An increasing attention is being payed to the scaling behaviour of stock returns. Several reasons motivate this interest: the assumption of self-affinity is implicit both in the standard financial theory (which states that the self-affinity parameter H equals 1/2) and in less consolidate frameworks, such as the fractal gaussian models (for whom H belongs to the interval (0,1)). The scaling structure of prices is usually deduced by analysing the sample moments, but this approach could be misleading because of many reasons, the most ''embarassing'' one being the assumption of existence of the considered moments. Since self-affinity allows to distinguish between two large classes of processes (the fractal - uniscaling - ones and the multifractal - multiscaling - ones), both suggested as models in finance, we reformulate this notion by means of an equivalent definition based on a distance built on the set of the rescaled probability distribution functions generated by the scaling law which defines the notion of self-affinity itself. A general characterization of our measure provides two necessary conditions of self-affinity: monotonicity with respect to both the parameter H and the maximum lag of an increasing sequence of trading horizon sets. We also give the closed expression of our measure when the process is the fractional brownian motion. Furthermore, a proper choice of the metric allows to apply the well-known Kolmogorov-Smirnov goodness of fit test in order to evaluate the statistical significance of the self-affinity measure, also in the case of dependent data whenever uniscaling holds. Finally, an empirical analysis is performed on several market indices. The analysis shows that, for the considered horizons (from one up to fifty trading days), uniscaling does not generally hold in financial markets.
Download Info
To our knowledge, this item is not available for
download. To find whether it is available, there are three
options:
1. Check below under "Related research" 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 search for a similarly titled item that would be
available.
Publisher Info
Paper provided by Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance in its series CeNDEF Workshop Papers, January 2001 with number
4A.3.
Length: Date of creation: 04 Jan 2001 Date of revision: Handle: RePEc:ams:cdws01:4a.3
Contact details of provider: Postal: Dept. of Economics and Econometrics, Universiteit van Amsterdam, Roetersstraat 11, NL - 1018 WB Amsterdam, The Netherlands Phone: + 31 20 525 52 58 Fax: + 31 20 525 52 83 Web page: http://www.fee.uva.nl/cendef/ More information through EDIRC
For technical questions regarding this item, or to correct its listing, contact: (Christopher F. Baum).
Did you know? Citation analysis on IDEAS includes online papers that are freely accessible and whose text could be automatically analyzed, currently about 210000 papers.