Power-law shot noise and its relationship to long-memory α-stable processes

2000 ◽  
Vol 48 (7) ◽  
pp. 1883-1892 ◽  
Author(s):  
A.P. Petropulu ◽  
J.-C. Pesquet ◽  
Xueshi Yang
Keyword(s):  
Power Law ◽  
Shot Noise ◽  
Long Memory ◽  
Stable Processes

Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (04) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob. 34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

Breast tissue characterization based on modeling of ultrasonic echoes using the power-law shot noise model

2003 ◽  
Vol 24 (4-5) ◽  
pp. 741-756 ◽  
Author(s):  
M.Alper Kutay ◽  
Athina P Petropulu ◽  
Catherine W Piccoli
Keyword(s):  
Power Law ◽  
Shot Noise ◽  
Breast Tissue ◽  
Tissue Characterization ◽  
Noise Model

scholarly journals On Scaling Limits of Power Law Shot-Noise Fields

2015 ◽  
Vol 31 (2) ◽  
pp. 187-207 ◽  
Author(s):  
François Baccelli ◽  
Anup Biswas
Keyword(s):  
Power Law ◽  
Shot Noise ◽  
Scaling Limits

Power-law shot noise

1990 ◽  
Vol 36 (6) ◽  
pp. 1302-1318 ◽  
Author(s):  
S.B. Lowen ◽  
M.C. Teich
Keyword(s):  
Power Law ◽  
Shot Noise

Random coefficient autoregression, regime switching and long memory

2003 ◽  
Vol 35 (03) ◽  
pp. 737-754 ◽  
Author(s):  
Remigijus Leipus ◽  
Donatas Surgailis
Keyword(s):  
Probability Density ◽  
Power Law ◽  
Renewal Process ◽  
Long Memory ◽  
Regime Switching ◽  
Covariance Function ◽  
Random Coefficient ◽  
Levy Process ◽  
Partial Sums ◽  
Stable Lévy Process

We discuss long-memory properties and the partial sums process of the AR(1) process {X t , t ∈ 𝕫} with random coefficient {a t , t ∈ 𝕫} taking independent values A j ∈ [0,1] on consecutive intervals of a stationary renewal process with a power-law interrenewal distribution. In the case when the distribution of generic A j has either an atom at the point a=1 or a beta-type probability density in a neighborhood of a=1, we show that the covariance function of {X t } decays hyperbolically with exponent between 0 and 1, and that a suitably normalized partial sums process of {X t } weakly converges to a stable Lévy process.

Power-Law and Long-Memory Characteristics of the Atmospheric General Circulation

2009 ◽  
Vol 22 (11) ◽  
pp. 2890-2904 ◽  
Author(s):  
Dmitry I. Vyushin ◽  
Paul J. Kushner
Keyword(s):  
Climate Variability ◽  
Power Law ◽  
Long Memory ◽  
General Circulation ◽  
Fluctuation Analysis ◽  
Temperature Record ◽  
Power Law Model ◽  
Large Power ◽  
Internal Climate Variability ◽  
Power Law Function

Abstract The question of which statistical model best describes internal climate variability on interannual and longer time scales is essential to the ability to predict such variables and detect periodicities and trends in them. For over 30 yr the dominant model for background climate variability has been the autoregressive model of the first order (AR1). However, recent research has shown that some aspects of climate variability are best described by a “long memory” or “power-law” model. Such a model fits a temporal spectrum to a single power-law function, which thereby accumulates more power at lower frequencies than an AR1 fit. In this study, several power-law model estimators are applied to global temperature data from reanalysis products. The methods employed (the detrended fluctuation analysis, Geweke–Porter-Hudak estimator, Gaussian semiparametric estimator, and multitapered versions of the last two) agree well for pure power-law stochastic processes. However, for the observed temperature record, the power-law fits are sensitive to the choice of frequency range and the intrinsic filtering properties of the methods. The observational results converge once frequency ranges are made consistent and the lowest frequencies are included, and once several climate signals have been filtered. Two robust results emerge from the analysis: first, that the tropical circulation features relatively large power-law exponents that connect to the zonal-mean extratropical circulation; and second, that the subtropical lower stratosphere exhibits power-law behavior that is volcanically forced.

Power-law correlations, related models for long-range dependence and their simulation

2000 ◽  
Vol 37 (4) ◽  
pp. 1104-1109 ◽  
Author(s):  
Tilmann Gneiting
Keyword(s):  
Long Range ◽  
Power Law ◽  
Long Memory ◽  
Stationary Time Series ◽  
Long Range Dependence ◽  
Short Term ◽  
Permissible Range ◽  
Simultaneous Fitting ◽  
Straightforward Proof

Martin and Walker ((1997) J. Appl. Prob.34, 657–670) proposed the power-law ρ(v) = c|v|-β, |v| ≥ 1, as a correlation model for stationary time series with long-memory dependence. A straightforward proof of their conjecture on the permissible range of c is given, and various other models for long-range dependence are discussed. In particular, the Cauchy family ρ(v) = (1 + |v/c|α)-β/α allows for the simultaneous fitting of both the long-term and short-term correlation structure within a simple analytical model. The note closes with hints at the fast and exact simulation of fractional Gaussian noise and related processes.

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