Monitoring memory parameter change-points in long-memory time series

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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Bootstrapping long memory time series: Application in low frequency estimators

Econometrics and Statistics ◽

10.1016/j.ecosta.2021.06.002 ◽

2021 ◽

Author(s):

Josu Arteche

Keyword(s):

Time Series ◽

Long Memory ◽

Low Frequency ◽

Memory Time

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A harmonically weighted filter for cyclical long memory processes

AStA Advances in Statistical Analysis ◽

10.1007/s10182-021-00394-9 ◽

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.

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On nonparametric regression for bivariate circular long-memory time series

Statistical Papers ◽

10.1007/s00362-021-01228-1 ◽

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.

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