This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

A mathematical proof of the existence of trends in financial time series

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Michel Fliess () (LIX - Laboratoire d'informatique de l'école polytechnique - CNRS : UMR7161 - Polytechnique - X, INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - CNRS : UMR - Ecole Centrale de Lille)
Cédric Join () (INRIA Saclay - Ile de France - ALIEN - INRIA - Polytechnique - X - CNRS : UMR - Ecole Centrale de Lille, CRAN - Centre de recherche en automatique de Nancy - CNRS : UMR7039 - Université Henri Poincaré - Nancy I - Institut National Polytechnique de Lorraine - INPL)
Abstract

We are settling a longstanding quarrel in quantitative finance by proving the existence of trends in financial time series thanks to a theorem due to P. Cartier and Y. Perrin, which is expressed in the language of nonstandard analysis (Integration over finite sets, F. & M. Diener (Eds): Nonstandard Analysis in Practice, Springer, 1995, pp. 195--204). Those trends, which might coexist with some altered random walk paradigm and efficient market hypothesis, seem nevertheless difficult to reconcile with the celebrated Black-Scholes model. They are estimated via recent techniques stemming from control and signal theory. Several quite convincing computer simulations on the forecast of various financial quantities are depicted. We conclude by discussing the rôle of probability theory.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. 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://hal.inria.fr/docs/00/35/28/34/PDF/FES-Finance.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by HAL in its series Post-Print with number inria-00352834_v1.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length:
Date of creation: 2009
Date of revision:
Publication status: Published - Presented, Systems Theory: Modelling, Analysis and Control, 2009, Fes, Morocco
Handle: RePEc:hal:journl:inria-00352834_v1

Note: View the original document on HAL open archive server: http://hal.inria.fr/inria-00352834/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/

For technical questions regarding this item, or to correct its listing, contact: (CCSD).

Related research
Keywords: Financial time series; mathematical finance; technical analysis; trends; random walks; efficient markets; forecasting; volatility; heteroscedasticity; quickly fluctuating functions; low-pass filters; nonstandard analysis; operational calculus.;

Other versions of this item:

This paper has been announced in the following NEP Reports: 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.:
  1. Ait-Sahalia, Yacine & Lo, Andrew W., 2000. "Nonparametric risk management and implied risk aversion," Journal of Econometrics, Elsevier, vol. 94(1-2), pages 9-51. [Downloadable!] (restricted)
    Other versions:
  2. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June. [Downloadable!] (restricted)
Full references

Cited by:
(explanations, 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.)

  1. Michel Fliess & C\'edric Join, 2008. "Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance," Quantitative Finance Papers 0811.1561, arXiv.org, revised Nov 2008. [Downloadable!]
  2. Michel Fliess & Cédric Join, 2008. "Time Series Technical Analysis via New Fast Estimation Methods: A Preliminary Study in Mathematical Finance," Post-Print inria-00338099_v2, HAL. [Downloadable!]
Statistics
Access and download statistics

Did you know? All full texts are decentralized with the publishers, none reside on this server, thus making it possible to offer this service for free to all parties.

This page was last updated on 2009-12-9.

This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.