scholarly journals Local Whittle Estimation of Long‐Range Dependence for Functional Time Series

2020 ◽  
Author(s):  
Degui Li ◽  
Peter M. Robinson ◽  
Han Lin Shang
Keyword(s):  
Time Series ◽  
Long Range ◽  
Long Range Dependence ◽  
Functional Time Series ◽  
Whittle Estimation

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 Long Range Dependence Prognostics for Bearing Vibration Intensity Chaotic Time Series

Entropy ◽  
2016 ◽  
Vol 18 (1) ◽  
pp. 23 ◽  
Author(s):  
Qing Li ◽  
Steven Liang ◽  
Jianguo Yang ◽  
Beizhi Li
Keyword(s):  
Time Series ◽  
Long Range ◽  
Chaotic Time Series ◽  
Long Range Dependence ◽  
Vibration Intensity ◽  
Bearing Vibration

Representative Time Series Fractal Analysis of the Traffic Flows of a Dedicated High-Speed Link

2021 ◽  
Author(s):  
Ginno Millan ◽  
manuel vargas ◽  
Guillermo Fuertes
Keyword(s):  
Time Series ◽  
Traffic Flow ◽  
Long Range ◽  
Computer Networks ◽  
Fractal Analysis ◽  
High Speed ◽  
Long Range Dependence ◽  
Traffic Flows ◽  
Speed Computer

Fractal behavior and long-range dependence are widely observed in measurements and characterization of traffic flow in high-speed computer networks of different technologies and coverage levels. This paper presents the results obtained when applying fractal analysis techniques on a time series obtained from traffic captures coming from an application server connected to the internet through a high-speed link. The results obtained show that traffic flow in the dedicated high-speed network link exhibited fractal behavior since the Hurst exponent was in the range of 0.5, 1, the fractal dimension between 1, 1.5, and the correlation coefficient between -0.5, 0. Based on these results, it is ideal to characterize both the singularities of the fractal traffic and its impulsiveness during a fractal analysis of temporal scales. Finally, based on the results of the time series analyzes, the fact that the traffic flows of current computer networks exhibited fractal behavior with a long-range dependence was reaffirmed.

scholarly journals Investigating Long-Range Dependence of Emerging Asian Stock Markets Using Multifractal Detrended Fluctuation Analysis

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1157
Author(s):  
Faheem Aslam ◽  
Saima Latif ◽  
Paulo Ferreira
Keyword(s):  
Time Series ◽  
Long Range ◽  
Stock Markets ◽  
Detrended Fluctuation Analysis ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Fluctuation Analysis ◽  
Multifractal Detrended Fluctuation Analysis ◽  
Financial Time ◽  
Detrended Fluctuation

The use of multifractal approaches has been growing because of the capacity of these tools to analyze complex properties and possible nonlinear structures such as those in financial time series. This paper analyzes the presence of long-range dependence and multifractal parameters in the stock indices of nine MSCI emerging Asian economies. Multifractal Detrended Fluctuation Analysis (MFDFA) is used, with prior application of the Seasonal and Trend Decomposition using the Loess (STL) method for more reliable results, as STL separates different components of the time series and removes seasonal oscillations. We find a varying degree of multifractality in all the markets considered, implying that they exhibit long-range correlations, which could be related to verification of the fractal market hypothesis. The evidence of multifractality reveals symmetry in the variation trends of the multifractal spectrum parameters of financial time series, which could be useful to develop portfolio management. Based on the degree of multifractality, the Chinese and South Korean markets exhibit the least long-range dependence, followed by Pakistan, Indonesia, and Thailand. On the contrary, the Indian and Malaysian stock markets are found to have the highest level of dependence. This evidence could be related to possible market inefficiencies, implying the possibility of institutional investors using active trading strategies in order to make their portfolios more profitable.

scholarly journals Broadband log-periodogram regression of time series with long-range dependence

1999 ◽  
Vol 27 (4) ◽  
pp. 1415-1439 ◽  
Author(s):  
Eric Moulines ◽  
Philippe Soulier
Keyword(s):  
Time Series ◽  
Long Range ◽  
Long Range Dependence

scholarly journals Fractional Laplace motion

2006 ◽  
Vol 38 (02) ◽  
pp. 451-464 ◽  
Author(s):  
T. J. Kozubowski ◽  
M. M. Meerschaert ◽  
K. Podgórski
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Hydraulic Conductivity ◽  
Fractional Brownian Motion ◽  
Long Range ◽  
Financial Time Series ◽  
Long Range Dependence ◽  
Self Similarity ◽  
One Dimensional ◽  
Financial Time

Fractional Laplace motion is obtained by subordinating fractional Brownian motion to a gamma process. Used recently to model hydraulic conductivity fields in geophysics, it might also prove useful in modeling financial time series. Its one-dimensional distributions are scale mixtures of normal laws, where the stochastic variance has the generalized gamma distribution. These one-dimensional distributions are more peaked at the mode than is a Gaussian distribution, and their tails are heavier. In this paper we derive the basic properties of the process, including a new property called stochastic self-similarity. We also study the corresponding fractional Laplace noise, which may exhibit long-range dependence. Finally, we discuss practical methods for simulation.

Long-Range Dependence of Traffic Flow and Speed of a Motorway: Dynamics and Correlation with Historical Incidents

2017 ◽  
Vol 2616 (1) ◽  
pp. 49-57 ◽  
Author(s):  
Sai Chand ◽  
Gregory Aouad ◽  
Vinayak V. Dixit
Keyword(s):  
Time Series ◽  
Long Range ◽  
Traffic Congestion ◽  
Hurst Exponent ◽  
Fractal Theory ◽  
Urban Traffic ◽  
Spatial And Temporal Variation ◽  
Long Range Dependence ◽  
Incident Rates ◽  
Sydney Australia

Speed and flow of vehicles tend to have several effects on the dynamics of a transport system. Fluctuations of these variables can implicate congestion, can lower predictability, and may even catalyze crashes. A concept of fractal theory called the Hurst exponent—a measure of the long-range dependence (LRD) of a time series—was used to understand the fluctuations in flow and speed of a motorway in Sydney, Australia. The spatial and temporal variation of the LRD for flow ( Hflow) and speed ( Hspeed) at several monitor sites is discussed. Furthermore, the effects of number of lanes on flow and speed predictability are explored. It was observed that the flow predictability of two-lane sections was significantly lower when compared with three-lane and four-lane sections. Conversely, the speed predictability of four-lane sections was considerably higher than that of two-lane and three-lane sections. Finally, traffic congestion was defined with regard to the LRD of speed, and its correlation with historical incident rates was measured. It was ascertained that monitor sites with a historically high proportion of large Hspeed were correlated with unsafe locations. This study could lead to many applications of fractal analysis on highways and urban traffic.

scholarly journals Clustering of Rainfall Stations in RH-24 Mexico Region Using the Hurst Exponent in Semivariograms

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Francisco Gerardo Benavides-Bravo ◽  
F-Javier Almaguer ◽  
Roberto Soto-Villalobos ◽  
Víctor Tercero-Gómez ◽  
Javier Morales-Castillo
Keyword(s):  
Time Series ◽  
Long Range ◽  
Hurst Exponent ◽  
Historical Data ◽  
Regional Frequency Analysis ◽  
Long Range Dependence ◽  
National Commission ◽  
Long Range Correlations ◽  
Rainfall Variations ◽  
Regional Frequency

An important topic in the study of the time series behavior and, in particular, meteorological time series is the long-range dependence. This paper explores the behavior of rainfall variations in different periods, using long-range correlations analysis. Semivariograms and Hurst exponent were applied to historical data in different pluviometric stations of the Río Bravo-San Juan watershed, at the hydrographic RH-24 Mexico region. The database was provided by the Water National Commission (CONAGUA). Using the semivariograms, the Hurst exponent was obtained and used as an input to perform a cluster analysis of rainfall stations. Groups of homogeneous samples that might be useful in a regional frequency analysis were obtained through the process.

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