Fractality of Stock Markets
|Year:||2009 - winter|
|Leaders:|| doc. PhDr. Jozef Baruník Ph.D.
|Work type:|| Doctoral
|Awards and prizes:|
|Abstract:||The main focus of the thesis is the introduction of new method for interpretation of fractality
aspects of financial time series together with its application. We begin with description of
various techniques of estimation of Hurst exponent – rescaled range, modified rescaled range
and detrended fluctuation analysis. Further on, we present original theoretical results based on
simulations of three mentioned procedures which have not been presented in literature yet.
The results are then used in the new method of time-dependent Hurst exponent with
confidence intervals developed in this thesis. Moreover, we show important advantage of
using the mentioned techniques together to clearly distinguish between independent, trending,
short-term dependent and long-term dependent properties of the time series. We eventually
apply the proposed procedure on 13 different world stock indices and come to interesting
results. To the author’s best knowledge, the thesis presents the broadest application of timedependent
Hurst exponent on stock indices yet.