ESTIMATORS FOR LONG-RANGE DEPENDENCE: AN EMPIRICAL STUDY

Fractals ◽  
1995 ◽  
Vol 03 (04) ◽  
pp. 785-798 ◽  
Author(s):  
MURAD S. TAQQU ◽  
VADIM TEVEROVSKY ◽  
WALTER WILLINGER
Keyword(s):  
Time Series ◽  
Long Range ◽  
Gaussian Noise ◽  
The Self ◽  
Long Range Dependence ◽  
Fractional Gaussian Noise ◽  
Self Similarity ◽  
Theoretical Justification ◽  
Similarity Parameter ◽  
Fractional Arima

Various methods for estimating the self-similarity parameter and/or the intensity of long-range dependence in a time series are available. Some are more reliable than others. To discover the ones that work best, we apply the different methods to simulated sequences of fractional Gaussian noise and fractional ARIMA (0, d, 0). We also provide here a theoretical justification for the method of residuals of regression.

scholarly journals Bayesian estimation of the self-similarity exponent of the Nile River fluctuation

2011 ◽  
Vol 18 (3) ◽  
pp. 441-446 ◽  
Author(s):  
S. Benmehdi ◽  
N. Makarava ◽  
N. Benhamidouche ◽  
M. Holschneider
Keyword(s):  
Time Series ◽  
Gaussian Noise ◽  
Hurst Exponent ◽  
Noise Signal ◽  
The Self ◽  
Nile River ◽  
Fractional Gaussian Noise ◽  
Self Similarity ◽  
Error Bars ◽  
Integrated Time Series

Abstract. The aim of this paper is to estimate the Hurst parameter of Fractional Gaussian Noise (FGN) using Bayesian inference. We propose an estimation technique that takes into account the full correlation structure of this process. Instead of using the integrated time series and then applying an estimator for its Hurst exponent, we propose to use the noise signal directly. As an application we analyze the time series of the Nile River, where we find a posterior distribution which is compatible with previous findings. In addition, our technique provides natural error bars for the Hurst exponent.

scholarly journals WHY FARIMA MODELS ARE BRITTLE

Fractals ◽  
2013 ◽  
Vol 21 (02) ◽  
pp. 1350012 ◽  
Author(s):  
D. VEITCH ◽  
A. GORST-RASMUSSEN ◽  
A. GEFFERTH
Keyword(s):  
Time Series ◽  
Convergence Rate ◽  
Long Range ◽  
Gaussian Noise ◽  
Additive Noise ◽  
Time Function ◽  
Long Range Dependence ◽  
Fractional Gaussian Noise ◽  
Precise Characterization

The FARIMA models, which have long-range-dependence (LRD), are widely used in many areas. Through the derivation of a precise characterization of the spectrum and variance time function, we show that this family is very atypical among LRD processes, being extremely close to the fractional Gaussian noise in a precise sense which results in ultra-fast convergence to fGn under rescaling. Furthermore, we show that this closeness property is not robust to additive noise. We argue that the use of FARIMA, and more generally fractionally differenced time series, should be reassessed in some contexts, in particular when convergence rate under rescaling is important and noise is expected.

scholarly journals Variance Bound of ACF Estimation of One Block of fGn with LRD

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao
Keyword(s):  
Long Range ◽  
Autocorrelation Function ◽  
Gaussian Noise ◽  
Block Size ◽  
Long Range Dependence ◽  
Hurst Parameter ◽  
Sample Length ◽  
Fractional Gaussian Noise ◽  
Variance Bound ◽  
Data Points

This paper discusses the estimation of autocorrelation function (ACF) of fractional Gaussian noise (fGn) with long-range dependence (LRD). A variance bound of ACF estimation of one block of fGn with LRD for a given value of the Hurst parameter (H) is given. The present bound provides a guideline to require the block size to guarantee that the variance of ACF estimation of one block of fGn with LRD for a givenHvalue does not exceed the predetermined variance bound regardless of the start point of the block. In addition, the present result implies that the error of ACF estimation of a block of fGn with LRD depends only on the number of data points within the sample and not on the actual sample length in time. For a given block size, the error is found to be larger for fGn with stronger LRD than that with weaker LRD.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (2) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

scholarly journals Estimation of the self-similarity parameter in long memory processes

1970 ◽  
Vol 38 ◽  
pp. 32-37 ◽  
Author(s):  
MMA Sarker
Keyword(s):  
Long Memory ◽  
The Self ◽  
Similar Process ◽  
Long Range Dependence ◽  
Self Similarity ◽  
Similarity Parameter ◽  
Data Set ◽  
Memory Processes ◽  
Long Memory Processes ◽  
Self Similar

Long memory processes, where positive correlations between observations far apart in time and space decay very slowly to zero with increasing time lag, occur quite frequently in fields such as hydrology and economics. Stochastic processes that are invariant in distribution under judicious scaling of time and space, called self-similar process, can parsimoniously model the long-run properties of phenomena exhibiting long-range dependence. Four of the heuristic estimation approaches have been presented in this study so that the self-similarity parameter, H that gives the correlation structure in long memory processes, can be effectively estimated. Finally, the methods presented in this paper were applied to two observed time series, namely Nile River Data set and the VBR (Variable- Bit-Rate) data set. The estimated values of H for two data sets found from different methods suggest that all methods are not equally good for estimation. Keywords: Long memory process, long-range dependence, Self-similar process, Hurst Parameter, Gaussian noise. DOI: 10.3329/jme.v38i0.898 Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.32-37  

scholarly journals Supervised Learning of Neural Networks for Active Queue Management in the Internet

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 4979
Author(s):  
Jakub Szyguła ◽  
Adam Domański ◽  
Joanna Domańska ◽  
Dariusz Marek ◽  
Katarzyna Filus ◽  
...  
Keyword(s):  
Neural Networks ◽  
Gaussian Noise ◽  
Waiting Times ◽  
Active Queue Management ◽  
The Self ◽  
Queue Management ◽  
Fractional Gaussian Noise ◽  
Self Similarity ◽  
Management Mechanism ◽  
Training Samples

The paper examines the AQM mechanism based on neural networks. The active queue management allows packets to be dropped from the router’s queue before the buffer is full. The aim of the work is to use machine learning to create a model that copies the behavior of the AQM PIα mechanism. We create training samples taking into account the self-similarity of network traffic. The model uses fractional Gaussian noise as a source. The quantitative analysis is based on simulation. During the tests, we analyzed the length of the queue, the number of rejected packets and waiting times in the queues. The proposed mechanism shows the usefulness of the Active Queue Management mechanism based on Neural Networks.

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.

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