scholarly journals ASYMPTOTIC PROPERTIES OF SELF-NORMALIZED LINEAR PROCESSES WITH LONG MEMORY

2011 ◽  
Vol 28 (3) ◽  
pp. 548-569 ◽  
Author(s):  
Magda Peligrad ◽  
Hailin Sang
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Heavy Tails ◽  
Asymptotic Properties ◽  
The Self ◽  
Linear Processes ◽  
Economic Applications ◽  
Memory Time

In this paper we study the convergence to fractional Brownian motion for long memory time series having independent innovations with infinite second moment. For the sake of applications we derive the self-normalized version of this theorem. The study is motivated by models arising in economic applications where often the linear processes have long memory, and the innovations have heavy tails.

OPERATOR FRACTIONAL BROWNIAN MOTION AS LIMIT OF POLYGONAL LINES PROCESSES IN HILBERT SPACE

2011 ◽  
Vol 11 (01) ◽  
pp. 49-70 ◽  
Author(s):  
ALFREDAS RAČKAUSKAS ◽  
CHARLES SUQUET
Keyword(s):  
Hilbert Space ◽  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Partial Sums ◽  
Functional Time Series ◽  
Hurst Coefficient

In this paper, we study long memory phenomenon of functional time series. We consider an operator fractional Brownian motion with values in a Hilbert space defined via operator-valued Hurst coefficient. We prove that this process is a limiting one for polygonal lines constructed from partial sums of time series having space varying long memory.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

2021 ◽  
Author(s):  
Jan Beran ◽  
Britta Steffens ◽  
Sucharita Ghosh
Keyword(s):  
Time Series ◽  
Nonparametric Regression ◽  
Long Range ◽  
Long Memory ◽  
Regression Function ◽  
Confidence Bands ◽  
Long Range Dependence ◽  
Asymptotic Results ◽  
Memory Time ◽  
Circular Time Series

AbstractWe consider nonparametric regression for bivariate circular time series with long-range dependence. Asymptotic results for circular Nadaraya–Watson estimators are derived. Due to long-range dependence, a range of asymptotically optimal bandwidths can be found where the asymptotic rate of convergence does not depend on the bandwidth. The result can be used for obtaining simple confidence bands for the regression function. The method is illustrated by an application to wind direction data.

scholarly journals Semiparametric Analysis of Long-Memory Time Series

1994 ◽  
Vol 22 (1) ◽  
pp. 515-539 ◽  
Author(s):  
P. M. Robinson
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Semiparametric Analysis ◽  
Memory Time

scholarly journals Serotonergic Axons as Fractional Brownian Motion Paths: Insights into the Self-organization of Regional Densities

2019 ◽  
Author(s):  
Skirmantas Janušonis ◽  
Nils Detering ◽  
Ralf Metzler ◽  
Thomas Vojta
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Adult Brain ◽  
The Self ◽  
Self Organization ◽  
Dense Matrix ◽  
Two Dimensional ◽  
Wide Range ◽  
Motion Paths ◽  
Key Features

ABSTRACTAll vertebrate brains contain a dense matrix of thin fibers that release serotonin (5-hydroxytryptamine), a neurotransmitter that modulates a wide range of neural, glial, and vascular processes. Perturbations in the density of this matrix have been associated with a number of mental disorders, including autism and depression, but its self-organization and plasticity remain poorly understood. We introduce a model based on reflected Fractional Brownian Motion (FBM), a rigorously defined stochastic process, and show that it recapitulates some key features of regional serotonergic fiber densities. Specifically, we use supercomputing simulations to model fibers as FBM-paths in two-dimensional brain-like domains and demonstrate that the resultant steady state distributions approximate the fiber distributions in physical brain sections immunostained for the serotonin transporter (a marker for serotonergic axons in the adult brain). We suggest that this framework can support predictive descriptions and manipulations of the serotonergic matrix and that it can be further extended to incorporate the detailed physical properties of the fibers and their environment.

Sign in / Sign up

Export Citation Format

Share Document