scholarly journals Nonparametric regression with non-Gaussian long memory

2013 ◽  
Vol 7 (2) ◽  
Author(s):  
Mariela Sued ◽  
Soledad Torres
Keyword(s):  
Nonparametric Regression ◽  
Long Memory ◽  
Non Gaussian

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.

Non-Gaussian and Long Memory Statistical Characterizations for Internet Traffic with Anomalies

2007 ◽  
Vol 4 (1) ◽  
pp. 56-70 ◽  
Author(s):  
Antoine Scherrer ◽  
Nicolas Larrieu ◽  
Philippe Owezarski ◽  
Pierre Borgnat ◽  
Patrice Abry
Keyword(s):  
Long Memory ◽  
Internet Traffic ◽  
Non Gaussian

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 Cramér type moderate deviations for random fields

2019 ◽  
Vol 56 (01) ◽  
pp. 223-245 ◽  
Author(s):  
Aleksandr Beknazaryan ◽  
Hailin Sang ◽  
Yimin Xiao
Keyword(s):  
Random Field ◽  
Nonparametric Regression ◽  
Random Fields ◽  
Long Memory ◽  
Moderate Deviation ◽  
Moderate Deviations ◽  
Partial Sums ◽  
Field Errors

AbstractWe study the Cramér type moderate deviation for partial sums of random fields by applying the conjugate method. The results are applicable to the partial sums of linear random fields with short or long memory and to nonparametric regression with random field errors.

scholarly journals REPRESENTATION AND WEAK CONVERGENCE OF STOCHASTIC INTEGRALS WITH FRACTIONAL INTEGRATOR PROCESSES

2009 ◽  
Vol 25 (6) ◽  
pp. 1589-1624 ◽  
Author(s):  
James Davidson ◽  
Nigar Hashimzade
Keyword(s):  
Long Memory ◽  
Moving Average ◽  
Full Range ◽  
Sample Covariance ◽  
Fractional Integrator ◽  
The Mean ◽  
Non Gaussian ◽  
The Time Domain ◽  
The Relationship ◽  
Harmonic Representation

This paper considers the asymptotic distribution of the sample covariance of a nonstationary fractionally integrated process with the stationary increments of another such process—possibly itself. Questions of interest include the relationship between the harmonic representation of these random variables, which we have analyzed in a previous paper (Davidson and Hashimzade, 2008), and the construction derived from moving average representations in the time domain. Depending on the values of the long memory parameters and choice of normalization, the limiting integral is shown to be expressible as the sum of a constant and two Itô-type integrals with respect to distinct Brownian motions. In certain cases the latter terms are of small order relative to the former. The mean is shown to match that of the harmonic representation, where the latter is defined, and satisfies the required integration by parts rule. The advantages of our approach over the harmonic analysis include the facts that our formulas are valid for the full range of the long memory parameters and that they extend to non-Gaussian processes.

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