Bootstrapping the log-periodogram estimator of the long-memory parameter: is it worth weighting

2021 ◽  
Vol 11 (3) ◽  
pp. 201
Author(s):  
Saeed M. Heravi ◽  
Kerry D. Patterson
Keyword(s):  
Long Memory ◽  
Memory Parameter

scholarly journals A harmonically weighted filter for cyclical long memory processes

2021 ◽  
Author(s):  
Federico Maddanu
Keyword(s):  
Spectral Density ◽  
Long Memory ◽  
Convergence In Probability ◽  
Simulation Methods ◽  
Integrated Process ◽  
Paleoclimatic Data ◽  
Memory Time ◽  
Long Memory Processes ◽  
Short Memory ◽  
Memory Parameter

AbstractThe estimation of the long memory parameter d is a widely discussed issue in the literature. The harmonically weighted (HW) process was recently introduced for long memory time series with an unbounded spectral density at the origin. In contrast to the most famous fractionally integrated process, the HW approach does not require the estimation of the d parameter, but it may be just as able to capture long memory as the fractionally integrated model, if the sample size is not too large. Our contribution is a generalization of the HW model, denominated the Generalized harmonically weighted (GHW) process, which allows for an unbounded spectral density at $$k \ge 1$$ k ≥ 1 frequencies away from the origin. The convergence in probability of the Whittle estimator is provided for the GHW process, along with a discussion on simulation methods. Fit and forecast performances are evaluated via an empirical application on paleoclimatic data. Our main conclusion is that the above generalization is able to model long memory, as well as its classical competitor, the fractionally differenced Gegenbauer process, does. In addition, the GHW process does not require the estimation of the memory parameter, simplifying the issue of how to disentangle long memory from a (moderately persistent) short memory component. This leads to a clear advantage of our formulation over the fractional long memory approach.

scholarly journals Wavelet estimation of the long memory parameter for Hermite polynomial of Gaussian processes

2013 ◽  
Vol 18 ◽  
pp. 42-76 ◽  
Author(s):  
M. Clausel ◽  
F. Roueff ◽  
M.S. Taqqu ◽  
C. Tudor
Keyword(s):  
Gaussian Processes ◽  
Long Memory ◽  
Hermite Polynomial ◽  
Wavelet Estimation ◽  
Memory Parameter

Wavelet-based Estimation of Generalized Fractional Process

2007 ◽  
Vol 46 (02) ◽  
pp. 117-120 ◽  
Author(s):  
A. Kawanaka ◽  
A. Gonzaga
Keyword(s):  
Long Memory ◽  
General Model ◽  
Weighted Least Squares ◽  
Estimation Procedure ◽  
Heart Rate Data ◽  
Biomedical Signals ◽  
Weighted Least Squares Estimator ◽  
Short Memory ◽  
Wavelet Variance ◽  
Memory Parameter

Summary Objectives : This paper aims to propose an estimation procedure for the parameters of a generalized fractional process, a fairly general model of long-memory applicable in modeling biomedical signals whose autocorrelations exhibit hyperbolic decay. Methods : We derive a wavelet-based weighted least squares estimator of the long-memory parameter based on the maximal-overlap estimator of the wavelet variance. Short-memory parameters can then be estimated using standard methods. We illustrate our approach by an example applying ECG heart rate data. Results and Conclusion : The proposed method is relatively computationally and statistically efficient. It allows for estimation of the long-memory parameter without knowledge of the short-memory parameters. Moreover it provides a more general model of biomedical signals that exhibit periodic long-range dependence, such as ECG data, whose relatively unobtrusive recording may be advantageous in assessing or predicting some physiological or pathological conditions from the estimated values of the parameters.

Local Whittle estimation of the long-memory parameter

2020 ◽  
Vol 20 (3) ◽  
pp. 565-583
Author(s):  
Christopher F. Baum ◽  
Stan Hurn ◽  
Kenneth Lindsay
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Fractional Integration ◽  
Whittle Estimation ◽  
Memory Parameter

In this article, we describe and implement the local Whittle and exact local Whittle estimators of the order of fractional integration of a time series.

scholarly journals TESTING THE ORDER OF FRACTIONAL INTEGRATION OF A TIME SERIES IN THE POSSIBLE PRESENCE OF A TREND BREAK AT AN UNKNOWN POINT

2018 ◽  
Vol 35 (6) ◽  
pp. 1201-1233 ◽  
Author(s):  
Fabrizio Iacone ◽  
Stephen J. Leybourne ◽  
A.M. Robert Taylor
Keyword(s):  
Time Series ◽  
Power Function ◽  
Long Memory ◽  
Fractional Integration ◽  
Monte Carlo Study ◽  
Local Power ◽  
Finite Sample ◽  
Lm Test ◽  
Unknown Point ◽  
Memory Parameter

We develop a test, based on the Lagrange multiplier [LM] testing principle, for the value of the long memory parameter of a univariate time series that is composed of a fractionally integrated shock around a potentially broken deterministic trend. Our proposed test is constructed from data which are de-trended allowing for a trend break whose (unknown) location is estimated by a standard residual sum of squares estimator applied either to the levels or first differences of the data, depending on the value specified for the long memory parameter under the null hypothesis. We demonstrate that the resulting LM-type statistic has a standard limiting null chi-squared distribution with one degree of freedom, and attains the same asymptotic local power function as an infeasible LM test based on the true shocks. Our proposed test therefore attains the same asymptotic local optimality properties as an oracle LM test in both the trend break and no trend break environments. Moreover, this asymptotic local power function does not alter between the break and no break cases and so there is no loss in asymptotic local power from allowing for a trend break at an unknown point in the sample, even in the case where no break is present. We also report the results from a Monte Carlo study into the finite-sample behaviour of our proposed test.

Wavelet estimation of a local long memory parameter

2000 ◽  
Vol 31 (1-2) ◽  
pp. 94-103 ◽  
Author(s):  
Brandon Whitcher ◽  
Mark J. Jensen
Keyword(s):  
Long Memory ◽  
Wavelet Estimation ◽  
Memory Parameter
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