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.

scholarly journals Study on Linear Combination of Long Memory Processes Corrupted by Additive Noises for fMRI Time Series Analysis

2017 ◽  
Author(s):  
Wonsang You ◽  
Catherine Limperopoulos
Keyword(s):  
Time Series ◽  
Neural Activity ◽  
Long Memory ◽  
Physiological Noise ◽  
Memory Processes ◽  
Fractal Properties ◽  
Long Memory Processes ◽  
Fmri Time Series ◽  
The Brain ◽  
Memory Parameter

AbstractEstimating the long memory parameter of the fMRI time series enables us to understand the fractal behavior of neural activity of the brain through fMRI time series. However, the existence of white noise and physiological noise compounds which also have fractal properties prevent us from making the estimation precise. As basic strategies to overcome noises, we address how to estimate the long memory parameter in the presence of additive noises, and how to estimate the long memory parameters of linearly combined long memory processes.

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 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.

scholarly journals DETECTION OF NONCONSTANT LONG MEMORY PARAMETER

2013 ◽  
Vol 29 (5) ◽  
pp. 1009-1056 ◽  
Author(s):  
Frédéric Lavancier ◽  
Remigijus Leipus ◽  
Anne Philippe ◽  
Donatas Surgailis
Keyword(s):  
Time Series ◽  
Long Memory ◽  
General Setting ◽  
Partial Sums ◽  
Gradual Change ◽  
Test Statistics ◽  
Finite Sample ◽  
Testing Procedures ◽  
Finite Sample Properties ◽  
Memory Parameter

This article deals with detection of a nonconstant long memory parameter in time series. The null hypothesis presumes stationary or nonstationary time series with a constant long memory parameter, typically an I (d) series with d > −.5 . The alternative corresponds to an increase in persistence and includes in particular an abrupt or gradual change from I (d1) to I (d2), −.5 < d1 < d2. We discuss several test statistics based on the ratio of forward and backward sample variances of the partial sums. The consistency of the tests is proved under a very general setting. We also study the behavior of these test statistics for some models with a changing memory parameter. A simulation study shows that our testing procedures have good finite sample properties and turn out to be more powerful than the KPSS-based tests (see Kwiatkowski, Phillips, Schmidt and Shin, 1992) considered in some previous works.

scholarly journals INFERENCE ON NONSTATIONARY TIME SERIES WITH MOVING MEAN

2014 ◽  
Vol 32 (2) ◽  
pp. 431-457 ◽  
Author(s):  
Jiti Gao ◽  
Peter M. Robinson
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Monte Carlo Study ◽  
Semiparametric Model ◽  
Nonstationary Time Series ◽  
Finite Sample ◽  
Trend Function ◽  
Deterministic Trend ◽  
Short Memory ◽  
Memory Parameter

A semiparametric model is proposed in which a parametric filtering of a nonstationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I(1) and other hypotheses are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance.

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 THE EFFECTS OF SYSTEMATIC SAMPLING AND TEMPORAL AGGREGATION ON DISCRETE TIME LONG MEMORY PROCESSES AND THEIR FINITE SAMPLE PROPERTIES

2000 ◽  
Vol 16 (3) ◽  
pp. 347-372 ◽  
Author(s):  
Soosung Hwang
Keyword(s):  
Decay Rate ◽  
Discrete Time ◽  
Long Memory ◽  
Absolute Magnitude ◽  
Systematic Sampling ◽  
Finite Sample ◽  
Autocorrelation Functions ◽  
Long Memory Processes ◽  
Sampling Intervals ◽  
Memory Parameter

This study investigates the effects of varying sampling intervals on the long memory characteristics of certain stochastic processes. We find that although different sampling intervals do not affect the decay rate of discrete time long memory autocorrelation functions in large lags, the autocorrelation functions in short lags are affected significantly. The level of the autocorrelation functions moves upward for temporally aggregated processes and downward for systematically sampled processes, and these effects result in a bias in the long memory parameter. For the ARFIMA(0,d,0) process, the absolute magnitude of the long memory parameter, |d|, of the temporally aggregated process is greater than the |d| of the true process, which is greater than the |d| of the systematically sampled process. We also find that the true long memory parameter can be obtained if we use a decay rate that is not affected by different sampling intervals.

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

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