RATE OPTIMAL SEMIPARAMETRIC ESTIMATION OF THE MEMORY PARAMETER OF THE GAUSSIAN TIME SERIES WITH LONG‐RANGE DEPENDENCE

1997 ◽  
Vol 18 (1) ◽  
pp. 49-60 ◽  
Author(s):  
Liudas Giraitis ◽  
Peter M. Robinson ◽  
Alexander Samarov
Keyword(s):  
Time Series ◽  
Long Range ◽  
Semiparametric Estimation ◽  
Long Range Dependence ◽  
Gaussian Time ◽  
Gaussian Time Series ◽  
Memory Parameter

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 A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series

2008 ◽  
Vol 36 (4) ◽  
pp. 1925-1956 ◽  
Author(s):  
E. Moulines ◽  
F. Roueff ◽  
M. S. Taqqu
Keyword(s):  
Time Series ◽  
Gaussian Time ◽  
Gaussian Time Series ◽  
Memory Parameter

scholarly journals NON-GAUSSIAN LOG-PERIODOGRAM REGRESSION

2000 ◽  
Vol 16 (1) ◽  
pp. 44-79 ◽  
Author(s):  
Carlos Velasco
Keyword(s):  
Time Series ◽  
Long Range ◽  
Asymptotic Properties ◽  
Asymptotic Results ◽  
Regression Estimate ◽  
Finite Samples ◽  
Non Gaussian ◽  
Periodogram Estimate ◽  
Gaussian Time ◽  
Gaussian Time Series

We show the consistency of the log-periodogram regression estimate of the long memory parameter for long range dependent linear, not necessarily Gaussian, time series when we make a pooling of periodogram ordinates. Then, we study the asymptotic behavior of the tapered periodogram of long range dependent time series for frequencies near the origin, and we obtain the asymptotic distribution of the log-periodogram estimate for possibly non-Gaussian observation when the tapered periodogram is used. For these results we rely on higher order asymptotic properties of a vector of periodogram ordinates of the linear innovations. Finally, we assess the validity of the asymptotic results for finite samples via Monte Carlo simulation.

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