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3 produkter
3 produkter
1 533 kr
Skickas inom 5-8 vardagar
Box and Jenkins (1970) made the idea of obtaining a stationary time series by differencing the given, possibly nonstationary, time series popular. Numerous time series in economics are found to have this property. Subsequently, Granger and Joyeux (1980) and Hosking (1981) found examples of time series whose fractional difference becomes a short memory process, in particular, a white noise, while the initial series has unbounded spectral density at the origin, i.e. exhibits long memory.Further examples of data following long memory were found in hydrology and in network traffic data while in finance the phenomenon of strong dependence was established by dramatic empirical success of long memory processes in modeling the volatility of the asset prices and power transforms of stock market returns.At present there is a need for a text from where an interested reader can methodically learn about some basic asymptotic theory and techniques found useful in the analysis of statistical inference procedures for long memory processes. This text makes an attempt in this direction. The authors provide in a concise style a text at the graduate level summarizing theoretical developments both for short and long memory processes and their applications to statistics. The book also contains some real data applications and mentions some unsolved inference problems for interested researchers in the field.
536 kr
Skickas inom 10-15 vardagar
This volume contains several contributions on the general theme of dependence for several classes of stochastic processes, andits implicationson asymptoticproperties of various statistics and on statistical inference issues in statistics and econometrics. The chapter by Berkes, Horvath and Schauer is a survey on their recent results on bootstrap and permutation statistics when the negligibility condition of classical central limit theory is not satis ed. These results are of interest for describing the asymptotic properties of bootstrap and permutation statistics in case of in nite va- ances, and for applications to statistical inference, e.g., the change-point problem. The paper by Stoev reviews some recent results by the author on ergodicity of max-stable processes. Max-stable processes play a central role in the modeling of extreme value phenomena and appear as limits of component-wise maxima. At the presenttime,arathercompleteandinterestingpictureofthedependencestructureof max-stable processes has emerged,involvingspectral functions, extremalstochastic integrals, mixed moving maxima, and other analytic and probabilistic tools.For statistical applications, the problem of ergodicity or non-ergodicity is of primary importance.
- Nyhet
Anisotropic Scaling Of Random Fields With Long-range Dependence: Scaling Limits Of Random Fields With Applications
Inbunden, Engelska, 2026
1 227 kr
Kommande
Anisotropic Scaling of Random Fields with Long-Range Dependence is primarily interested in two questions: are there scaling limits for all γ>0 ratios? And if so, what are they? By introducing the concept of a scaling transition and discussing its existence for Gaussian models, moving-average models, and their subordinated planar models, the very cutting-edge of research and theory within scaling transition is explored, interrogated, and understood.If a scaling parameter tends to zero or infinity (infinite scaling), this can lead to a limit which is self-similar and much simpler than the original object. In the case of a random field indexed by a two-dimensional, both types of scaling can be anisotropic — meaning that the horizontal and vertical axes are scaled at different rates determined by the ratio γ>0 of the scaling exponents along the axes. Within this text, a wide class of linear and nonlinear random fields are analysed through the critically underdiscussed concept of a scaling transition. A central engagement of this research involves joint temporal and contemporaneous aggregation of spatio-temporal models with long-range dependence in applied sciences (telecommunications and econometrics) and the scaling transition arising when the number of spatial components and time scale increase at different rates.This book is intended for advanced graduate and PhD students, as well as researchers and practitioners in the fields of stochastic processes, spatial statistics, econometrics and telecommunications, although researchers working in applied sciences such as geophysics will also find value in its study.