We consider five fractional generalizations of the Markovian α-stable Ornstein–Uhlenbeck process and explore the dependence structure of these stochastic models. Since the variance of α-stable distributed random variables is infinite, we describe the dependence structure of the introduced...

The contributions of this short paper are two-fold. We shall show two interesting properties of fractional Gaussian noise (fGn), namely, its bandlimitedness and lag-limitedness. The computation formulas for the maximum frequency of bandlimited fGn and the maximum lag of lag-limited fGn are...

We introduce a new measure for capital market efficiency. The measure takes into consideration the correlation structure of the returns (long-term and short-term memory) and local herding behavior (fractal dimension). The efficiency measure is taken as a distance from an ideal efficient market...

This study explores the dynamic interaction between stock market returns and changes in nominal exchange rates. Many financial variables are known to exhibit fat tails and autoregressive variance structure. It is well-known that unconditional covariance and correlation coefficients also vary...

Using Granger (1969), Sim (1972) and Geweke et al. (1982) causality tests, this study finds a feedback causal relationship between exchange rate and stock price in Malaysia, whereas a unidirectional causal relationship running from exchange rate to stock price in Thailand. The stock markets of...

We present here a detailed multifractal scaling study for the electronic transmission resonances with the system size for an infinitely large one-dimensional perfect and imperfect quasiperiodic system represented by a sequence of δ-function potentials. The electronic transmission resonances in...

The classical financial models are based on the standard Brownian diffusion-type processes. However, in the exhibition of some real market data (like interest or exchange rates) we observe characteristic periods of constant values. Moreover, in the case of financial data, the assumption of...

Geological systems such as petroleum reservoirs can be investigated using Tsallis entropy and multiplicative hierarchical cascade models. The occurrence of non-Gaussianity is a sign of uncertainty and a phase transition, which could indicate the existence of a petroleum reservoir. Two important...