Ordinal Pattern Dependence in the Context of Long-Range Dependence

Long Range Dependence

The notion of long range dependence is discussed from a variety of points of view, and a new approach is suggested. A number of related topics is also discussed, including connections with non-stationary processes, with ergodic theory, self-similar processes and fractionally differenced processes, heavy tails and light tails, limit theorems and large deviations.

Ordinal Pattern Dependence between hydrological time series

Short Range and Long Range Dependence

In this section a discussion of the evolution of a notion of strong mixing as a measure of short range dependence and with additional restrictions a sufficient condition for a central limit theorem, is given. In the next section I will give a characterization of strong mixing for stationary Gaussian sequences. In Sect. 3 I will give a discussion of processes subordinated to Gaussian processes a...

Long Range Dependence in Copula Models

Modeling short and long time dependence in univariate time series may be successfully accomplished through existing time series processes. In the multivariate setting just a few complex models exist to take care of the di®erent marginal dynamics as well as of the dynamic covariance matrix. The copula approach factors the joint distribution into the marginals and a dependence function, its copul...

Long-range Dependence in Daily Stock Volatilities

Recent empirical studies show that the squares of high-frequency stock returns are long-range dependent and can be modeled as fractionally integrated processes, using, for example, long-memory stochastic volatility models. Are such long-range dependencies common among stocks? Are they caused by the same sources of variation? In this paper, we classify daily stock returns of S&P 500 companies on...