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Analysis of H-sssi processes using the crossing tree: An alternative to wavelets
В печати
В работе описывается экспериментальное исследование динамических характеристик самоподобных разномасштабных финансовых временных рядов и проверка качества статистических, эконометрических и интеллектуальных методов их анализа и прогнозирования. Исследование проводилось на 20 различных финансовых временных рядах, в том числе на рядах цен акций российских и зарубежных компаний, цен на золото, нефть, индексов ММВБ, S&P, курсов валют и т.д. Анализ этих рядов подтвердил наличие общих закономерностей в изменении структуры ряда в зависимости от масштаба.
We present a new class of multifractal process on R, constructed using an embedded branching process. The construction makes use of known results on multitype branching random walks, and along the way constructs cascade measures on the boundaries of multitype Galton–Watson trees. Our class of processes includes Brownian motion subjected to a continuous multifractal time-change. In addition, if we observe our process at a fixed spatial resolution, then we can obtain a finite Markov representation of it, which we can use for on-line simulation. That is, given only the Markov representation at step n, we can generate step n+1 in O(log n) operations. Detailed pseudo-code for this algorithm is provided.R
nn+1O(logn)
In this paper, we consider the model of server traffic when the traffic is separated into several streams. The amount of transferred data differs for different streams. Based on real traffic measurements we proposed the server traffic model where traffic of every stream is described by the same independent processes, but each process has its own time scale. We show that for traffic analysis as well as for developing of the most effective methods of control of this traffic, it is necessary to correctly identify the time scale for each stream, as well as the time scale of traffic fluctuations those have a significant effect to QoS.