Long-memory processes are known to play an important part in many areas of science and technology, including physics, geophysics, hydrology, telecommunications, economics, finance, climatology, and network engineering. In the last 20 years enormous progress has been made in understanding the probabilistic foundations and statistical principles of such processes. This book provides a timely and comprehensive review, including a thorough discussion of mathematical and probabilistic foundations and statistical methods, emphasizing their practical motivation and mathematical justification. Proofs of the main theorems are provided and data examples illustrate practical aspects. This book will be a valuable resource for researchers and graduate students in statistics, mathematics, econometrics and other quantitative areas, as well as for practitioners and applied researchers who need to analyze data in which long memory, power laws, self-similar scaling or fractal properties are relevant.is represented as the sum of a stationary Gaussian sequence and the log of a x: Irana dom variables. The tail of Y, has a complicated form, nevertheless it belongs to the domain of attraction of the Gumbel law. A modification of the normalanbsp;...
|Author||:||Jan Beran, Yuanhua Feng, Sucharita Ghosh, Rafal Kulik|
|Publisher||:||Springer Science & Business Media - 2013-05-14|