The aggregation procedure is a natural way to analyse signals which exhibit long-range dependent features and has been used as a basis for estimation of the Hurst parameter, H. In this paper it is shown how aggregation can be naturally rephrased within the wavelet transform framework, being directly related to approximations of the signal in the sense of a Haar-multiresolution analysis. A natur...

Since Merton (1969), the description of a contingent claim as a Brownian motion is commonly accepted. Thus an option price, a future price, a share price, a bond price, interest rates etc., can be modelled with a Brownian motion. In summary, any financial series which present value depends on only a few previous values, may be modelled with a continuous–time diffusion–type process. The general ...

The dependence of large values in a stochastic process is an important topic in risk, insurance and finance. The idea of risk contagion is based on the idea of large value dependence. The Gaussian copula notoriously fails to capture this phenomenon. Two notions in a process context which attempt to summarize this extremal dependence in a function comparable to a sample correlation function are ...

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...

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...

Abstract. A popular modeling technique in mortgage banking involves regarding mortgage terminations observed in a continuously replenished system (such as a servicing portfolio) as a Markov process of …nite order k > 0 with values in a …nite state space. In this article, we consider the rami…cations of such an assumption. In particular,we conduct hypothesis tests of long-range dependence on a w...