scholarly journals Study on Linear Combination of Long Memory Processes Corrupted by Additive Noises for fMRI Time Series Analysis

2017 ◽  
Author(s):  
Wonsang You ◽  
Catherine Limperopoulos
Keyword(s):  
Time Series ◽  
Neural Activity ◽  
Long Memory ◽  
Physiological Noise ◽  
Memory Processes ◽  
Fractal Properties ◽  
Long Memory Processes ◽  
Fmri Time Series ◽  
The Brain ◽  
Memory Parameter

AbstractEstimating the long memory parameter of the fMRI time series enables us to understand the fractal behavior of neural activity of the brain through fMRI time series. However, the existence of white noise and physiological noise compounds which also have fractal properties prevent us from making the estimation precise. As basic strategies to overcome noises, we address how to estimate the long memory parameter in the presence of additive noises, and how to estimate the long memory parameters of linearly combined long memory processes.

scholarly journals MEMORY PARAMETER ESTIMATION IN THE PRESENCE OF LEVEL SHIFTS AND DETERMINISTIC TRENDS

2013 ◽  
Vol 29 (6) ◽  
pp. 1196-1237 ◽  
Author(s):  
Adam Mccloskey ◽  
Pierre Perron
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Level Shift ◽  
Finite Sample ◽  
Memory Processes ◽  
Trade Offs ◽  
Level Shifts ◽  
Long Memory Processes ◽  
Short Memory ◽  
Memory Parameter

We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts, and deterministic time trends. The estimators are simple trimmed versions of the popular log-periodogram regression estimator that employ certain sample-size-dependent and, in some cases, data-dependent trimmings that discard low-frequency components. We also show that a previously developed trimmed local Whittle estimator is robust to the same forms of data contamination. Regardless of whether the underlying long- or short-memory process is contaminated by level shifts or deterministic trends, the estimators are consistent and asymptotically normal with the same limiting variance as their standard untrimmed counterparts. Simulations show that the trimmed estimators perform their intended purpose quite well, substantially decreasing both finite-sample bias and root mean-squared error in the presence of these contaminating components. Furthermore, we assess the trade-offs involved with their use when such components are not present but the underlying process exhibits strong short-memory dynamics or is contaminated by noise. To balance the potential finite-sample biases involved in estimating the memory parameter, we recommend a particular adaptive version of the trimmed log-periodogram estimator that performs well in a wide variety of circumstances. We apply the estimators to stock market volatility data to find that various time series typically thought to be long-memory processes actually appear to be short- or very weak long-memory processes contaminated by level shifts or deterministic trends.

Estimating the memory parameter for potentially non-linear and non-Gaussian time series with wavelets

2022 ◽  
Author(s):  
Chen Xu ◽  
Ye Zhang
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Asymptotic Theory ◽  
Financial Time Series ◽  
Non Linear ◽  
Long Memory Processes ◽  
Non Gaussian ◽  
Gaussian Time ◽  
Gaussian Time Series ◽  
Memory Parameter

Abstract The asymptotic theory for the memory-parameter estimator constructed from the log-regression with wavelets is incomplete for 1/$f$ processes that are not necessarily Gaussian or linear. Having a complete version of this theory is necessary because of the importance of non-Gaussian and non-linear long-memory models in describing financial time series. To bridge this gap, we prove that, under some mild assumptions, a newly designed memory estimator, named LRMW in this paper, is asymptotically consistent. The performances of LRMW in three simulated long-memory processes indicate the efficiency of this new estimator.

scholarly journals A harmonically weighted filter for cyclical long memory processes

2021 ◽  
Author(s):  
Federico Maddanu
Keyword(s):  
Spectral Density ◽  
Long Memory ◽  
Convergence In Probability ◽  
Simulation Methods ◽  
Integrated Process ◽  
Paleoclimatic Data ◽  
Memory Time ◽  
Long Memory Processes ◽  
Short Memory ◽  
Memory Parameter

AbstractThe estimation of the long memory parameter d is a widely discussed issue in the literature. The harmonically weighted (HW) process was recently introduced for long memory time series with an unbounded spectral density at the origin. In contrast to the most famous fractionally integrated process, the HW approach does not require the estimation of the d parameter, but it may be just as able to capture long memory as the fractionally integrated model, if the sample size is not too large. Our contribution is a generalization of the HW model, denominated the Generalized harmonically weighted (GHW) process, which allows for an unbounded spectral density at $$k \ge 1$$ k ≥ 1 frequencies away from the origin. The convergence in probability of the Whittle estimator is provided for the GHW process, along with a discussion on simulation methods. Fit and forecast performances are evaluated via an empirical application on paleoclimatic data. Our main conclusion is that the above generalization is able to model long memory, as well as its classical competitor, the fractionally differenced Gegenbauer process, does. In addition, the GHW process does not require the estimation of the memory parameter, simplifying the issue of how to disentangle long memory from a (moderately persistent) short memory component. This leads to a clear advantage of our formulation over the fractional long memory approach.

scholarly journals Slow Cortical Waves via Cyclicity

2021 ◽  
Author(s):  
Ivan Abraham ◽  
Bahar Shahsavarani ◽  
Ben Zimmerman ◽  
Fatima Husain ◽  
yuliy baryshnikov
Keyword(s):  
Time Series ◽  
Dynamic Structure ◽  
Resting State Fmri ◽  
Brain Regions ◽  
Fine Grained ◽  
Human Connectome Project ◽  
Fmri Time Series ◽  
The Brain ◽  
Cortical Waves ◽  
Temporal Ordering

Fine-grained information about dynamic structure of cortical networks is crucial in unpacking brain function. Here,we introduced a novel analytical method to characterize the dynamic interaction between distant brain regions,based on cyclicity analysis, and applied it to data from the Human Connectome Project. Resting-state fMRI time series are aperiodic and, hence, lack a base frequency. Cyclicity analysis, which is time-reparametrization invariant, is effective in recovering dynamic temporal ordering of such time series along a circular trajectory without assuming any time scale. Our analysis detected the propagation of slow cortical waves across thebrain with consistent shifts in lead-lag relationships between specific brain regions. We also observed short bursts of strong temporal ordering that dominated overall lead-lag relationships between pairs of regions in the brain, which were modulated by tasks. Our results suggest the possible role played by slow waves of ordered information between brain regions that underlie emergent cognitive function.

Statistics for Long-Memory Processes

Technometrics ◽  
1997 ◽  
Vol 39 (1) ◽  
pp. 105-106
Author(s):  
Jeffrey Glosup
Keyword(s):  
Long Memory ◽  
Memory Processes ◽  
Long Memory Processes
Sign in / Sign up

Export Citation Format

Share Document