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 MEMORY PARAMETER ESTIMATION IN THE PRESENCE OF LEVEL SHIFTS AND DETERMINISTIC TRENDS

2013 ◽  
Vol 29 (6) ◽  
pp. 1196-1237 ◽  
Author(s):  
Adam Mccloskey ◽  
Pierre Perron
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Level Shift ◽  
Finite Sample ◽  
Memory Processes ◽  
Trade Offs ◽  
Level Shifts ◽  
Long Memory Processes ◽  
Short Memory ◽  
Memory Parameter

We propose estimators of the memory parameter of a time series that are robust to a wide variety of random level shift processes, deterministic level shifts, and deterministic time trends. The estimators are simple trimmed versions of the popular log-periodogram regression estimator that employ certain sample-size-dependent and, in some cases, data-dependent trimmings that discard low-frequency components. We also show that a previously developed trimmed local Whittle estimator is robust to the same forms of data contamination. Regardless of whether the underlying long- or short-memory process is contaminated by level shifts or deterministic trends, the estimators are consistent and asymptotically normal with the same limiting variance as their standard untrimmed counterparts. Simulations show that the trimmed estimators perform their intended purpose quite well, substantially decreasing both finite-sample bias and root mean-squared error in the presence of these contaminating components. Furthermore, we assess the trade-offs involved with their use when such components are not present but the underlying process exhibits strong short-memory dynamics or is contaminated by noise. To balance the potential finite-sample biases involved in estimating the memory parameter, we recommend a particular adaptive version of the trimmed log-periodogram estimator that performs well in a wide variety of circumstances. We apply the estimators to stock market volatility data to find that various time series typically thought to be long-memory processes actually appear to be short- or very weak long-memory processes contaminated by level shifts or deterministic trends.

On the estimation of short memory components in long memory time series models

2016 ◽  
Vol 20 (4) ◽  
Author(s):  
Richard T. Baillie ◽  
George Kapetanios
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Time Series Models ◽  
Memory Process ◽  
Long Memory Process ◽  
Fractional Differencing ◽  
Memory Time ◽  
Short Memory ◽  
Short Memory Process ◽  
Memory Parameter

AbstractA substantial amount of recent time series research has emphasized semi-parameteric estimators of a long memory parameter and we provide a selective review of the literature on this issue. We consider such estimators applied to the issue of estimating the parameters relating to a short memory process which is embedded within the long memory process. We consider the fractional differencing filter and the subsequent properties of a two step estimator of the short memory parameters. We conclude that while the semi-parametric estimators can have excellent properties in terms of estimating the long memory parameter, they do not have good properties when applied to the two step estimator of short memory

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.

scholarly journals Spatial long memory

2019 ◽  
Vol 3 (1) ◽  
pp. 243-256
Author(s):  
Peter M. Robinson
Keyword(s):  
Time Series ◽  
Statistical Modeling ◽  
Spatial Data ◽  
Long Memory ◽  
The Other ◽  
Future Prospects ◽  
Memory Time ◽  
Short Memory ◽  
The One ◽  
Relevant Work

AbstractWe discuss developments and future prospects for statistical modeling and inference for spatial data that have long memory. While a number of contributons have been made, the literature is relatively small and scattered, compared to the literatures on long memory time series on the one hand, and spatial data with short memory on the other. Thus, over several topics, our discussions frequently begin by surveying relevant work in these areas that might be extended in a long memory spatial setting.

Spectral Analysis for Bivariate Time Series with Long Memory

1996 ◽  
Vol 12 (5) ◽  
pp. 773-792 ◽  
Author(s):  
J. Hidalgo
Keyword(s):  
Time Series ◽  
Density Matrix ◽  
Spectral Density ◽  
Long Memory ◽  
Limit Theorems ◽  
Stationary Process ◽  
Absolute Summability ◽  
Spectral Density Matrix ◽  
Mixing Coefficients ◽  
Long Memory Processes

This paper provides limit theorems for spectral density matrix estimators and functionals of it for a bivariate covariance stationary process whose spectral density matrix has singularities not only at the origin but possibly at some other frequencies and, thus, applies to time series exhibiting long memory. In particular, we show that the consistency and asymptotic normality of the spectral density matrix estimator at a frequency, say λ, which hold for weakly dependent time series, continue to hold for long memory processes when λ lies outside any arbitrary neighborhood of the singularities. Specifically, we show that for the standard properties of spectral density matrix estimators to hold, only local smoothness of the spectral density matrix is required in a neighborhood of the frequency in which we are interested. Therefore, we are able to relax, among other conditions, the absolute summability of the autocovariance function and of the fourth-order cumulants or summability conditions on mixing coefficients, assumed in much of the literature, which imply that the spectral density matrix is globally smooth and bounded.

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 CONDITIONS FOR THE PROPAGATION OF MEMORY PARAMETER FROM DURATIONS TO COUNTS AND REALIZED VOLATILITY

2009 ◽  
Vol 25 (3) ◽  
pp. 764-792 ◽  
Author(s):  
Rohit Deo ◽  
Clifford M. Hurvich ◽  
Philippe Soulier ◽  
Yi Wang
Keyword(s):  
Long Memory ◽  
Sufficient Conditions ◽  
Finite Variance ◽  
Microstructure Noise ◽  
Stochastic Duration ◽  
Short Memory ◽  
Variance Estimates ◽  
Noise Contamination ◽  
Finite Moments ◽  
Memory Parameter

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter$d \in [0,{\textstyle{1 \over 2}})$to ensure that the corresponding counting processN(t) satisfies VarN(t) ~Ct2d+1(C> 0) ast→ ∞, with the same memory parameter$d \in [0,{\textstyle{1 \over 2}})$that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the counts. We then show that any autoregressive conditional duration ACD(1,1) model with a sufficient number of finite moments yields short memory in counts, whereas any long memory stochastic duration model withd> 0 and all finite moments yields long memory in counts, with the samed. Finally, we provide some results about the propagation of long memory to the empirically relevant case of realized variance estimates affected by market microstructure noise contamination.

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