Modeling Continuous Time Series Driven by Fractional Gaussian Noise

2004 ◽  
pp. 239-255
Author(s):  
Winston C. Chow ◽  
Edward J. Wegman
Keyword(s):  
Time Series ◽  
Gaussian Noise ◽  
Continuous Time ◽  
Fractional Gaussian Noise

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.

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 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 Generalized Wavelet Fisher’s Information of1/fαSignals

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Julio Ramírez-Pacheco ◽  
Homero Toral-Cruz ◽  
Luis Rizo-Domínguez ◽  
Joaquin Cortez-Gonzalez
Keyword(s):  
Fisher Information ◽  
Gaussian Noise ◽  
Structural Breaks ◽  
Wavelet Domain ◽  
Fractional Gaussian Noise ◽  
Domain Definition ◽  
Potential Applications ◽  
Definition Of ◽  
The Time Domain ◽  
Fisher's Information

This paper defines the generalized wavelet Fisher information of parameterq. This information measure is obtained by generalizing the time-domain definition of Fisher’s information of Furuichi to the wavelet domain and allows to quantify smoothness and correlation, among other signals characteristics. Closed-form expressions of generalized wavelet Fisher information for1/fαsignals are determined and a detailed discussion of their properties, characteristics and their relationship with waveletq-Fisher information are given. Information planes of1/fsignals Fisher information are obtained and, based on these, potential applications are highlighted. Finally, generalized wavelet Fisher information is applied to the problem of detecting and locating weak structural breaks in stationary1/fsignals, particularly for fractional Gaussian noise series. It is shown that by using a joint Fisher/F-Statistic procedure, significant improvements in time and accuracy are achieved in comparison with the sole application of theF-statistic.

On the Discretization of Continuous-Time Filters for Nonstationary Stock and Flow Time Series

2011 ◽  
Vol 30 (5) ◽  
pp. 475-513 ◽  
Author(s):  
Tucker McElroy ◽  
Thomas M. Trimbur
Keyword(s):  
Time Series ◽  
Continuous Time ◽  
Flow Time ◽  
Continuous Time Filters

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

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