaller scale, with proper parameters,according to the desired scaling function. Obviously this assumption holds if we assume the self-affinity of process under examination. However, this appear to be not too much conditioning. To such purpose, the shape of the scaling function tau of Dow Jones daily returns will be estimated, and hence compared to those derived from time series generated by different stochastic processes (mostly self-affine). first set of conclusions will be hence drawn, since the analysis of the shape of scaling functions suggests a possible criterion to choose the best matching stochastic process to model empirical data.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://zai.ini.unizh.ch/www_complexity2003/doc/Paper_Resta.pdf
Our checks indicate that this address may not be valid because: 500 Can't connect to zai.ini.unizh.ch:80 (Bad hostname). If this is indeed the case, please notify (Christopher F. Baum)
Download Restriction: no

Bibliographic Info

Paper provided by Society for Computational Economics in its series Modeling, Computing, and Mastering Complexity 2003 with number 13.

as in new window
Length:
Date of creation:
Date of revision:
Handle: RePEc:sce:cplx03:13

Contact details of provider:
Web page: http://zai.ini.unizh.ch/complexity2003/
More information through EDIRC

Related research

Keywords: Self-affinity; scaling function.;

Find related papers by JEL classification:

This paper has been announced in the following NEP Reports:

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Laurent Calvet & Adlai Fisher, 2002. "Multifractality In Asset Returns: Theory And Evidence," The Review of Economics and Statistics, MIT Press, vol. 84(3), pages 381-406, August.
  2. Neil Shephard & Ole E. Barndorff-Nielsen, 1999. "Non-Gaussian OU Based Models and some of their use in Financial Economics," Economics Series Working Papers 1999-W09, University of Oxford, Department of Economics.
  3. Laurent Calvet, 2000. "Forecasting Multifractal Volatility," Harvard Institute of Economic Research Working Papers 1902, Harvard - Institute of Economic Research.
Full references (including those not matched with items on IDEAS)

Citations

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:sce:cplx03:13. 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: (Christopher F. Baum).

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.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with 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 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.