Not all long‐memory estimators are born equal: The case of nonstationary functional time series

2021 ◽  
Author(s):  
Han Lin Shang
Keyword(s):  
Time Series ◽  
Long Memory ◽  
Functional Time Series

OPERATOR FRACTIONAL BROWNIAN MOTION AS LIMIT OF POLYGONAL LINES PROCESSES IN HILBERT SPACE

2011 ◽  
Vol 11 (01) ◽  
pp. 49-70 ◽  
Author(s):  
ALFREDAS RAČKAUSKAS ◽  
CHARLES SUQUET
Keyword(s):  
Hilbert Space ◽  
Time Series ◽  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Long Memory ◽  
Partial Sums ◽  
Functional Time Series ◽  
Hurst Coefficient

In this paper, we study long memory phenomenon of functional time series. We consider an operator fractional Brownian motion with values in a Hilbert space defined via operator-valued Hurst coefficient. We prove that this process is a limiting one for polygonal lines constructed from partial sums of time series having space varying long memory.

scholarly journals On nonparametric regression for bivariate circular long-memory time series

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.

scholarly journals The CSS and The Two-Staged Methods for Parameter Estimation in SARFIMA Models

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Erol Egrioglu ◽  
Cagdas Hakan Aladag ◽  
Cem Kadilar
Keyword(s):  
Time Series ◽  
Parameter Estimation ◽  
Root Mean Square Error ◽  
Mean Square Error ◽  
Simulation Study ◽  
Long Memory ◽  
Moving Average ◽  
Mean Square ◽  
Sample Sizes ◽  
Advantages And Disadvantages

Seasonal Autoregressive Fractionally Integrated Moving Average (SARFIMA) models are used in the analysis of seasonal long memory-dependent time series. Two methods, which are conditional sum of squares (CSS) and two-staged methods introduced by Hosking (1984), are proposed to estimate the parameters of SARFIMA models. However, no simulation study has been conducted in the literature. Therefore, it is not known how these methods behave under different parameter settings and sample sizes in SARFIMA models. The aim of this study is to show the behavior of these methods by a simulation study. According to results of the simulation, advantages and disadvantages of both methods under different parameter settings and sample sizes are discussed by comparing the root mean square error (RMSE) obtained by the CSS and two-staged methods. As a result of the comparison, it is seen that CSS method produces better results than those obtained from the two-staged method.

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