scholarly journals Towards Generic Simulation for Demanding Stochastic Processes

2021 ◽  
Author(s):  
Demetris Koutsoyiannis ◽  
Panayiotis Dimitriadis
Keyword(s):  
Stochastic Processes ◽  
White Noise ◽  
Marginal Distribution ◽  
Moving Average ◽  
Gaussian White Noise ◽  
Simulation Method ◽  
Average Scheme ◽  
Non Gaussian ◽  
Generalized Time ◽  
Bounded Form

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly without any transformation (e.g. normalization). We illustrate the method in a number of synthetic and real-world applications with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded form below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

scholarly journals Towards Generic Simulation for Demanding Stochastic Processes

Sci ◽  
2021 ◽  
Vol 3 (3) ◽  
pp. 34
Author(s):  
Demetris Koutsoyiannis ◽  
Panayiotis Dimitriadis
Keyword(s):  
Stochastic Processes ◽  
White Noise ◽  
Marginal Distribution ◽  
Moving Average ◽  
Gaussian White Noise ◽  
Simulation Method ◽  
Dependence Structure ◽  
Average Scheme ◽  
Non Gaussian ◽  
Generalized Time

We outline and test a new methodology for genuine simulation of stochastic processes with any dependence structure and any marginal distribution. We reproduce time dependence with a generalized, time symmetric or asymmetric, moving-average scheme. This implements linear filtering of non-Gaussian white noise, with the weights of the filter determined by analytical equations, in terms of the autocovariance of the process. We approximate the marginal distribution of the process, irrespective of its type, using a number of its cumulants, which in turn determine the cumulants of white noise, in a manner that can readily support the generation of random numbers from that approximation, so that it be applicable for stochastic simulation. The simulation method is genuine as it uses the process of interest directly, without any transformation (e.g., normalization). We illustrate the method in a number of synthetic and real-world applications, with either persistence or antipersistence, and with non-Gaussian marginal distributions that are bounded, thus making the problem more demanding. These include distributions bounded from both sides, such as uniform, and bounded from below, such as exponential and Pareto, possibly having a discontinuity at the origin (intermittence). All examples studied show the satisfactory performance of the method.

scholarly journals EMD OF GAUSSIAN WHITE NOISE: EFFECTS OF SIGNAL LENGTH AND SIFTING NUMBER ON THE STATISTICAL PROPERTIES OF INTRINSIC MODE FUNCTIONS

2009 ◽  
Vol 01 (04) ◽  
pp. 517-527 ◽  
Author(s):  
GASTÓN SCHLOTTHAUER ◽  
MARÍA EUGENIA TORRES ◽  
HUGO L. RUFINER ◽  
PATRICK FLANDRIN
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Kernel Smoothing ◽  
Gaussian White Noise ◽  
Large Data ◽  
Intrinsic Mode Functions ◽  
Mode Decomposition ◽  
Non Gaussian ◽  
Data Length ◽  
Number Of Iterations

This work presents a discussion on the probability density function of Intrinsic Mode Functions (IMFs) provided by the Empirical Mode Decomposition of Gaussian white noise, based on experimental simulations. The influence on the probability density functions of the data length and of the maximum allowed number of iterations is analyzed by means of kernel smoothing density estimations. The obtained results are confirmed by statistical normality tests indicating that the IMFs have non-Gaussian distributions. Our study also indicates that large data length and high number of iterations produce multimodal distributions in all modes.

scholarly journals Filtering with a limiter

1998 ◽  
Vol 11 (3) ◽  
pp. 289-300 ◽  
Author(s):  
R. Liptser ◽  
P. Muzhikanov
Keyword(s):  
Weak Convergence ◽  
Diffusion Process ◽  
White Noise ◽  
Discrete Time ◽  
Diffusion Approximation ◽  
Conditional Expectation ◽  
Gaussian White Noise ◽  
Sampling Step ◽  
Non Gaussian ◽  
Filtering Problem

We consider a filtering problem for a Gaussian diffusion process observed via discrete-time samples corrupted by a non-Gaussian white noise. Combining the Goggin's result [2] on weak convergence for conditional expectation with diffusion approximation when a sampling step goes to zero we construct an asymptotic optimal filter. Our filter uses centered observations passed through a limiter. Being asymptotically equivalent to a similar filter without centering, it yields a better filtering accuracy in a prelimit case.

scholarly journals A Cautionary Note on the Reproduction of Dependencies through Linear Stochastic Models with Non-Gaussian White Noise

Water ◽  
2018 ◽  
Vol 10 (6) ◽  
pp. 771 ◽  
Author(s):  
Ioannis Tsoukalas ◽  
Simon Papalexiou ◽  
Andreas Efstratiadis ◽  
Christos Makropoulos
Keyword(s):  
White Noise ◽  
Stochastic Models ◽  
Gaussian White Noise ◽  
Cautionary Note ◽  
Non Gaussian

scholarly journals Description of the macroscopic dynamics of populations of phase elements with white non-Gaussian noise based on the circular cumulant approach

2021 ◽  
pp. 05-12
Author(s):  
A. V. Dolmatova ◽  
◽  
I. V. Tiulkina ◽  
D. S. Goldobin ◽  
◽  
...  
Keyword(s):  
White Noise ◽  
Probability Density ◽  
Gaussian Noise ◽  
Gaussian White Noise ◽  
Macroscopic Description ◽  
Reduced Equations ◽  
Non Gaussian ◽  
Dynamics Of Populations ◽  
Stable Noise ◽  
Good Agreement

We use the method of circular cumulants, which allows us to construct a low-mode macroscopic description of the dynamics of populations of phase elements subject to non-Gaussian white noise. In this work, we have obtained two-cumulant reduced equations for alpha-stable noise. The application of the approach is demonstrated for the case of the Kuramoto ensemble with non-Gaussian noise. The results of numerical calculations for the ensemble of N = 1500 elements, the numericalsimulation of the chain of equations for the Kuramoto–Daido order parameters (Fourier modes of the probability density) with 200 terms (in the thermodynamic limit of an infinitely large ensemble) and the theoretical solution on the basis of the two-cumulant approximation are in good agreement with each other.

scholarly journals Asymptotic dependence of moving average type self-similar stable random Fields

1993 ◽  
Vol 130 ◽  
pp. 85-100 ◽  
Author(s):  
Piotr S. Kokoszka ◽  
Murad S. Taqqu
Keyword(s):  
Stochastic Processes ◽  
Random Fields ◽  
Covariance Function ◽  
Moving Average ◽  
Dependence Structure ◽  
Asymptotic Dependence ◽  
Second Moments ◽  
Self Similar ◽  
Non Gaussian ◽  
Stable Random Fields

As non-Gaussian stable stochastic processes have infinite second moments, one cannot use the covariance function to describe their dependence structure.

TESTING FOR WHITE NOISE UNDER UNKNOWN DEPENDENCE AND ITS APPLICATIONS TO DIAGNOSTIC CHECKING FOR TIME SERIES MODELS

2010 ◽  
Vol 27 (2) ◽  
pp. 312-343 ◽  
Author(s):  
Xiaofeng Shao
Keyword(s):  
White Noise ◽  
Moving Average ◽  
Asymptotic Properties ◽  
Null Distribution ◽  
Nonlinear Dependence ◽  
Test Statistics ◽  
Test Statistic ◽  
Diagnostic Checking ◽  
Non Gaussian ◽  
Zero Autocorrelation

Testing for white noise has been well studied in the literature of econometrics and statistics. For most of the proposed test statistics, such as the well-known Box–Pierce test statistic with fixed lag truncation number, the asymptotic null distributions are obtained under independent and identically distributed assumptions and may not be valid for dependent white noise. Because of recent popularity of conditional heteroskedastic models (e.g., generalized autoregressive conditional heteroskedastic [GARCH] models), which imply nonlinear dependence with zero autocorrelation, there is a need to understand the asymptotic properties of the existing test statistics under unknown dependence. In this paper, we show that the asymptotic null distribution of the Box–Pierce test statistic with general weights still holds under unknown weak dependence as long as the lag truncation number grows at an appropriate rate with increasing sample size. Further applications to diagnostic checking of the autoregressive moving average (ARMA) and fractional autoregressive integrated moving average (FARIMA) models with dependent white noise errors are also addressed. Our results go beyond earlier ones by allowing non-Gaussian and conditional heteroskedastic errors in the ARMA and FARIMA models and provide theoretical support for some empirical findings reported in the literature.

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